TS EAMCET · Physics · Thermodynamics

A one mole of ideal gas goes through a process in which pressure $P$ varies with volume $V$ as $P = 3 - g {(\frac{V}{V_{0}})}^{2}$ , where $V_{0}$ is a constant. The maximum attainable temperature by the ideal gas during this process is (All quantities are in $SI$ units and $R$ is gas constant)

A $\frac{2 V_{0}}{3 R}$
B $\frac{2 V_{0}}{R}$
C $\frac{3 V_{0}}{2 R}$
D $\frac{3 V_{0}}{R}$

Verified Solution

Answer & Solution

Correct Answer

(A) $\frac{2 V_{0}}{3 R}$

Step-by-step Solution

Detailed explanation

Given that, P=3-gVV02 We know PV=nRT ⇒3-gVV02v=RT∴N=0 ⇒ T=3V-gVV02R=3VR-gV2RV02 For maximum value of T, dTdV=0 ⇒ dTdV=3R-gRV022V ⇒ 3R-2gVRV02=0 ⇒ 3R-2gVRV02 V=3V022g

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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A one mole of ideal gas goes through a process in which pressure P varies with volume V as P=3-gVV02, where V0 is a constant. The maximum attainable temperature by the ideal gas during this process is (All quantities are in SI units and R is gas constant)

Step-by-step Solution

A one mole of ideal gas goes through a process in which pressure $P$ varies with volume $V$ as $P = 3 - g {(\frac{V}{V_{0}})}^{2}$ , where $V_{0}$ is a constant. The maximum attainable temperature by the ideal gas during this process is (All quantities are in $SI$ units and $R$ is gas constant)