Question

Find the rate v with which monoatomic gas of molar mass M flows out of a thermally insulated vessel into vacuum through a small hole. The flow rate of the gas inside the vessel is assumed to be negligible under these conditions. The temperature of gas in the vessel is T.

• A. $\sqrt{\frac{3RT}{M}}$
• B. $\sqrt{\frac{5RT}{2M}}$
• C. $\sqrt{\frac{3RT}{2M}}$
• D. $\sqrt{\frac{5RT}{M}}$

Answer 1

Answer: (D)

$\sqrt{\frac{5RT}{M}}$

Answer 2

The gas undergoes adiabatic expansion into vacuum. For a monoatomic gas, the molar enthalpy is $\frac{5}{2}RT$. This enthalpy is converted entirely into kinetic energy ($\frac{1}{2}Mv^2$) of the effusing gas jet, leading to the speed $v = \sqrt{\frac{5RT}{M}}$.