Question

A gas in a rigid vessel is at ambient temperature and at a pressure, P₁, slightly higher than ambient pressure, P₀. A valve on the vessel is opened, so gas escapes and the pressure drops quickly to ambient pressure. The valve is closed and after a long time the remaining gas returns to ambient temperature at which point the pressure is P₂. Develop an expression that allows a determination of the ratio of specific heats, k, in terms of the pressures.  

Answer 1

C.V.: air remaining in tank,

First part of the process is an isentropic expansion s = constant