Given below are two statements: Statement (I): Dimensions of specific heat is [L²T⁻²K⁻¹]. Statement (II): Dimensions of gas constant is [ML²T⁻¹K⁻¹]. In the light of the above statements, choose the most appropriate answer from the options given below. (a) Statement (I) is incorrect but statement (II) is correct (b) Both statement (I) and statement (II) are incorrect (c) Both statement (I) and statement (II) are correct (d) Statement (I) is correct but statement (II) is incorrect

Answer: (d). Specific heat c = (Q)/(m Δ T) = [ML²T⁻²][M][K] = [L²T⁻²K⁻¹], so Statement I is correct. Gas constant R = PV/nT = energy per mole per kelvin = [ML²T⁻²K⁻¹mol⁻¹]. Statement II has T⁻¹ (and no mol), so it is incorrect. So the answer is (d).

Given below are two statements: Statement (I): Dimensions of specific… | JEE Main 2024 (6 Apr, Shift 2)

Q31JEE Main 2024 · 6 APR · SHIFT 2Medium

Units & Dimensions

Given below are two statements:

Statement (I): Dimensions of specific heat is $[\mathrm{L^{2}T^{-2}K^{-1}}]$ .

Statement (II): Dimensions of gas constant is $[\mathrm{ML^{2}T^{-1}K^{-1}}]$ .

In the light of the above statements, choose the most appropriate answer from the options given below.

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Answer: (d)

Specific heat $c = \dfrac{Q}{m\,\Delta T} = \dfrac{[\mathrm{ML^2T^{-2}}]}{[\mathrm{M}][\mathrm{K}]} = [\mathrm{L^2T^{-2}K^{-1}}]$ , so Statement I is correct.
Gas constant $R = \dfrac{PV}{nT}$ = energy per mole per kelvin $= [\mathrm{ML^2T^{-2}K^{-1}mol^{-1}}]$ .
Statement II has $\mathrm{T^{-1}}$ (and no mol), so it is incorrect.
So the answer is (d).

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Units & Dimensions question from JEE Main 2024 (6 Apr, Shift 2)

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