COMEDK · Physics · 2. Units and Dimensions

Which of the given dimensional formula represents heat capacity

A \(\left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]\)
B \(\left[\mathrm{ML}^2 \mathrm{~T}^{-1} \mathrm{~K}^{-1}\right]\)
C \(\left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-2}\right]\)
D \(\left[\mathrm{MLT}^{-2} \mathrm{~K}^{-1}\right]\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]\)

Step-by-step Solution

Detailed explanation

Heat capacity \(C\) is defined as the amount of heat energy \(Q\) required to raise the temperature of a substance by an amount \(\Delta T\). The formula is \(C = \dfrac{Q}{\Delta T}\). The dimensional formula for heat energy \(Q\) is the same as work or energy, which is…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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