Chemistry - Thermodynamics - I Question with Solution | TestHub

ChemistryThermodynamics - IAdiabatic Process/PolytropicHard2 minQB

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Passage / Comprehension

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

Which relation holds for this gas in a reversible adiabatic process?

Options:

Answer:

Solution:

Reversible adiabatic: $d U = - P d V$ .

$n C_{V} d T - β n^{2} / V^{2} d V = - [n RT / V + β n^{2} / V^{2}] d V$ .

The $β$ terms are $- β n^{2} / V^{2} d V$ on the left and $- β n^{2} / V^{2} d V$ on the right, so they cancel.

$n C_{V} d T = - (n RT / V) d V$ , so $(C_{V} / R) ln T + ln V = const$ .

Thus $T^{C_{V} / R} V = const$ . Answer: (D).

Stream:JEESubject:ChemistryTopic:Thermodynamics - ISubtopic:Adiabatic Process/Polytropic

⏱ 2mℹ️ Source: QB

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