TS EAMCET · Physics · Thermodynamics

One mole of ideal gas goes through a process $P V^{3} =$ constant, where $P$ and $V$ are pressure and volume respectively. Let $W$ be the work done by the gas as its temperature is increased by $Δ T$ . The value of $|W|$ is ( $R$ is the universal gas constant)

A $R Δ T$
B $\frac{1}{4} R Δ T$
C $R^{3} Δ T$
D $\frac{R}{2} Δ T$

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Answer & Solution

Correct Answer

(D) $\frac{R}{2} Δ T$

Step-by-step Solution

Detailed explanation

Given, One mole of ideal gas n=1 goes through a process is given by PV3= constant Where, P and V are pressure and volume respectively. This equation can be compared with the equation of adiabatic process, PVγ= constant We get, γ=3 Work done in adiabatic process 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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One mole of ideal gas goes through a process PV3= constant, where P and V are pressure and volume respectively. Let W be the work done by the gas as its temperature is increased by ΔT. The value of W is (R is the universal gas constant)

Step-by-step Solution

One mole of ideal gas goes through a process $P V^{3} =$ constant, where $P$ and $V$ are pressure and volume respectively. Let $W$ be the work done by the gas as its temperature is increased by $Δ T$ . The value of $|W|$ is ( $R$ is the universal gas constant)