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Unformatted text preview: PHYS4125 Fall 2011
Exam 1 [Schroeder Ch. 1—21 Name Kat}? Z 2/18/11
There are 4 roblerns. Answer all 4 to the best of your ability. 1. (25 points) A Diesel engine requires no spark plug. instead, the air in the
cylinder is compressed. so highly that the fuel ignites spontaneously when
sprayed into the cylinder. 3) If the air is initially at room temperature (taken as T0=300 K) and then is
compressed adiabatically by a factor of 15, what temperature is attained
(before fuel injection)? Note: for air take the number of degrees of freedom
to be S. a 56...} a mu .1... Wm ammo. 7‘7 Tf/ay V 9/75 . 1 7L3.
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'PVY: Cwaﬂ one I"); ; EEC/0 3’ LACHA 3/: 7L 2—3;
W c.) Calculate the work done on the gas, the heat added to the gas, and the
change in internal energy of the gas during the compression. Express your
answer in terms of N, To, and k3. USN? +1.9 15+ Leno AU : Q + o) amé We idea 44/wa adfotba'hk
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” T: (W ° ' b”) v0 2. (20 points) Oxygen gas (02) is contained in a oneliter ﬂask at
atmospheric pressure and a temperature of 300° K 3) Approximately how many collisions per second are made by any one
molecule, with the other molecules? oewmcswwam \7 /2: We 43:th
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/ V k3?” Libs/mo“ ‘7: Book a _ as; “4/5 ‘ m _. a mQ : Baﬂmu —— €311 XIO~JQE2 ON Wm : 5.7‘l‘gl0cyf’ b) How many molecules strike one square centimeter of the surface of the
ﬂask, per second? Tasmmw/auorwag/AEMV; M M lama/U? r» Aﬂ~ﬁfems
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ﬁll/61E moluuﬂeo C: )0an .3}? 13% 'xO{Uéms 3. (25 points) An otherwise empty room contains 6X1026 air molecules. ,3) How many times more probable is it to have them split exactly 5050
between front and back halves of the room then. to have a 49—51 split?
but BMW/ml dish; L (147?“ ﬁr “Ms A lee Wm  . N l ’1’ PP I « ”/61 ‘ '
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m no“ SW“) :C 3M 4. (30 points) Show that the multiplicity of a two state paramagnet in the
limit of low temperature can be approximated to be .Q=(Ne IN 1)“ where
N l is the number of dipoles that point downward. You will find it useful
to start with a binomial distribution, calculate 111(0) , make use of the
Stirling approximation for the factorials and the approximation ln(1+x)~x 4}
“NJ?— é: N \Y} H ‘ 6‘)’ “all“ (N’UQA ‘ NM \WUJ/ SW02 V¢3Mawv
In); N pm; — m— Histami— 5‘}qu  or, mu ...
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