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JEE Main 20246 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
6 April
Shift
Evening Shift
Subject
Physics
Chapter
Units and Dimensions

JEE Main 2024 · 6 April · Evening Shift · Physics · Units and Dimensions

Given below are two statements : Statement (I) : Dimensions of...

Given below are two statements : Statement (I) : Dimensions of specific heat is [L2 T−2 K−1]\left[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]. Statement (II) : Dimensions of gas constant is [ML2 T−1 K−1]\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.

Options

  1. ABoth statement (I) and statement (II) are correct
  2. BStatement (I) is correct but statement (II) is incorrect
  3. CBoth statement (I) and statement (II) are incorrect Statement (I) is incorrect but statement (II) is correct
  4. DStatement (I) is incorrect but statement (II) is correct

Correct answer

B. Statement (I) is correct but statement (II) is incorrect

Step-by-step solution

ΔQ=mSΔTs=ΔQmΔT[s]=[ML2 T−2MK][s]=[L2 T−2 K−1]\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 PV=nRT⇒R=PVnT[R]=[ML−1 T−2][L3][mol][K][R]=[ML2 T−2 mol−1 K−1]\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
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