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Work done in a polytropic process (P V^n constant or V proportional to a power of T)

This type of question, asked 2 times: 2021 Paper 26, 1 Feb 2024. All 2 questions below, oldest first.

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  1. Question 1

    2021 Paper 26

    29
    The volume VV of a given mass of monatomic gas changes with temperature TT according to the relation V=KT23V=KT^{\frac{2}{3}}. The work done when temperature changes by 90 K90\text{ }K will be xRxR. The value of xx is
  2. Question 2

    1 Feb 2024

    9
    The pressure and volume of an ideal gas are related as PV3/2=KPV^{3/2}= K (Constant). The work done when the gas is taken from state A(P1, V1, T1)A\left( P_{1},{\text{ }V}_{1},{\text{ }T}_{1} \right) to state B(P2, V2, T2)B\left( P_{2},{\text{ }V}_{2},{\text{ }T}_{2} \right) is:

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