InterviewSolution
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InterviewSolution
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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 to `T`, find the height at which the centre of gravity of the gas is located. |
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Answer» As the gravitational field is constant the centre of gravity and the centre of mass are same. The location of `C.M.` `h = (int_0^oo h dm)/(int_0^oo dm) = (int_0^oo h rho dh)/(int_0^oo rho dh)` But from Barametric formula and gas law `rho = rho_0 e^(-Mg h//RT)` So, `h = (int_0^alpha h(e^(-Mg h//RT))dh)/(int_0^alpha (e^(-Mg h//RT))dh) = (RT)/(Mg)`. |
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