A mass of ideal gas at pressure P is expanded isothermally to four tim

1.	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.
Answer» 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' V^γ = \(\frac{P}{4}\) (4V)^γ ; P' = \(\frac{P}{4}\) (4)^{\(\frac{3}{2}\)} P' = 2P

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.

Answer»

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

P' = 2P