Question

One mole of a monoatomic gas and one mole of a diatomic gas are initially in the same state. Both gases are expanded isothermally and then adiabatically, such that they acquire the same final state. Choose the correct statement.

• A. Work done by diatomic gas is more than that by monoatomic gas
• B. Work done by monoatomic gas is more than that by diatomic gas
• C. Work done by both the gases are equal
• D. Change in internal energies of both the gases are equal

Answer 1

Answer: (A)

As, slope of an adiabatic curve = $-\gamma\left(\frac{p}{V}\right)$
Also, $\gamma_{\text{diatomic}}\left(=\frac{7}{5}\right)<\gamma_{\text{monoatomic}}\left(=\frac{5}{3}\right)$
So, adiabatic expansion will be moresteep for monoatomic gas, whereasisotherms for both gases are nearly same.As, work done = area under $p-V$ graph $\therefore $ Work done is more for diatomic gas