Suppose that 110 moles of a monatomic ideal gas is initially contained in a pist
ID: 1424737 • Letter: S
Question
Suppose that 110 moles of a monatomic ideal gas is initially contained in a piston with a volume of 1.38 m3 at a temperature of 315 K. The piston is connected to a hot reservoir with a temperature of 1021 K and a cold reservoir with a temperature of 315 K. The gas undergoes a quasi-static Stirling cycle with the following steps:
The temperature of the gas is increased to 1021 K while maintaining a constant volume.
The volume of the gas is increased to 4.27 m3 while maintaining a constant temperature.
The temperature of the gas is decreased to 315 K while maintaining a constant volume.
The volume of the gas is decreased to 1.38 m3 while maintaining a constant temperature.
It may help you to recall that CVCV = 12.47 J/K/mole for a monatomic ideal gas, and that the number of gas molecules is equal to Avagadros number (6.022 × 1023) times the number of moles of the gas.
1-What is the pressure of the gas under its initial conditions?
2-How much energy is transferred into the gas from the hot reservoir?
3-How much energy is transferred out of the gas into the cold reservoir?
4-How much work is done by the gas during this cycle?
5-What is the efficiency of this Stirling cycle?
6-What is the maximum (Carnot) efficiency of a heat engine running between these two reservoirs?
Explanation / Answer
1)
Pi = nNkT(i)/V(i)
2)
Q=L
Q=pV=nRTln(V2/V1)
3)
Q=-U
Q=-3/2nRT
4)
L=-nRT(V2/V1)=nRT(V1/V2)
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