MHT CET · Physics · Thermodynamics

If \(\mathrm{R}\) is universal gas constant the amount of heat needed to raise the temperature of 2 moles of an ideal monoatomic gas from \(273 \mathrm{~K}\) to \(373 \mathrm{~K}\) when no work is done is

A \(150 \mathrm{R}\)
B \(100 \mathrm{R}\)
C \(500 \mathrm{R}\)
D \(300 \mathrm{R}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(300 \mathrm{R}\)

Step-by-step Solution

Detailed explanation

For an ideal gas, the internal energy in only a function of the gas temperature and is a measure of the mean translational kinetic energy of the atoms.
\(\Delta \mathrm{Q}=\Delta \mathrm{U}+\Delta \mathrm{Q}=0 \Rightarrow \Delta \mathrm{Q}=\Delta \mathrm{U}=\frac{\mathrm{n}}{2} \mathrm{R} \Delta \mathrm{T}\)
When \(\mathrm{n}=\) degree of freedom for monoatomic gas i.e \(=3\)
\(=\frac{3}{2} \times 2 \mathrm{R}(373-273)=300 \mathrm{R}\)

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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