{"id":555,"date":"2018-04-28T13:54:09","date_gmt":"2018-04-28T20:54:09","guid":{"rendered":"https:\/\/sites.evergreen.edu\/thermo1718\/?page_id=555"},"modified":"2018-04-28T13:54:09","modified_gmt":"2018-04-28T20:54:09","slug":"reading-response-week-15","status":"publish","type":"page","link":"https:\/\/sites.evergreen.edu\/thermo1718\/reading-response-week-15\/","title":{"rendered":"Reading Response, Week 15"},"content":{"rendered":"<div class=\"frm_forms  with_frm_style frm_style_formidable-style\" id=\"frm_form_25_container\" >\n<form enctype=\"multipart\/form-data\" method=\"post\" class=\"frm-show-form  frm_pro_form \" id=\"form_70ed32222222222222\"  >\n<div class=\"frm_form_fields \">\n<fieldset>\n<legend class=\"frm_hidden\">Reading Response - Week 15<\/legend>\n<h3 class=\"frm_form_title\">Reading Response - Week 15<\/h3>\n<div class=\"frm_fields_container\">\n<input type=\"hidden\" name=\"frm_action\" value=\"create\" \/>\n<input type=\"hidden\" name=\"form_id\" value=\"25\" \/>\n<input type=\"hidden\" name=\"frm_hide_fields_25\" id=\"frm_hide_fields_25\" value=\"\" \/>\n<input type=\"hidden\" name=\"form_key\" value=\"70ed32222222222222\" \/>\n<input type=\"hidden\" name=\"item_meta[0]\" value=\"\" \/>\n<input type=\"hidden\" id=\"frm_submit_entry_25\" name=\"frm_submit_entry_25\" value=\"da3b4a653b\" \/><input type=\"hidden\" name=\"_wp_http_referer\" value=\"\/thermo1718\/wp-json\/wp\/v2\/pages\/555\" \/><div id=\"frm_field_312_container\" class=\"frm_form_field form-field  frm_required_field frm_top_container\">\n    <label for=\"field_ruvfe3333332\" class=\"frm_primary_label\">Last Name, First Name\n        <span class=\"frm_required\">*<\/span>\n    <\/label>\n    <input type=\"text\" id=\"field_ruvfe3333332\" name=\"item_meta[312]\" value=\"\"  data-reqmsg=\"This field cannot be blank.\" aria-required=\"true\" data-invmsg=\"Last Name, First Name is invalid\" aria-invalid=\"false\"  \/>\n    \n    \n<\/div>\n<div id=\"frm_field_313_container\" class=\"frm_form_field form-field  frm_required_field frm_top_container\">\n    <label for=\"field_dmsrp3333332\" class=\"frm_primary_label\">email\n        <span class=\"frm_required\">*<\/span>\n    <\/label>\n    <input type=\"text\" id=\"field_dmsrp3333332\" name=\"item_meta[313]\" value=\"\"  data-reqmsg=\"This field cannot be blank.\" aria-required=\"true\" data-invmsg=\"email is invalid\" aria-invalid=\"false\"  \/>\n    \n    \n<\/div>\n<div id=\"frm_field_314_container\" class=\"frm_form_field form-field  frm_top_container\">\n    <label for=\"field_snr0q3333332\" class=\"frm_primary_label\">1: Let's explore some consequences of indistinguishability and probability in the context of a situation we know quite well: rolling two (fair) six-sided dice. For \"classical\" dice, which are identical but distinguishable, the probability of rolling a \"2\" is 1\/36, while the probability of rolling a \"7\" is 6\/36. Now, consider two (fair) six-sided \"quantum\" dice, which are indistinguishable. What's the probability of rolling a \"2\"? What's the probability of rolling a \"7\"? (Hint: it might be easiest to make an exhaustive list of combinations).\n        <span class=\"frm_required\"><\/span>\n    <\/label>\n    <textarea name=\"item_meta[314]\" id=\"field_snr0q3333332\" rows=\"5\"  data-invmsg=\"1: Let&#039;s explore some consequences of indistinguishability and probability in the context of a situation we know quite well: rolling two (fair) six-sided dice. For &quot;classical&quot; dice, which are identical but distinguishable, the probability of rolling a &quot;2&quot; is 1\/36, while the probability of rolling a &quot;7&quot; is 6\/36. Now, consider two (fair) six-sided &quot;quantum&quot; dice, which are indistinguishable. What&#039;s the probability of rolling a &quot;2&quot;? What&#039;s the probability of rolling a &quot;7&quot;? (Hint: it might be easiest to make an exhaustive list of combinations). is invalid\" aria-invalid=\"false\"  ><\/textarea>\n    \n    \n<\/div>\n<div id=\"frm_field_315_container\" class=\"frm_form_field form-field  frm_top_container\">\n    <label for=\"field_c9ic63333332\" class=\"frm_primary_label\">2: In your notes, reproduce an annotated version of the derivations of the grand partition function and occupancy (from the section Distribution Functions on p. 266-268,) related to the (a) Fermi-Dirac (FD) distribution, (b) the Bose-Einstein (BE) distribution, and (c) the Boltzmann (also sometimes called the Maxwell-Boltzmann (MB)) distribution. What questions do you have about the material in this section? Please be specific so I will know how much class time to spend on these derivations.\n        <span class=\"frm_required\"><\/span>\n    <\/label>\n    <textarea name=\"item_meta[315]\" id=\"field_c9ic63333332\" rows=\"5\"  data-invmsg=\"2: In your notes, reproduce an annotated version of the derivations of the grand partition function and occupancy (from the section Distribution Functions on p. 266-268,) related to the (a) Fermi-Dirac (FD) distribution, (b) the Bose-Einstein (BE) distribution, and (c) the Boltzmann (also sometimes called the Maxwell-Boltzmann (MB)) distribution. What questions do you have about the material in this section? Please be specific so I will know how much class time to spend on these derivations. is invalid\" aria-invalid=\"false\"  ><\/textarea>\n    \n    \n<\/div>\n<div id=\"frm_field_316_container\" class=\"frm_form_field form-field  frm_top_container\">\n    <label for=\"field_nkptg3333332\" class=\"frm_primary_label\">3. In your notes, copy and annotate the important features of Figure 7.6 and Figure 7.7. On Figure 7.7, the occupancy for the MB distribution when epsilon = mu is shown directly, and the occupancy for the BE distribution is implied. Add in the value for the FD distribution when epsilon = mu. What are those values?\n        <span class=\"frm_required\"><\/span>\n    <\/label>\n    <textarea name=\"item_meta[316]\" id=\"field_nkptg3333332\" rows=\"5\"  data-invmsg=\"3. In your notes, copy and annotate the important features of Figure 7.6 and Figure 7.7. On Figure 7.7, the occupancy for the MB distribution when epsilon = mu is shown directly, and the occupancy for the BE distribution is implied. Add in the value for the FD distribution when epsilon = mu. What are those values? is invalid\" aria-invalid=\"false\"  ><\/textarea>\n    \n    \n<\/div>\n<div id=\"frm_field_326_container\" class=\"frm_form_field form-field  frm_top_container\">\n    <label for=\"field_bkjjc\" class=\"frm_primary_label\">4: Consider the Fermi-Dirac distribution.  (a) What's the value of the Fermi-Dirac distribution as T --&gt; 0 (assume epsilon &gt; mu)?  (b) What's the value of the Fermi-Dirac distribution as T --&gt; infinity (assume epsilon &gt; mu)?  (c) What's the value of the Fermi-Dirac distribution when epsilon = mu?\n        <span class=\"frm_required\"><\/span>\n    <\/label>\n    <textarea name=\"item_meta[326]\" id=\"field_bkjjc\" rows=\"5\"  data-invmsg=\"4: Consider the Fermi-Dirac distribution.  (a) What&#039;s the value of the Fermi-Dirac distribution as T --&gt; 0 (assume epsilon &gt; mu)?  (b) What&#039;s the value of the Fermi-Dirac distribution as T --&gt; infinity (assume epsilon &gt; mu)?  (c) What&#039;s the value of the Fermi-Dirac distribution when epsilon = mu? is invalid\" aria-invalid=\"false\"  ><\/textarea>\n    \n    \n<\/div>\n<div id=\"frm_field_325_container\" class=\"frm_form_field form-field  frm_top_container\">\n    <label for=\"field_r7x7s\" class=\"frm_primary_label\">5. Starting from the Fermi-Dirac distribution given in eq. (7.23), explain (mathematically) how it becomes the step function shown in Figure 7.9, valid for T = 0.\n        <span class=\"frm_required\"><\/span>\n    <\/label>\n    <textarea name=\"item_meta[325]\" id=\"field_r7x7s\" rows=\"5\"  data-invmsg=\"5. Starting from the Fermi-Dirac distribution given in eq. (7.23), explain (mathematically) how it becomes the step function shown in Figure 7.9, valid for T = 0. is invalid\" aria-invalid=\"false\"  ><\/textarea>\n    \n    \n<\/div>\n<div id=\"frm_field_324_container\" class=\"frm_form_field form-field  frm_top_container\">\n    <label for=\"field_xhzpl\" class=\"frm_primary_label\">6. How is the Fermi energy related to the chemical potential?\n        <span class=\"frm_required\"><\/span>\n    <\/label>\n    <textarea name=\"item_meta[324]\" id=\"field_xhzpl\" rows=\"5\"  data-invmsg=\"6. How is the Fermi energy related to the chemical potential? is invalid\" aria-invalid=\"false\"  ><\/textarea>\n    \n    \n<\/div>\n<div id=\"frm_field_323_container\" class=\"frm_form_field form-field  frm_top_container\">\n    <label for=\"field_va8md\" class=\"frm_primary_label\">7. In your notes, reproduce an annotated version of the derivations on p. 273 \u2013 275 that lead to eqs. (7.38) and (7.42). What questions do you have about the material in this section? Please be specific so I will know how much class time to spend on these derivations.\n        <span class=\"frm_required\"><\/span>\n    <\/label>\n    <textarea name=\"item_meta[323]\" id=\"field_va8md\" rows=\"5\"  data-invmsg=\"7. In your notes, reproduce an annotated version of the derivations on p. 273 \u2013 275 that lead to eqs. (7.38) and (7.42). What questions do you have about the material in this section? Please be specific so I will know how much class time to spend on these derivations. is invalid\" aria-invalid=\"false\"  ><\/textarea>\n    \n    \n<\/div>\n<div id=\"frm_field_322_container\" class=\"frm_form_field form-field  frm_top_container\">\n    <label for=\"field_blllc\" class=\"frm_primary_label\">8. In eq. (7.38) and eq. (7.40), there is a factor of 2. Where does this factor of two come from? How would this factor change if these particles weren\u2019t electrons (but were still fermions)?\n        <span class=\"frm_required\"><\/span>\n    <\/label>\n    <textarea name=\"item_meta[322]\" id=\"field_blllc\" rows=\"5\"  data-invmsg=\"8. In eq. (7.38) and eq. (7.40), there is a factor of 2. Where does this factor of two come from? How would this factor change if these particles weren\u2019t electrons (but were still fermions)? is invalid\" aria-invalid=\"false\"  ><\/textarea>\n    \n    \n<\/div>\n<div id=\"frm_field_321_container\" class=\"frm_form_field form-field  frm_top_container\">\n    <label for=\"field_30l27\" class=\"frm_primary_label\">9. What's degeneracy pressure? What is its physical origin?\n        <span class=\"frm_required\"><\/span>\n    <\/label>\n    <textarea name=\"item_meta[321]\" id=\"field_30l27\" rows=\"5\"  data-invmsg=\"9. What&#039;s degeneracy pressure? What is its physical origin? is invalid\" aria-invalid=\"false\"  ><\/textarea>\n    \n    \n<\/div>\n<div id=\"frm_field_320_container\" class=\"frm_form_field form-field  frm_top_container\">\n    <label for=\"field_c8mcx\" class=\"frm_primary_label\">10. Describe the density of states g(\u03b5) in words. What's the \"purpose in life\" of the density of states?\n        <span class=\"frm_required\"><\/span>\n    <\/label>\n    <textarea name=\"item_meta[320]\" id=\"field_c8mcx\" rows=\"5\"  data-invmsg=\"10. Describe the density of states g(\u03b5) in words. What&#039;s the &quot;purpose in life&quot; of the density of states? is invalid\" aria-invalid=\"false\"  ><\/textarea>\n    \n    \n<\/div>\n<div id=\"frm_field_319_container\" class=\"frm_form_field form-field  frm_top_container\">\n    <label for=\"field_e76eg\" class=\"frm_primary_label\">11. As T increases, does the chemical potential \u03bc increase or decrease? In your own words, explain why the chemical potential must change as the temperature increases.\n        <span class=\"frm_required\"><\/span>\n    <\/label>\n    <textarea name=\"item_meta[319]\" id=\"field_e76eg\" rows=\"5\"  data-invmsg=\"11. As T increases, does the chemical potential \u03bc increase or decrease? In your own words, explain why the chemical potential must change as the temperature increases. is invalid\" aria-invalid=\"false\"  ><\/textarea>\n    \n    \n<\/div>\n<div id=\"frm_field_317_container\" class=\"frm_form_field form-field  frm_top_container\">\n    <label for=\"field_c12j1333332\" class=\"frm_primary_label\">What material from this reading (or previous classes) would you like us to go over in more detail?\n        <span class=\"frm_required\"><\/span>\n    <\/label>\n    <textarea name=\"item_meta[317]\" id=\"field_c12j1333332\" rows=\"5\"  data-invmsg=\"What material from this reading (or previous classes) would you like us to go over in more detail? is invalid\" aria-invalid=\"false\"  ><\/textarea>\n    \n    \n<\/div>\n\t<input type=\"hidden\" name=\"item_key\" value=\"\" \/>\n\t<input name=\"frm_state\" type=\"hidden\" value=\"xNFysRh2gLotMRfD+ArbSx8CDECpDYoiWcNysinMx8M=\" \/><div class=\"frm_submit\">\n\n<button class=\"frm_button_submit frm_final_submit\" type=\"submit\"  >Submit<\/button>\n\n<\/div><\/div>\n<\/fieldset>\n<\/div>\n<p style=\"display: none !important;\"><label>&#916;<textarea name=\"ak_hp_textarea\" cols=\"45\" rows=\"8\" maxlength=\"100\"><\/textarea><\/label><input type=\"hidden\" id=\"ak_js_1\" name=\"ak_js\" value=\"77\"\/><script>document.getElementById( \"ak_js_1\" ).setAttribute( \"value\", ( new Date() ).getTime() );<\/script><\/p><\/form>\n<\/div>\n\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":219,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_mi_skip_tracking":false,"_s2mail":""},"_links":{"self":[{"href":"https:\/\/sites.evergreen.edu\/thermo1718\/wp-json\/wp\/v2\/pages\/555"}],"collection":[{"href":"https:\/\/sites.evergreen.edu\/thermo1718\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.evergreen.edu\/thermo1718\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.evergreen.edu\/thermo1718\/wp-json\/wp\/v2\/users\/219"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.evergreen.edu\/thermo1718\/wp-json\/wp\/v2\/comments?post=555"}],"version-history":[{"count":0,"href":"https:\/\/sites.evergreen.edu\/thermo1718\/wp-json\/wp\/v2\/pages\/555\/revisions"}],"wp:attachment":[{"href":"https:\/\/sites.evergreen.edu\/thermo1718\/wp-json\/wp\/v2\/media?parent=555"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}