Question

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

• A. Statement (I) is incorrect but statement (II) is correct
• B. Both statement (I) and statement (II) are incorrect
• C. Statement (I) is correct but statement (II) is incorrect
• D. Both statement (I) and statement (II) are correct

Answer 1

Answer: (C)

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

Answer 2

$\Delta Q = m S \Delta T$
$s = \frac{\Delta Q}{m \Delta T}$
$[s] = \frac{\left[ M L^2 T^{-2} \right]}{M \cdot K}$
$[s] = \left[ L^2 T^{-2} K^{-1} \right]$
Statement-(I) is correct.
From $PV = nRT$, we have:
$R = \frac{PV}{nT}$
Substitute dimensions:
$[R] = \frac{\left[ M L^{-1} T^{-2} L^3 \right]}{\left[ \text{mol} \right] \cdot \left[ K \right]}$
Simplify:
$[R] = \left[ M L^2 T^{-2} \text{mol}^{-1} K^{-1} \right]$
Statement-(II) is incorrect.