Thermal Physics PHYS
‐
253
Assignment 5, due 22 October (2010) in class
1)
Fig 1 represents a simplified pV diagram of the Joule ideal
‐
gas cycle. All processes are quasi
‐
static,
and
C
p
is constant. Prove that the thermal efficiency of an engine performing this cycle is:
ൌ1െ ቀ
భ
మ
ቁ
ሺఊିଵሻ ఊ
⁄
2)
Fig 2 represents a simplified pV diagram of the Sargent ideal
‐
gas cycle. All processes are quasi
‐
static,
and the heat capacities are constant. Prove that the thermodynamic efficiency an engine performing
this cycle is:
ൌ1െߛ
ܶ
ସ
െ ܶ
ଵ
ܶ
ଷ
െ ܶ
ଶ
3)
Fig 3 represents an imaginary ideal
‐
gas cycle. Assuming constant heat capacities, show that the
thermal efficiency is:
ൌ1െߛ
ቀ
ܸ
ଵ
ܸ
ଶ
ൗቁെ1
ሺ
ଷ
ଶ
ሻെ1
⁄
4)
An imaginary ideal
‐
gas engine operates in a cycle, which forms a rectangle with sides parallel to the
axis of the
pV
diagram. Call
p
1
and
p
2
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 Fall '10
 PeterGrutter
 Physics, Thermodynamics, PV diagram, constant heat capacities

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