A piston contains 270 moles of an ideal monatomic gas that initally has a pressu

Question

A piston contains 270 moles of an ideal monatomic gas that initally has a pressure of 2.74 Times 105 Pa and a volume of 4.4 m3. The piston is connected to a hot and cold reservoir and the gas goes through the following quasi-static cycle accepting energy from the hot reservoir and exhausting energy into the cold reservoir. The pressure of the gas is increased to 5.74 Times 105 Pa while maintaining a constant volume. The volume of the gas is increased to 11.4 m3 while maintaining a constant pressure. The pressure of the gas is decreased to 2.74 Times 105 Pa while maintaining a constant volume.The volume of the gas is decreased to 4.4 m3 while maintaining a constant pressure. It may help you to recall that Cv = 12.47 J/K/mole and Cp = 20.79 J/K/mole for a monatomic ideal gas. How much energy is transferred into the gas from the hot reservoir during the first step? How much work is done by the gas during the first step?

Explanation / Answer

1. ?U = Q - W

at constant V; W = 0

?U = nCv?T

P1V1 = nRT1

(2.74x105)(4.4) = 270(8.314)T1

T1 = 537.07K

P2V2 = nRT2

(5.74x105)(4.4) = 270(8.314)T2

T2 = 1125.1K

?U = nCv?T = 270(12.47)(1125.1 - 537.07)

= 1979.84KJ = Q

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