Question

$N$ moles of diatomic gas in a cylinder is at a temperature $T$ . Heat is supplied to the cylinder such that the temperature remains constant but $n$ moles of the diatomic gas get converted into monoatomic gas. The change in the total kinetic energy of the gas is

• A. $0$
• B. $\frac{5}{2}nRT$
• C. $\frac{3}{2}nRT$
• D. $\frac{1}{2}nRT$

Answer 1

Answer: (D)

Initial kinetic energy of the system,
$U_{i}=N\frac{5}{2}RT$
Final kinetic energy of the system,
$U_{f}=2n\frac{3}{2} \, RT+\frac{\left(N - n\right) 5}{2}RT$
$\Rightarrow U_{f}=\frac{1}{2}nRT+\frac{5}{2}NRT$
$\Delta U=Q=\frac{1}{2}nRT$ .