All Problems Equation of the gas state processes
Problem 2.19
An ideal gas of molar mass \(M\) is located in the uniform gravitational field in which the free-fall acceleration is equal to \(g\). Find the gas pressure as a function of height \(h,\) if \(p=p_{0}\) at \(h=0,\) and the temperature varies with height as (a) \(T=T_{0}(1-a h)\) (b) \(T=T_{0}(1+a h)\) where \(a\) is a positive constant.
\text { (a) } p=p_{0}(1-a h)^{n}, h<1 / a \text { (b) } p=p_{0} /(1+a h)^{n} \text { . Here } n=M g / a R ar{T}_{0}