The heat capacity ratio of a gas determines the speed of sound in it through the formula cs = (γRT/M)1/2, where γ = Cp,m/CV,m and M is the molar mass of the gas. Deduce an expression for the speed of sound in a perfect gas of (a) diatomic, (b) linear triatomic, (c) nonlinear triatomic molecules at high temperatures (with translation and rotation active). Estimate the speed of sound in air at 25 °C. Hint: Note that Cp,m − CV,m = R for a perfect gas.

A cylinder of nitrogen and a cylinder of neon are at the same temperature and pressure. The mean free path of a nitrogen molecule is 130 nmnm.       What is the mean free path of a neon atom? Express your answer with the appropriate units.

The van der Waals coefficients of monatomic argon gas are a=0.1345a=0.1345 m66Pa/mol22 and b=32.19×106b=32.19×106 m33/mol. Calculate the correction to the internal energy of 3 mole of this monatomic van der Waals gas compared to that of 3 mole of a monatomic ideal gas at density 200 mol/L .

Xenon and helium are both ideal, monatomic gases, but they have very different molar masses (Mxenon = 33*Mhelium). If you have 1 mole of each gas and the gases are at the same temperature, which one of the following statements is true?     They both have the same internal energy, but xenon has a lower root-mean-square speed than helium.    They both have the same internal energy and root-mean-square speed.    They both have the same root-mean-square speed, but xenon has a greater internal energy than helium.    They both have the same internal energy, but helium has a lower root-mean-square speed than xenon.    They both have the same root-mean-square speed, but helium has a greater internal energy than xenon.