The volume of \(1\; mole\) of an ideal gas with the adiabatic exponent \(\gamma\) is changed according to the relation \(V=\frac bT\) where \(b =\) constant. The amount of heat absorbed by the gas in the process if the temperature is increased by \(\triangle T\) will be

A \(\frac{R}{{\gamma - 1}} \Delta T\)
B \(\left( {\frac{{2 - \gamma }}{{\gamma - 1}}} \right)R \Delta T\)
C \(\;\frac{{R \Delta T}}{{\gamma - 1}}\)
D \(\left( {\frac{{1 - \gamma }}{{\gamma + 1}}} \right)R \Delta T\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\left( {\frac{{2 - \gamma }}{{\gamma - 1}}} \right)R \Delta T\)

Step-by-step Solution

Detailed explanation

\(V=\frac bT\) \(VT=\)constant

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.

Same subject

Explore more questions on app

From NEET

Match the items given in Column \(I\) with those in Column \(II\) and select the correct option given below:

Column\(I\)	Column \(II\)
\((a)\) Glycosuria	\((i)\) Accumulation of uric acid in joints
\((b)\) Gout	\((ii)\) Mass of crystallised salts within the kidney
\((c)\) Renal calculi	\((iii)\) Inflammation in glomeruli
\((d)\) Glomerular nephritis	\((iv)\) Presence of glucose in urine

NEET 2018 Medium

Explore more questions on app

\((a)\) Fourth trophic level	\((i)\) Crow
\((b)\) Second trophic level	\((ii)\) Vulture
\((c)\) First trophic level	\((iii)\) Rabbit
\((d)\) Third trophic level	\((iv)\) Grass