Solve the following problem:
An ideal gas is contained in a cylinder equipped with a frictionless, nonleaking piston of area A. When the pressure is atmospheric Po, the piston face is a distance I from the closed end. The gas is compressed by moving the piston a distance x. Calculate the spring constant ζ/x of the gas:
(a) Under isothermal conditions.
(b) Under adiabatic conditions.
(c) In what respect is a gas cushion superior to a steel spring?
(d) Using Eq. , show that Cp - Cv = nR for the ideal gas.
Cp = Cv +[(∂U/∂V)r + P] Vβ,
(∂U/∂V)r = (Cp-Cv/Vβ) - P.