7B MT1 Saturday Review Problems
Patrick Varilly
*
21 Feb 2008
1
Liphardt, Spring 05, Prob 2
In an experiment liquid helium at an initial temperature of 1.0 K is to be cooled further by
bringing it into contact with a solid which is initially at a lower temperature
T
0
. The heat
capacity of the liquid helium may be expressed as
c
L
=
aT
3
where
a
= 0
.
128 J K

4
, and the heat capacity of the solid may be expressed as
c
S
=
bT

2
where
b
= 0
.
015 J K. Assume the mixture to be mechanically and thermally isolated from
the rest of the universe and no work is done in the process.
a) How much heat must leave the liquid helium to cool it from 1.0 K to 0.7 K?
b) What must be the initial temperature of the solid,
T
0
, if the final temperature of the
system, helium (initially at
T
= 1
.
0 K) plus solid (initially at
T
=
T
0
), is to be 0.5 K?
c) Find the total change in the entropy of the universe during this process. To minimize the
chance of math errors, leave this answer in terms of the parameters
a
and
b
.
2
Smoot, Fall 06, Prob 4ac
For a modern power plant, the pressure of the steam can be as high as 70 atmospheres at
300
◦
C (573 K); the exhaust is at one atmosphere and perhaps 40
◦
C (313 K).
*
Thanks to Steve Byrnes for typing up several of these problems and their solutions
1
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7B MT1 Saturday Review Session Problems
Patrick Varilly
a) For such a power plant, what is the maximum thermodynamic efficiency?
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 Spring '08
 ZETTLE
 Thermodynamics, Heat, Patrick Varilly, 7B MT1 Saturday, MT1 Saturday Review

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