1.
A
reversible
cyclic device does work while exchanging heat with three constant
temperature reservoirs as illustrated in the figure. The three reservoirs 1, 2, and 3 are at
temperatures of 1000 K, 300 K, and 500 K respectively. It is known that 400 kJ of heat
are transferred from reservoir 1 to the device, and the total work done by the cyclic
device is 100 kJ. Determine both the magnitude and direction of the heat transfer with the
other two reservoirs. [40]
100 = Q
2
+ Q
3
+ 400 (Q
2
,
Q
3
: heat from the device)
Since the equation has two unknowns, a second equation must be obtained. From the
second law
∆
S = (dQ/T)
rev
= 0
or Q
1
/T
1
+ Q
2
/T
2
+ Q
3
/T
3
= 0
Substituting,
400/1000 + Q2/300 +Q3/500 =0
0.4 + Q2/300 + Q3/500 = 0
Solving gives
0.4 + (300Q
3
)/300 + Q
3
/500 = 0,
Q
3
= 450 kJ
Q
2
= 150 kJ
Therefore, 150 kJ of heat is transferred from reservoir 2 to the device and 450 kJ of heat
are rejected to reservoir 3.
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Water at 15 kPa, 40°C enters a pump and leaves after the pressure has been raised to 5
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 Spring '08
 Gallivan
 Thermodynamics, Entropy, Heat

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