Given below are two statements : Statement (I) : Dimensions of specific heat is $\left[\mathrm{L}^2…

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.
  1. Both statement (I) and statement (II) are correct
  2. Statement (I) is correct but statement (II) is incorrect
  3. Both statement (I) and statement (II) are incorrect Statement (I) is incorrect but statement (II) is correct
  4. Statement (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

Asked in: JEE Main 2024 (06 Apr Shift 2)

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