An ideal gas is in thermodynamic equilibrium. If a molecule has n degrees of freedom, let U(n) be the internal energy of one mole and v(n) be the speed of sound at fixed temperature and pressure. Which option is correct?
Options

Question

An ideal gas is in thermodynamic equilibrium. If a molecule has n degrees of freedom, let U(n) be the internal energy of one mole and v(n) be the speed of sound at fixed temperature and pressure. Which option is correct?

Options

G1 Physics · Accepted Answer

For one mole, U(n)=(n/2)RT, so U increases with n. Also γ=1+2/n, and v(n)=√(γRT/M), so v decreases as n increases. Hence v₅>v₇ and U₅<U₇. Option C.