1
PHYS 414: Homework 6
This homework due Wednesday March 7
1. A Carnot engine is connected to thermal reservoirs at temperatures
T
2
and
T
1
through
two identical thermal resistors R. [The heat current
J
passing through a thermal resis
tor
R
connecting two points diﬀering in temperature by Δ
T
is given by
J
= Δ
T/R
.]
(a)
(2 points)
At what output power
P
does the engine have its maximum possible
eﬃciency?
(b)
(2 points)
What is the maximum possible eﬃciency that this engine could have?
(c)
(2 points)
What is the maximum possible output power
P
that can be extracted
using this engine?
(d)
(2 points)
What is the eﬃciency
η
of this engine when it is producing the maximum
possible power?
(e)
(2 points)
At what rate is entropy being created by this engine when it is producing
the maximum possible power?
2.
(6 points)
An evacuated container of volume
V
is initially thermally isolated from its
surroundings, and is initially at temperature
T
0
, which is neither very small nor very
large. The container has negligible heat capacity, so the heat energy of the system
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 Spring '12
 SHUBEITA
 Physics, Thermodynamics, Current, Work, Heat, Fundamental physics concepts, gas phase, Helmholtz

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