Phys 404 S11 Exam 1 Solutions

# Phys 404 S11 Exam 1 Solutions - SIGNATURE NAME Student ID...

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SIGNATURE _____________________ NAME ________________________ Student ID # _____________________ Physics 404 Spring 2011 Prof. Anlage First Mid-Term Exam 10 March, 2011 CLOSED BOOK, NO Calculator Permitted, CLOSED NOTES Point totals are given for each part of the question. If you run out of room, continue writing on the back of the same page. If you do so, make a note on the front part of the page! Note: You must solve the problem following the instructions given in the problem. Correct answers alone will not receive full credit. Partial Credit: Show Your Work! Answers written with no explanation will not receive full credit. You can receive credit for describing the method you would use to solve a problem, even if you missed an earlier part. ============================================================= Problem Credit Max. Credit 1 25 2 25 3 25 4 25 TOTAL 100 1/2 ++ 2 1/2 2 2 1/2 n n -- n = 0 11 exp(-x )dx = x exp(-x )dx = n! (2 n) n exp -n + x 2 12n 1 - x      ± ²³ ´µ¶·¸¹ ± º ² ³» ¼º·»½ ¾¹ ± ³¼» ² ¿¼¾ ¼ ·³½ ¾¹ ± ²»¼³ ² ¿¼¾ ¸ ± À ÁÂÃÄ²Å Æ Ç³È Æ É Ê ± Ë»ÇËºÌ Í½Î Ï ¾ ± Ëº Ë³ Ì ¾ ÐÑÒ ± À Ó·Å Ô ¹ Ô ¼·ÕÖ¹ ± Õ×¼Ö Ø Ö×¼Õ ´µ¶·ÙÚ¹ ± ´µ¶·Ù¹ Ø ´µ¶×·Ú¹ ´µ¶·Ù Ø Ú¹ Û ´µ¶·Ù¹ Ø ´µ¶×·Ú¹ Ü·Ñ½ Ô¹ ± ÎÝ Þ ß à áÆâÝÞ ß à ãÆâÝ ä å æ çÎ ×è Î ×é ãæÆ à ÇÎ Ü·Ô¹ ± À Ü É ·Ô É ¹Ü æ ·Ô ² Ô É ¹ Æ ××¿·Å Æ ¹ ± êëì Þ² í î Ê â Ç¸ ÐÕÒ ± À Õ·Ô¹¿·Ô¹ Ô Ã ± ² Þ ïð ïÍ â Ì ñ ± ³ Þ ïñ ïÍ â Ì ð ± ² Þ ïò ïÍ â Ì Ê

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1. a.) Explain clearly the differences between the microcanonical and canonical ensembles of statistical mechanics. Give your answer as a legible, grammatically-correct paragraph or two, carefully defining any terms that you use in the paragraph or in any equations that you write. (5 points) b.) For the microcanonical and canonical ensembles, what is the probability that the system will be in a particular quantum state ? (5 points) c.) A closed system has an internal insulating wall that divides the system in half.
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Phys 404 S11 Exam 1 Solutions - SIGNATURE NAME Student ID...

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