In a certain thermodynamical process, the pressure of a gas depends on its volume as kV3. The work done when the temperature changes from 100 ° C to 300 ° C will be ___________ nR, where n denotes number of moles of a gas. Numerical answer type. Work it out, then open the answer.

Answer: 50. P = kV³ ⇒ PV⁻³ = constant, a polytropic process with index x = -3. W = (nRΔ T)/(1 - x) = (nRΔ T)/(4) Δ T = 300 - 100 = 200 K, so W = 200/4nR = 50 nR. Answer: 50

In a certain thermodynamical process, the pressure of a gas depends… | JEE Main 2021 (25 Feb, Shift 1)

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Thermodynamic Processes

In a certain thermodynamical process, the pressure of a gas depends on its volume as kV3. The work done when the temperature changes from 100 $^\circ$ C to 300 $^\circ$ C will be ___________ nR, where n denotes number of moles of a gas.

Numerical answer type. Work it out, then open the answer.

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Answer: 50

$P = kV^3 \Rightarrow PV^{-3} =$ constant, a polytropic process with index $x = -3$ .
$W = \frac{nR\Delta T}{1 - x} = \frac{nR\Delta T}{4}$
$\Delta T = 300 - 100 = 200\text{ K}$ , so $W = \frac{200}{4}nR = 50\,nR$ .
Answer: 50

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