One mole of an ideal gas at temperature T 1 expands according to the law V 2 P = a (constant). The work done by the gas till temperature of gas becomes T 2 is:

P = a V 2 ; T = R P V = R a V 3 . W = ∫ a V 2 d V = 3 a ( V 2 3 − V 1 3 ) = 3 1 R ( T 2 − T 1 ) .

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PhysicsHeat & ThermoThermodynamicsMedium2 minQB

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One mole of an ideal gas at temperature $T_{1}$ expands according to the law $\frac{P}{V ^{2}} = a$ (constant). The work done by the gas till temperature of gas becomes $T_{2}$ is:

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Answer:

Solution:

$P = a V^{2}; T = \frac{P V}{R} = \frac{a V ^{3}}{R}$ .

$W = \int a V^{2} d V = \frac{a}{3} (V_{2}^{3} - V_{1}^{3}) = \frac{1}{3} R (T_{2} - T_{1}) .$

Stream:JEESubject:PhysicsTopic:Heat & ThermoSubtopic:Thermodynamics

⏱ 2mℹ️ Source: QB

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