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Q.

In a certain thermo dynamical process, the pressure of a gas depends on its volume as kV². The work done when the temperature changes from 100°C to 400°C will be_______ nR, where n denotes number of mole of a gas and R is universal gas constant.

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Detailed Solution

$P = {kV}^{2} T_{i} = 100^{\circ} C & T_{f} = 400^{\circ} C ΔT = 300^{\circ} C Given P = {kV}^{2} Now PV = nRT ∴ {kV}^{3} = nRT Now 3 {kV}^{2} dV = nRdT ∴ PdV = \frac{nRdT}{3} ∴ Work = \int PdV = \int \frac{nRdT}{3} = \frac{nR}{3} ΔT = \frac{300}{3} \times nR = 100 nR$

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