Question

$N$ moles of a diatomic gas in a cylinder are 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. What is the change in the total kinetic energy of the gas ?

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

Answer 1

Answer: (A)

$u_1=N\frac{5}{2}RT$
$u_f=2n\frac{3}{2}RT+\left(N-n\right)\frac{5}{2}RT$
$=\frac{1}{2}nRT+\frac{5}{2}nRT$
$\Delta u=Q=\frac{1}{2}nRT$