Suppose that 249 moles of a monatomic ideal gas is initially contained in a pist

Question

Suppose that 249 moles of a monatomic ideal gas is initially contained in a piston with a volume of 0.73 m3 at a temperature of 524 K. The piston is connected to a hot reservoir with a temperature of 1299 K and a cold reservoir with a temperature of 524 K. The gas undergoes a quasi-static Stirling cycle with the following steps:

The temperature of the gas is increased to 1299 K while maintaining a constant volume.

The volume of the gas is increased to 2.97 m3 while maintaining a constant temperature.

The temperature of the gas is decreased to 524 K while maintaining a constant volume.

The volume of the gas is decreased to 0.73 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

Explanation / Answer

1. Pressure of the gas under intial condition

PV = nRT

P = (249 mol)(0.0821 L atm/mol K)(524K)/(0.73 m3)(1000L/1m3)

P = 14.67 atm (101.325 Pa/1 atm) = 1486.85 Pa

2. Energy transferred into the gas from the hot reservior

q = nCvdeltaT

= (249 mol)(12.47 J/molK)(524-1299)K

= -2406.4 kJ

3. Energy transferred out of the gas into the cold reservior

q = nCvdeltaT

= (249 mol)(12.47 J/molK)(524-524)K

= 0 kJ

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