Q64 / 90 · JEE Main 2024 (06 Apr Shift 2) · Physics
Given below are two statements :
Statement (I) : Dimensions of specific heat is $\left[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]$.
Statement (II) : Dimensions of gas constant is $\left[\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-1} \mathrm{~K}^{-1}\right]$.
In the light of the above statements, choose the most appropriate answer from the options given below.
- ABoth statement (I) and statement (II) are correct
- Correct answerBStatement (I) is correct but statement (II) is incorrect
- CBoth statement (I) and statement (II) are incorrect Statement (I) is incorrect but statement (II) is correct
- DStatement (I) is incorrect but statement (II) is correct
Solution
$\begin{aligned}
& \Delta \mathrm{Q}=\mathrm{mS} \Delta \mathrm{T} \\
& \mathbf{s}=\frac{\Delta \mathrm{Q}}{\mathrm{m} \Delta \mathrm{T}} \\
& {[\mathrm{s}]=\left[\frac{\mathrm{ML}^2 \mathrm{~T}^{-2}}{\mathrm{MK}}\right]} \\
& {[\mathrm{s}]=\left[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]}
\end{aligned}$
Statement-(I) is correct $\begin{aligned} & \mathrm{PV}=\mathrm{nRT} \Rightarrow \mathrm{R}=\frac{\mathrm{PV}}{\mathrm{nT}} \\ & {[\mathrm{R}]=\frac{\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]\left[\mathrm{L}^3\right]}{[\mathrm{mol}][\mathrm{K}]}} \\ & {[\mathrm{R}]=\left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right]} \end{aligned}$
Statement-II is incorrect
Statement-(I) is correct $\begin{aligned} & \mathrm{PV}=\mathrm{nRT} \Rightarrow \mathrm{R}=\frac{\mathrm{PV}}{\mathrm{nT}} \\ & {[\mathrm{R}]=\frac{\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]\left[\mathrm{L}^3\right]}{[\mathrm{mol}][\mathrm{K}]}} \\ & {[\mathrm{R}]=\left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right]} \end{aligned}$
Statement-II is incorrect
Hence, the correct answer is option: 'B'.