( ∂ V ∂ U ) T for this gas is

( ∂ T ∂ P ) V = n R / V , so T ( ∂ T ∂ P ) V = n RT / V . Subtract P : n RT / V − n RT / V − β n 2 / V 2 = − β n 2 / V 2 . Answer: (D).

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ChemistryThermodynamics - IFirst law of ThermodynamicsEasy2 minQB

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Passage / Comprehension

Passage $Comprehension (Q.1 to Q.8) Use the thermodynamic equation of state (\frac{\partial U}{\partial V})_{T} = T (\frac{\partial P}{\partial T})_{V} - P to answer the following questions for n moles of a gas that obeys P = \frac{n RT}{V} + \frac{β n ^{2}}{V ^{2}} where β is a positive constant and C_{V} is independent of temperature.$

$(\frac{\partial U}{\partial V})_{T}$ for this gas is

Options:

Answer:

Solution:

$(\frac{\partial P}{\partial T})_{V} = n R / V$ , so $T (\frac{\partial P}{\partial T})_{V} = n RT / V$ .

Subtract $P$ : $n RT / V - n RT / V - β n^{2} / V^{2} = - β n^{2} / V^{2}$ . Answer: (D).

Stream:JEESubject:ChemistryTopic:Thermodynamics - ISubtopic:First law of Thermodynamics

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