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Question 1

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.

We need to evaluate two statements about dimensions.

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

Specific heat = Energy / (mass × temperature).

Dimensions: $$\frac{[ML^2T^{-2}]}{[M][K]} = [L^2T^{-2}K^{-1}]$$

Statement I is correct. ✓

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

Gas constant R = Energy / (mol × temperature) (from PV = nRT).

Dimensions: $$\frac{[ML^2T^{-2}]}{[\text{mol}][K]} = [ML^2T^{-2}K^{-1}\text{mol}^{-1}]$$

The given dimension has $$T^{-1}$$ instead of $$T^{-2}$$. Statement II is incorrect. ✗

The correct answer is Option 2: Statement (I) is correct but Statement (II) is incorrect.

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