All Problems

Equation of the gas state processes

Problem 2.19

An ideal gas of molar mass MM is located in the uniform gravitational field in which the free-fall acceleration is equal to gg. Find the gas pressure as a function of height h,h, if p=p0p=p_{0} at h=0,h=0, and the temperature varies with height as (a) T=T0(1−ah)T=T_{0}(1-a h) (b) T=T0(1+ah)T=T_{0}(1+a h) where aa is a positive constant.

Reveal Answer
\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}
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