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in Heat and Thermodynamics by (48.5k points)
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A mass of ideal gas at pressure P is expanded isothermally to four times the original volume and then slowly compressed adiabatically to its original volume. Assuming (γ = CP /CV ) to be 1.5, find the new pressure of the gas.

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Let the initial volume be V. After isothermal expansion, pressure = \(\frac{P}{4}\), volume = 4V

Let P' is the pressure after adiabatic compression.

Then volume then is V. Therefore,

P' Vγ = \(\frac{P}{4}\) (4V)γ ; P' = \(\frac{P}{4}\) (4)\(\frac{3}{2}\)

P' = 2P

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