Answer: 254513.1 pa 2) How much energy is transferred into the gas from the hot

Question

Answer: 254513.1 pa

2) How much energy is transferred into the gas from the hot reservoir?

Suppose that 128 moles of a monatomic ideal gas is initially contained in a piston with a volume of 1.43 m3 at a temperature of 342 K. The piston is connected to a hot reservoir with a temperature of 1056 K and a cold reservoir with a temperature of 342 K. The gas undergoes a quasi-static Stirling cycle with the following steps: 1. The temperature of the gas is increased to 1056 K while maintaining a constant volume. 2. The volume of the gas is increased to 4.36 m3 while maintaining a constant temperature 3. The temperature of the gas is decreased to 342 K while maintaining a constant volume 4. The volume of the gas is decreased to 1.43 m3 while maintaining a constant temperature It may help you to recall that Cv 12.47 J/K/mole for a monatomic ideal gas, and that the number of gas molecules is equal to Avagadros number (6.022 x 1023) times the number of moles of the gas

Explanation / Answer

(1)

Use ideal gas law to find pressure:

PV = nRT

Rewrite for pressure of the gas

P = nRT / V

Substitute given values

P = ( 128 ) (8.314 ) (342 K ) / 1.43 m3

= 254513.1 Pa

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(2)

Energy transferred into the gas:

Q = nRT ln (V2/V1)

Substitute given values

Q = ( 128 ) (8.314 ) (1056 K ) ln (4.36 / 1.43)

= 1.25 x 106 J

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