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 `gamma(=C_(P)//C_(V))` to be 1.5, find the new pressure of the gas.

Explanation

Let the initial volume be V. After isothermal expansion, pressure `=(P)/(4)`, volume = 4V
Let P. is the pressure after adiabatic compression. The volume then is V. Therefore,
`P.V^(gamma)=(P)/(4)(4V)^(gamma),P.=(P)/(4)(4)^((3)/(2))`
`".=2P`