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 $\left[\mathrm{ML}^{2} \mathrm{~T}^{-1} \mathrm{~K}^{-1}\right]$.\\ In the light of the above statements, choose the most appropriate answer from the options given below.

(B) Both statement (I) and statement (II) are incorrect

(C) Both statement (I) and statement (II) are correct

(D) Statement (I) is incorrect but statement (II) is correct

JEE Main · 2024 · 06 Apr 2024 · Shift 2 · Units & Measurement

Given below are two statements :\\
Statement (I) : Dimensions of specific heat is

[L^{2} T^{- 2} K^{- 1}]

.\\
Statement (II) : Dimensions of gas constant is

[ML^{2} T^{- 1} K^{- 1}]

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

Answer: (A)

From

Q = m S Δ T

S = \frac{Q}{m Δ T}

, so

[S] = \frac{M L ^{2} T ^{- 2}}{M K} = [L^{2} T^{- 2} K^{- 1}]

— statement (I) is correct. From

P V = n R T

R = \frac{P V}{n T}

, so

[R] = \frac{[ M L ^{- 1} T ^{- 2} ] [ L ^{3} ]}{[ mol ] [ K ]} = [M L^{2} T^{- 2} mol^{- 1} K^{- 1}]

, not

[M L^{2} T^{- 1} K^{- 1}]

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

JEE Main · 2024 · 06 Apr 2024 · Shift 2 · Single correct option