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1.Units, Dimensions and Measurement
hard
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 $\left[\mathrm{ML}^2 \mathrm{~T}^{-1} \mathrm{~K}^{-1}\right]$
AStatement $(I)$ is incorrect but statement $(II)$ is correct
B Both statement $(I)$ and statement $(II)$ are incorrect
CStatement $(I)$ is correct but statement $(II)$ is incorrect
DBoth statement $(I)$ and statement $(II)$ are correct
(JEE MAIN-2024)
Solution
$\Delta \mathrm{Q}=\mathrm{mS} \Delta \mathrm{T}$
$\mathrm{s}=\frac{\Delta \mathrm{Q}}{\mathrm{m} \Delta \mathrm{T}}$
${[\mathrm{s}]=\left[\frac{\mathrm{ML}^2 \mathrm{~T}^{-2}}{\mathrm{MK}}\right]}$
${[\mathrm{s}]=\left[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]}$
Statement-$(I)$ is correct
$\mathrm{PV}=\mathrm{nRT} \Rightarrow \mathrm{R}=\frac{\mathrm{PV}}{\mathrm{nT}}$
${[\mathrm{R}]=\frac{\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]\left[\mathrm{L}^3\right]}{[\mathrm{mol}][\mathrm{K}]}}$
${[\mathrm{R}]=\left[\mathrm{ML}^{-2} \mathrm{~T}^{-2} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right]}$
Statement$-II$ is incorrect
$\mathrm{s}=\frac{\Delta \mathrm{Q}}{\mathrm{m} \Delta \mathrm{T}}$
${[\mathrm{s}]=\left[\frac{\mathrm{ML}^2 \mathrm{~T}^{-2}}{\mathrm{MK}}\right]}$
${[\mathrm{s}]=\left[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]}$
Statement-$(I)$ is correct
$\mathrm{PV}=\mathrm{nRT} \Rightarrow \mathrm{R}=\frac{\mathrm{PV}}{\mathrm{nT}}$
${[\mathrm{R}]=\frac{\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]\left[\mathrm{L}^3\right]}{[\mathrm{mol}][\mathrm{K}]}}$
${[\mathrm{R}]=\left[\mathrm{ML}^{-2} \mathrm{~T}^{-2} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right]}$
Statement$-II$ is incorrect
Standard 11
Physics
