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Chemistry - Thermodynamics - I Question with Solution | TestHub

ChemistryThermodynamics - IAdiabatic Process/PolytropicMedium2 minQB

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Passage / Comprehension

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

Work done on the gas when $n$ moles of this gas are compressed or expanded by a reversible adiabatic process from ( $P_{1}$ , $V_{1}$ , $T_{1}$ ) to ( $P_{2}$ , $V_{2}$ , $T_{2}$ ) is

Options:

Answer:

Solution:

Adiabatic: $w_{o n} = Δ U$ .

$d U = n C_{V} d T - β n^{2} / V^{2} d V$ , so $U = n C_{V} T + β n^{2} / V + const$ .

$Δ U = n C_{V} (T_{2} - T_{1}) + β n^{2} (1/ V_{2} - 1/ V_{1})$ . Answer: (D).

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

⏱ 2mℹ️ Source: QB

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