Question

Match $\text{Column-I}$ and $\text{Column-II}$ and choose the correct match from the given choices.

$\begin{array}{cc}\text{Column-I}& \text{Column-II}\\ \text{(A) Root mean square}& \text{(P)}\frac{1}{3}nm{\overline{v}}^2\\ \text{speed of gas}& \\ \text{molecules}& \\ \text{(B) Pressure exerted}& \text{(Q)}\sqrt{\frac{3RT}{M}}\\ \text{by ideal gas}& \\ \text{(C) Average kinetic}& \text{(R)}\frac{5}{2}RT\\ \text{Energy of a}& \\ \text{molecule}& \\ \text{(D) Total internal}& \text{(R)}\frac{3}{2}{k}_{B}T\\ \text{energy of 1 mole}& \\ \text{of a diatomic gas}& \end{array}$

• A. $\text{(A)-(R), (B)-(Q), (C)-(P), (D)-(S)}$
• B. $\text{(A)-(R), (B)-(P), (C)-(S), (D)-(Q)}$
• C. $\text{(A)-(Q), (B)-(R), (C)-(S), (D)-(P)}$
• D. $\text{(A)-(Q), (B)-(P), (C)-(S), (D)-(R)}$

Answer 1

The correct option is D $\text{(A)-(Q), (B)-(P), (C)-(S), (D)-(R)}$

Root mean square speed of gas molecule $=\sqrt{\frac{3RT}{M}}$

Pressure exerted by ideal gas $=\frac{1}{3}nm{\overline{v}}^2$

Average kinetic energy of a molecule $=\frac{3}{2}{k}_{B}T$

Total internal energy of a gas is $\left(U\right)=\frac{1}{2}nfRT$
Here, $n=1$ and $f=5$

$\therefore U=\frac{5}{2}RT$

Therefore, option $\left(\text{D}\right)$ is the correct choice.