All Problems

Equation of the gas state processes

Problem 2.18

An ideal gas of molar mass \(M\) is contained in a very tall vertical cylindrical vessel in the uniform gravitational field in which the free-fall acceleration equals \(g\). Assuming the gas temperature to be the same and equal to \(T,\) find the height at which the centre of gravity of the gas is located.

Reveal Answer
hC=0hρdh/0ρdh=RT/Mgh_{C}=\int_{0}^{\infty} h \rho d h / \int_{0}^{\infty} \rho d h=R T / M g