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

The Correct Option is C

\[\Delta Q = m S \Delta T\]
\[s = \frac{\Delta Q}{m \Delta T}\]
\[[s] = \frac{\left[ M L^2 T^{-2} \right]}{M \cdot K}\]
\[[s] = \left[ L^2 T^{-2} K^{-1} \right]\]
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.