Phys 2201.100 (Fall 2017)http://www.physics.umn.edu/classes/2017/fall/Phys%202201.100/Introductory Thermodynamics and Statistical Physics2018-01-17T07:13:42ZXML::Atom::SimpleFeed2017-12-07T01:34:25Z<p><strong>The final exam for PHYS 2201 will be held on Tuesday, December 19, from 1:30 - 4:30 PM in Tate B50.</strong></p>
<p><strong>A review session will be held on Saturday, December 16, 3:00 - 5:00 PM in Tate B20. Post problems that you would like to go over on the course Moodle page by noon on Saturday. Problems must be posted in advance.</strong></p>
<p><strong>Professor Crowell will have an office hour this Thursday from 2:00 - 5:00. He will be in his office Monday from 4:00 - 6:00.</strong></p>
<p>The exam is cumulative.</p>
<p>I am posting the final exam from 2016 below. I have added a couple comments, particularly on the one problem that involved the type of derivation that I do not consider important.</p>
<p>I will post a formula sheet by early next week. Otherwise, the exam will be closed book. Although it will be similar in format to last year's exam, there may be more questions like the first problem of the second midterm (short answer, with no partial credit awarded).</p>
<p>I am posting below a summary of topics that I believe are important. If, after reading this, you have any questions along the lines of "What can be on the exam?", please ask them during Wednesday's class.</p>
<ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/478852-Formula_Sheet_for_Final.pdf" title="149 Kbytes, application/pdf">Formula Sheet for Final Exam</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/478852-Formula_Sheet_for_Final.pdf?download=1" title="149 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 17-Dec-2017 at 2:19AM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/479262-Accountability_list.pdf" title="245 Kbytes, application/pdf">Summary of important topics</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/479262-Accountability_list.pdf?download=1" title="245 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 11-Dec-2017 at 8:12PM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/478132-Final_Solutions.pdf" title="420 Kbytes, application/pdf">2016 Final Exam and Solutions</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/478132-Final_Solutions.pdf?download=1" title="420 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 6-Dec-2017 at 7:35PM</i></small>
</td></tr>
</table>
</ul>2017-12-17T08:19:25ZPaul Crowellcid:63472.eid:478122.updated:2017-12-17 02:19:25Final Exam (Updated)2017-09-19T19:28:34Z<i>This item is restricted: please visit the website to view it.</i>2017-12-13T17:54:34ZPaul Crowellcid:63472.eid:459772.updated:2017-12-13 11:54:34Homework Solutions (Updated)2017-09-09T23:39:39Z<p>I will post my lecture slides about once a week. These are not intended to be complete lecture notes. They are simply the visual aids I use in lecture. In some cases, I will add material, particularly when (as happened on Friday) I am not satisfied with an explanation I did in class. </p>
<ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/479602-Week_of_December_11.pdf" title="381 Kbytes, application/pdf">Week of December 11</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/479602-Week_of_December_11.pdf?download=1" title="381 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 13-Dec-2017 at 11:35AM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/478782-Week_of_December_4_v2.pdf" title="651 Kbytes, application/pdf">Week of December 4</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/478782-Week_of_December_4_v2.pdf?download=1" title="651 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 8-Dec-2017 at 5:51PM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/476562-Week_of_November_27th.pdf" title="819 Kbytes, application/pdf">Week of November 27</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/476562-Week_of_November_27th.pdf?download=1" title="819 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 1-Dec-2017 at 7:51PM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/474822-Week_of_November_20th.pdf" title="754 Kbytes, application/pdf">Week of November 20</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/474822-Week_of_November_20th.pdf?download=1" title="754 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 21-Nov-2017 at 7:52PM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/474312-Week_of_November_13.pdf" title="291 Kbytes, application/pdf">Week of November 13</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/474312-Week_of_November_13.pdf?download=1" title="291 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 19-Nov-2017 at 10:12PM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/472512-Week_of_November_6.pdf" title="716 Kbytes, application/pdf">Week of November 6</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/472512-Week_of_November_6.pdf?download=1" title="716 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 10-Nov-2017 at 11:07AM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/471062-Week_of_October_30.pdf" title="449 Kbytes, application/pdf">Week of October 30</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/471062-Week_of_October_30.pdf?download=1" title="449 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 6-Nov-2017 at 10:51AM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/469562-Week_of_October_23rd.pdf" title="759 Kbytes, application/pdf">Week of October 23</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/469562-Week_of_October_23rd.pdf?download=1" title="759 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 27-Oct-2017 at 7:44PM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/467652-Week_of_October_16.pdf" title="293 Kbytes, application/pdf">Week of October 16</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/467652-Week_of_October_16.pdf?download=1" title="293 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 22-Oct-2017 at 10:10AM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/466172-October_13.pdf" title="254 Kbytes, application/pdf">Week of October 9</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/466172-October_13.pdf?download=1" title="254 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 16-Oct-2017 at 12:43AM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/465022-Week_of_October_2nd.pdf" title="288 Kbytes, application/pdf">Week of October 2</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/465022-Week_of_October_2nd.pdf?download=1" title="288 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 9-Oct-2017 at 7:31PM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/463062-Week_of_September_25.pdf" title="842 Kbytes, application/pdf">Week of September 25</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/463062-Week_of_September_25.pdf?download=1" title="842 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 1-Oct-2017 at 11:05PM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/460882-September18_2017.pdf" title="749 Kbytes, application/pdf">Week of September 18</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/460882-September18_2017.pdf?download=1" title="749 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 22-Sep-2017 at 6:15PM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/459212-September11.pdf" title="495 Kbytes, application/pdf">Week of September 11</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/459212-September11.pdf?download=1" title="495 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 16-Sep-2017 at 4:08PM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/457422-Week_of_September_5.pdf" title="369 Kbytes, application/pdf">Week of September 4</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/457422-Week_of_September_5.pdf?download=1" title="369 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 9-Sep-2017 at 6:40PM</i></small>
</td></tr>
</table>
</ul>2017-12-13T17:35:50ZPaul Crowellcid:63472.eid:457412.updated:2017-12-13 11:35:50Lecture Slides (Updated)2017-09-12T01:02:31Z<ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/479592-PHYS_2201_Week15_Discussion.pdf" title="371 Kbytes, application/pdf">Week 15 Discussion</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/479592-PHYS_2201_Week15_Discussion.pdf?download=1" title="371 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 13-Dec-2017 at 11:29AM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/477502-PHYS_2201_Week14_Discussion.pdf" title="385 Kbytes, application/pdf">Week 14 Discussion</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/477502-PHYS_2201_Week14_Discussion.pdf?download=1" title="385 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 10-Dec-2017 at 7:17PM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/475912-PHYS_2201_Week13_Discussion_Solutions.pdf" title="498 Kbytes, application/pdf">Week 13 Discussion</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/475912-PHYS_2201_Week13_Discussion_Solutions.pdf?download=1" title="498 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 28-Nov-2017 at 11:41PM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/474812-Discussion12_Solutions.pdf" title="706 Kbytes, application/pdf">Week 12 Discussion</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/474812-Discussion12_Solutions.pdf?download=1" title="706 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 21-Nov-2017 at 7:44PM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/473452-PHYS2201_Discussion11_Solutions.pdf" title="533 Kbytes, application/pdf">Week 11 Discussion</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/473452-PHYS2201_Discussion11_Solutions.pdf?download=1" title="533 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 15-Nov-2017 at 8:29PM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/471962-PHYS_2201_Week10_Discussion_Solutions.pdf" title="342 Kbytes, application/pdf">Week 10 Discussion</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/471962-PHYS_2201_Week10_Discussion_Solutions.pdf?download=1" title="342 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 8-Nov-2017 at 1:39PM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/470202-Week_9_Discussion_Solutions.pdf" title="1970 Kbytes, application/pdf">Week 9 Discussion</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/470202-Week_9_Discussion_Solutions.pdf?download=1" title="1970 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 1-Nov-2017 at 11:40AM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/468372-PHYS_2201_Week8_Discussion_Solutions.pdf" title="2453 Kbytes, application/pdf">Week 8 Discussion</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/468372-PHYS_2201_Week8_Discussion_Solutions.pdf?download=1" title="2453 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 25-Oct-2017 at 8:41PM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/466832-Discussion_7_solutions.pdf" title="1625 Kbytes, application/pdf">Week 7 Discussion</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/466832-Discussion_7_solutions.pdf?download=1" title="1625 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 25-Oct-2017 at 12:02AM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/465072-PHYS_2201_Week6_Discussion.pdf" title="337 Kbytes, application/pdf">Week 6 Discussion</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/465072-PHYS_2201_Week6_Discussion.pdf?download=1" title="337 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 11-Oct-2017 at 12:10AM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/463642-2201_Week5_DiscussionSolutions.pdf" title="3105 Kbytes, application/pdf">Week 5 Discussion</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/463642-2201_Week5_DiscussionSolutions.pdf?download=1" title="3105 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 3-Oct-2017 at 7:50PM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/461712-2201_Week4_Discussion.pdf" title="685 Kbytes, application/pdf">Week 4 Discussion</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/461712-2201_Week4_Discussion.pdf?download=1" title="685 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 26-Sep-2017 at 4:24PM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/459792-2201_Week3_Discussionv2.pdf" title="626 Kbytes, application/pdf">Week 3 Discussion</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/459792-2201_Week3_Discussionv2.pdf?download=1" title="626 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 19-Sep-2017 at 2:41PM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/458142-Week_2_Discussion.pdf" title="413 Kbytes, application/pdf">Week 2 Discussion</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/458142-Week_2_Discussion.pdf?download=1" title="413 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 12-Sep-2017 at 5:22PM</i></small>
</td></tr>
</table>
</ul>2017-12-13T17:30:13ZPaul Crowellcid:63472.eid:457902.updated:2017-12-13 11:30:13Discussion Problems and Solutions (Updated)2017-12-09T17:17:44Z<p>No new reading or problems. You should have read Chapter 5 up through p. 172, which represents the official "end" of the material covered by this class. In summary, the material which we have covered (and which therefore may appear on the final) is Chapter 1 (except 1.7), Chapter 2, Chapter 3 (keeping in mind that some of the material covered in Chapter 3, such as the paramagnet, is handled more efficiently using the canonical ensemble in Chapter 6), Chapter 4 through p. 132, Chapter 5 through p. 172, and Chapter 6. As a rule, the homework and discussion problems provide a guide for the types of problems that are likely to appear on the final exam.</p>
<p>I will attempt to schedule a review session, and we will discuss potential times in class on Monday. In the meantime, please post questions that you would like to review on the Moodle page.</p>2017-12-09T17:17:44ZPaul Crowellcid:63472.eid:478792Week 152017-12-02T00:35:59Z<p>We will conclude by considering free energy, electrochemical work, and perhaps a little bit on phase transitions.</p>
<p>Reading<br />
By Monday, December 4, 5.1 through p. 152 and 156 - 158<br />
By Wednesday, December 6, pp. 152 - 156 <br />
By Friday, December 8, 5.2<br />
By Monday, December 11, 5.3 through p. 172</p>
<p>Problems posted under Week 13</p>
<p>The link below is to a lecture I gave a year ago. You may want to listen to it:</p>
<p><a href="https://www.youtube.com/watch?v=OHK2utrLRLg&feature=youtu.be">https://www.youtube.com/watch?v=OHK2utrLRLg&feature=youtu.be</a></p>2017-12-02T00:35:59ZPaul Crowellcid:63472.eid:476552Week 142017-11-25T06:50:58Z<p>The lectures on Monday and Wednesday will be catching up with the reading</p>
<p>By Monday, November 27: 6.4 and 6.5<br />
By Wednesday, November 29: 6.6 and 6.7<br />
By Friday, December 1: 5.1 through p. 152</p>
<p><strong>Problems Due Friday, December 8:</strong><br />
<strong>5.1, 5.2, 5.8, 5.9</strong></p>
<p><strong>Due Tuesday, December 12:</strong><br />
<strong>5.22, 5.29, 5.30</strong> </p>2017-11-29T23:00:14ZPaul Crowellcid:63472.eid:475172.updated:2017-11-29 17:00:14Week 13 (Updated)2017-11-18T18:36:16Z<p>We will continue with statistical mechanics using the canonical ensemble. </p>
<p>Reading<br />
By Monday, November 20: 6.4<br />
By Wednesday, November 22: 6.5<br />
By Monday, November 27, 6.6 and 6.7</p>
<p>Note that 6.5 assumes familiarity with the Helmholtz free energy, which is introduced in Chapter 5. You only need to know two things. First the definition of the Helmholtz free energy is <i>F</i> = <i>U</i> - <i>T</i><i>S</i>
. Second, you should read the argument on p. 161, which shows that for a system of fixed volume (and with a fixed number of particles) in contact with a reservoir at temperature T, the Helmholtz free energy is minimized in equilibrium. Make sure you understand Fig. 6.14.</p>
<p>Problems Due Tuesday, November 28<br />
<strong>6.26, 6.31, 6.34</strong>, 6.36</p>
<p><strong>Problems Due Tuesday, December 5</strong><br />
6.39, <strong>6.41, 6.47, 6.48, 6.52</strong><br />
For 6.39(c), start by assuming that the moon once had an atmosphere with a composition and temperature similar to that of the Earth. For 6.47, you can apply the logic we used for rotational systems, in which we worried only about the ground state and the first excited state when calculating the Boltzmann factors at low temperature. Finally, for 6.48, you will need to calculate the rotational partition function, but do assume that you are in the high temperature limit. The rotational energy for O2 is given in Problem 6.24.</p>
<p>If you are bored over Thanksgiving, take a look at this (optional) problem. It is not mathematically difficult, but it introduces the concept of a phase transition. If you understand it, you are on the way to becoming a certified statistical mechanic.</p>
<ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/474222-DNA_problem.pdf" title="232 Kbytes, application/pdf">DNA Problem</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/474222-DNA_problem.pdf?download=1" title="232 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 18-Nov-2017 at 12:40PM</i></small>
</td></tr>
</table>
</ul>2017-11-29T22:47:55ZPaul Crowellcid:63472.eid:474212.updated:2017-11-29 16:47:55Week 12 (Updated)2017-10-20T16:14:44Z<i>This item is restricted: please visit the website to view it.</i>2017-11-22T01:46:58ZPaul Crowellcid:63472.eid:467312.updated:2017-11-21 19:46:58Exam Solutions (Updated)2017-11-10T16:59:42Z<h1>Quiz 2 will be given on Wednesday, November 15</h1>
<p>It will cover material through 4.3 (NOT 4.4, and nothing on steam engines)<br />
There will not be any questions on chemical potential on this quiz, although there may some on the final exam (after we have done part of Chapter 5).</p>
<p>Last year's quiz and the formula sheet that will be provided are posted under Week 10.</p>
<p><strong>NOTE THE DIFFERENT ALPHABETICAL SPLIT:</strong></p>
<p>Tate B20: A-M<br />
Tate 110: N – Z</p>
<p>As a reminder, in Monday's class, I will do any relevant problem that is posted on the Moodle page by 7 PM Sunday.</p>
<p>I will hold my office hour this week on Tuesday, from 2:00 - 4:30. I will not hold regular office hours on Thursday, but I will probably be in my office from 2 - 3:15.</p>
<p>Reading:</p>
<p>By Monday, November 13, Read 6.1<br />
By Friday, November 17, Read 6.2 and 6.3<br />
By Monday, November 20, Read 6.4 </p>
<p>Problems (due Tuesday, November 21):<br />
<strong>6.6, 6.11</strong>, 6.14, 6.16, <strong>6.20 (b - e) 6.22 (parts b, c, and d)</strong></p>
<p>For 6.20, you can use the result from part (a) without proof. It is just the standard expression for the sum of an infinite geometric series. For Problem 6.22, you can use without proof the result given in part (a). Use Excel, Matlab,or Mathematica to complete the graphs in 6.22(c). You do not need to do parts (e) and (f) of 6.22. Note, however, that the magnetization at high temperature obey's Curie's Law (<img src="/texvc/95bfe7a8e6d410569abbe18e94ae9639.png" alt="M \propto 1/T ">
), just like the two-state paramagnet. </p>2017-11-14T07:35:27ZPaul Crowellcid:63472.eid:472482.updated:2017-11-14 01:35:27Week 11 (Updated)2017-10-27T20:35:42Z<p>We will complete our discussion of the consequences of maximizing entropy in equilibrium by relaxing the assumption that the total number of particles in a system is fixed. This will lead us to the concept of chemical potential. To sump up, systems in thermal equilibrium (exchanging energy) have the same temperature, those in mechanical equilibrium (exchanging volume) have the same pressure, and those in chemical equilibrium (exchanging particles) have the same chemical potential. A common example of chemical equilibrium is water in coexistence with water vapor. If the air above a pool of water is too dry, water will evaporate until the chemical potential of the water vapor (water in air) is the same as that of liquid vapor. </p>
<p>Note that this week Chris will be holding his office hour on Wednesday at 3 pm rather than on Tuesday. </p>
<p>Reading:</p>
<p>By Monday, October 30: Schroeder 3.5 and 3.6<br />
By Wednesday, November 1: 4.1<br />
By Friday, November 3: 4.2 and 4.3 </p>
<p>Problems Due Tuesday, November 7<br />
<strong>4.1</strong>, 4.2, <strong>4.3</strong>, 4.5, <strong>4.6</strong><br />
The attached file contains some hints for 4.6, which does require some slightly messy algebra.</p>
<p>Due Friday, November 10<br />
4.10, <strong>4.13, 4.15, 4.18</strong><br />
For 4.13, you can ignore the last sentence ("Discsuss the implications, giving a numerical example..")</p>
<p>In addition, we will do several problems in class:<br />
4.5, 4.7 - 4.9, 4.14, and the Diesel and Stirling engines. Take a look at these....</p>
<ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/469932-Problem_4.6.pdf" title="120 Kbytes, application/pdf">Hint for 4.6</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/469932-Problem_4.6.pdf?download=1" title="120 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 30-Oct-2017 at 7:11PM</i></small>
</td></tr>
</table>
</ul>2017-11-08T19:42:36ZPaul Crowellcid:63472.eid:469492.updated:2017-11-08 13:42:36Week 9 (Updated)2017-11-06T17:38:14Z<p>In part (c), you are asked to compute the "rate at which water would evaporate" (due to the exhaust heat). There is an ambiguity here, which is whether you are to assume that the water is heated up to 100 C and then evaporates, OR whether it simply evaporates at the temperature of the environment. If the cooling towers are large enough, you can assume that the water evaporates at the same temperature as the river, and the latent heat in this case is the latent heat of evaporation of water at 298 K. This is perfectly well-defined, even though the water is not "boiling." You can look up the relevant number... </p>2017-11-08T19:41:58ZPaul Crowellcid:63472.eid:471482.updated:2017-11-08 13:41:58Note on Problem 4.3 (Updated)2017-11-04T00:58:13Z<p><strong>I am away until Friday and will not be able to hold office hours this week. I will answer questions posted to the Moodle page, and I will hold an extra office hour next Tuesday (probably 2:00 - 4:00). Chris Conklin will do the lecture on Wednesday.</strong></p>
<p>On Schroeder 3.37: As I noted in class, the "physical" solution of this problem goes as follows: If I have a volume of gas at z = 0 and then raise that same volume of gas by a height z, then the energy per molecule in that gas must have increased by mgz. Therefore the chemical potential at height z is just the chemical potential at z=0 PLUS mgz.</p>
<p>For the "rigorous" solution, see the file below.</p>
<p>See slides 15 - 18 of the "Week of October 30th" under Lecture Slides for a calculation of the Carnot efficiency without (I hope) any sign errors! I will go over this very quickly on Monday.</p>
<p>There is a very useful website for visualizing engines:</p>
<p><a href="http://www.animatedengines.com/">http://www.animatedengines.com/</a></p>
<p>In particular, we will discuss the Stirling cycle, Otto cycle (used in the two-stroke engine), and Diesel cycle. The common four-stroke engine is also shown, but I will not discuss it in any detail. </p>
<p>Reading for Week 10:<br />
By Monday, November 6: 4.1 and 4.3<br />
By Wednesday, November 8: 4.2 and 4.4 (through p. 144)<br />
We will not be discussing steam engines in any detail. <br />
By Friday, November 10: 6.1 (through p. 225)</p>
<p>Problems due <strong>Friday, November 17:</strong><br />
<strong>6.1, 6.3, 6.5</strong></p>
<h1>Quiz 2 will be given on Wednesday, November 15</h1>
<p>It will cover material through 4.3 (NOT 4.4, and nothing on steam engines)<br />
There will not be any questions on chemical potential on this quiz, although there may some on the final exam (after we have done part of Chapter 5).</p>
<p>The second quiz from 2016 is posted below.</p>
<ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/471112-Numbers_and_Formulae_Quiz2.pdf" title="137 Kbytes, application/pdf">Formula Sheet for Quiz 2</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/471112-Numbers_and_Formulae_Quiz2.pdf?download=1" title="137 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 4-Nov-2017 at 4:24PM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/471102-2201_2016_Crowell_Q2v4wSolutions.pdf" title="411 Kbytes, application/pdf">Quiz 2 from 2016</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/471102-2201_2016_Crowell_Q2v4wSolutions.pdf?download=1" title="411 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 4-Nov-2017 at 4:21PM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/471052-Schroeder_3.37.pdf" title="90 Kbytes, application/pdf">Schroeder 3.37</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/471052-Schroeder_3.37.pdf?download=1" title="90 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 3-Nov-2017 at 8:00PM</i></small>
</td></tr>
</table>
</ul>2017-11-06T17:23:22ZPaul Crowellcid:63472.eid:471042.updated:2017-11-06 11:23:22Week 10 (Updated)2017-10-22T15:07:51Z<p>Note that there will not be any problems due on Friday, October 27. Week 7 problems are due on Tuesday, October 24, and the next problem set (to be posted later) will be due on Tuesday, October 31.</p>
<p>This week we will generalize the concept of maximizing entropy in equilibrium to systems in which the volume and particle number can vary.</p>
<p>Reading<br />
By Monday, October 23rd: 3.4 through p. 110<br />
By Wednesday, October 25th: Rest of 3.4<br />
By Friday, October 27th: 3.5 and 3.6</p>
<p><strong>Homework: Due Tuesday, October 31</strong><br />
<strong>3.31, 3.32, 3.34</strong>,</p>
<p><strong>Homework: Due Friday, November 3</strong><br />
<strong>3.36, 3.37,</strong> 3.38<br />
Note: for Problem 3.36, start with the multiplicity function of the Einstein solid given in Problem 3.25. </p>2017-11-01T21:03:59ZPaul Crowellcid:63472.eid:467642.updated:2017-11-01 16:03:59Week 8 (Updated)2017-10-16T06:36:31Z<p>We will continue working through the consequences of our assumption that the entropy of two systems will be maximized in equilibrium. In the first case, the volume and particle number are fixed, and the two systems can exchange energy. We will then deal with the cases in which the volumes and particle number can change.</p>
<p>Note that Professor Crowell will be away Tuesday - Thursday and will not be holding office hours this week.</p>
<p>Reading<br />
By Monday, October 16: 3.1 <br />
By Tuesday, October 17: pp. 98 - 99 and 103 - 104. You will need this for discussion section.<br />
By Wednesday, October 18: 3.2<br />
By Friday, October 20: rest of 3.3 and 3.4 through p. 111</p>
<p>Problems<br />
Due, Tuesday, October 24<br />
<strong>3.19, 3.20</strong>, 3.22, 3.25(d-e)</p>
<p>More problems will be posted later.</p>
<p>Most of 3.19 will be done in discussion section on October 17.<br />
<br />
For 3.20, you will need to invert the hyperbolic tangent to complete the last part. This is not difficult! If you write out the hyperbolic tangent in the form <i>t</i><i>a</i><i>n</i><i>h</i>(<i>x</i>) = (<i>e</i><sup>2<i>x</i></sup> - 1) / (<i>e</i><sup>2<i>x</i></sup> + 1)
, you can invert the expression <i>t</i><i>a</i><i>n</i><i>h</i>(<i>x</i>) = 0.99
, with a couple lines of algebra. Alternatively, both Mathematica and Matlab have inverse hyperbolic functions (ArcTanh in Mathematica, atanh in Matlab ). </p>
<p>Although calculating the energy and magnetization of the system as a fraction of their maximum values is relatively easy, the entropy takes a little more work. There are two options, but my intention is for you to do the following: Use your answer for <i>M</i> / <i>M</i><sub><i>m</i><i>a</i><i>x</i></sub>
to determine the fraction of the moments that are up or down. Then you can calculate the entropy using an expression you will have derived in discussion section. </p>
<p>It would be possible to use the result of Problem 3.23 to compute the entropy in 3.20, but I do not want you to waste time deriving the expression in 3.23. There is no physics in that....</p>2017-10-16T06:37:25ZPaul Crowellcid:63472.eid:466182.updated:2017-10-16 01:37:25Week 7 (Updated)2017-10-07T00:17:04Z<p>Homework problems:</p>
<p>Due Tuesday, October 17<br />
2.37, 2.40, <strong>2.42, 3.1</strong>, 3.3, <strong>3.5</strong>, 3.6</p>
<p>Due Friday, October 20<br />
<strong>3.7, 3.10, 3.12</strong>, 3.13, <strong>3.14</strong>, 3.16</p>
<p>More problems will be added later.</p>
<p>NOTE that Quiz 1 covers material through Schroeder 2.4, but NOT Section 1.7.<br />
This week I will hold an office hour on Tuesday from 2.</p>
<p>Quiz 1 is Wednesday, October 11. Please read the announcement under Week 5<br />
Last name A - Sc: Tate B20<br />
Last name Sp-Z: Tate 110</p>
<p>On Monday, October 9, I will address any question posted on the course Moodle site (under the Week of October 9). Please post your questions before 6 PM Sunday evening.</p>
<p>Reading:<br />
By Friday, October 13: Schroeder 3.1</p>
<p>Problems (due the week of October 16) will be posted later.</p>2017-10-12T22:55:49ZPaul Crowellcid:63472.eid:464482.updated:2017-10-12 17:55:49Week 6 (Updated)2017-09-29T23:21:09Z<p>I am looking for a good MatLab tutorial and will post it when I get a response.</p>
<p>Someone made a comment today about an error when using Matlab's nchoosek function. For sufficiently large values of n and k, it will give a warning stating that the answer may not have full double precision accuracy (16 digits). You can ignore this, as 15 digits is more than enough. There is nothing wrong with the function. It will definitely overflow when the arguments get too large, but for values less than 200 it is perfectly correct.</p>
<p>However, we will soon be dealing with numbers so large that this will all be moot, and the only choice for computing the factorials of genuinely large numbers (e.g. 10^23) will be Stirling's approximation.</p>
<p>Two scripts are below. One can be adapted for making plots of functions. The second implements Schroeder2.10. Note that actually doing the math is easy. Making the table requested with labels takes a few extra steps.<br />
</p>
<ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/463462-Schroeder2_10.m" title="1 Kbytes, application/octet-stream">Matlab script for problems like Schroeder2.10</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/463462-Schroeder2_10.m?download=1" title="1 Kbytes, application/octet-stream">Download</a></small>
</td><td align="right">
<small><i>posted 3-Oct-2017 at 12:33AM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/463452-simpleplot.m" title="0 Kbytes, application/octet-stream">Matlab script for plotting a function</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/463452-simpleplot.m?download=1" title="0 Kbytes, application/octet-stream">Download</a></small>
</td><td align="right">
<small><i>posted 3-Oct-2017 at 12:33AM</i></small>
</td></tr>
</table>
</ul>2017-10-03T05:33:56ZPaul Crowellcid:63472.eid:462812.updated:2017-10-03 00:33:56MatLab (Updated)2017-09-30T21:36:44Z<p>Reading:</p>
<p>By Monday, 10/2: 2.5 through the top of p. 72<br />
By Wednesday, 10/4: remainder of 2.5 and 2.6 through p. 76<br />
By Friday, 10/6: remainder of 2.6</p>
<p>Problems</p>
<p>No problems due Tuesday (exam on Wednesday)</p>
<p>Due <strong>Friday, October 13th</strong><br />
<strong>2.32, 2.34</strong>, 2.35, 2.36</p>
<h1>Quiz 1</h1>
<p>Quiz 1 will be held on <strong>Wednesday, October 11</strong> at the usual class time. Please go to the correct room:<br />
Last name A - Sc: Tate B20<br />
Last name Sp-Z: Tate 110<br />
The quiz will cover material through Section 2.4, with most of the questions on Chapter 1. I am posting last year's quiz as an example. This year's will be similar in format. My exams consist of problems (not multiple choice). Some may be very short, and others longer. There will be 4 - 5 total. I will post a sheet with numbers and formulae that will be provided. The quiz is otherwise "closed book." <strong>You will need a simple scientific calculator.</strong> </p>
<ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/462892-Numbers_and_Formulae_Crowell.pdf" title="238 Kbytes, application/pdf">Data, constants, and formulae to be provided for Quiz</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/462892-Numbers_and_Formulae_Crowell.pdf?download=1" title="238 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 30-Sep-2017 at 4:44PM</i></small>
</td></tr>
</table>
</ul><ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/fall/Phys 2201.100/downloads/462882-2201_2016_Crowell_Q1_Solutions.pdf" title="471 Kbytes, application/pdf">Quiz 1 from 2016</a>
<small>| <a href="/classes/2017/fall/Phys 2201.100/downloads/462882-2201_2016_Crowell_Q1_Solutions.pdf?download=1" title="471 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 30-Sep-2017 at 4:38PM</i></small>
</td></tr>
</table>
</ul>2017-09-30T21:44:41ZPaul Crowellcid:63472.eid:462872.updated:2017-09-30 16:44:41Week 5 (Updated)2017-09-22T23:56:26Z<p>Reading</p>
<p>By Monday, September 25: 2.1, 2.2, and 2.4 through the top of p. 63<br />
By Wednesday, September 27, 2.3<br />
By Friday, September 29, 2.4 (pp. 63 - 67)</p>
<p>Problems to be done by Tuesday, October 3rd in discussion section<br />
<strong>2.17</strong>, 2.19, <strong>2.21, 2.23</strong></p>
<p>Problems to be done by Friday, October 6th in lecture<br />
<strong>2.26, 2.27,</strong> 2.28, <strong>2.29, 2.30</strong></p>
<p>Professor Crowell has a research program review Wed. and Thurs. Chris Conklin will lecture on Wed. Professor Crowell will hold office hours on Thursday 5:00 - 6:00, but he will not be able to hold the earlier office hour. </p>2017-09-29T16:12:32ZPaul Crowellcid:63472.eid:460912.updated:2017-09-29 11:12:32Week 4 (Updated)2017-09-22T23:22:50Z<p>Starting the week of September 25th, all problem sets must be handed in IN CLASS on the day due. <strong>Email submissions will not be accepted. Late homework will not be accepted.</strong></p>
<p>Assignments due on Tuesday can be handed in in ANY discussion section. If for some reason, you have to miss your discussion section, you can hand the assignment in at another discussion section. You can give your problem set to someone else to hand in if necessary.</p>
<p>Assignments due on M, W, or F must be handed in during lecture.</p>
<p>Exceptions to this policy will be made only for university-approved absences arranged in advance.</p>2017-09-23T19:15:41ZPaul Crowellcid:63472.eid:460892.updated:2017-09-23 14:15:41Important announcement about problem sets (Updated)