Chemistry - Thermodynamics - II Question with Solution | TestHub

ChemistryThermodynamics - IICarnot Cycle/Cyclic processMedium2 minQB

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Passage / Comprehension

An ideal gas undergoes a single stage expansion against a constant opposing pressure from $(P_{1}, V_{1}, T)$ to $(P_{2}, V_{2}, T)$ .

What is the net mass lowered through height h in the cyclic transformation in (Q.13) and (Q.14) ?

Options:

Answer:

Solution:

The net mass lowered is related to the work done by the gas. In a cyclic process, the net work done is equal to the heat exchanged. For an ideal gas undergoing an isothermal expansion and compression between pressures P₁ and P₂, the work done is $W = n RT ln (\frac{P _{1}}{P _{2}})$ . The change in potential energy is $m g h$ . Equating work done to potential energy change for the net mass, we derive the expression.

The solution is:

$m^{'} - m = \frac{n RT}{g h} (\frac{( P _{1} - P _{2} ) ^{2}}{P _{1} P _{2}})$

Stream:JEESubject:ChemistryTopic:Thermodynamics - IISubtopic:Carnot Cycle/Cyclic process

⏱ 2mℹ️ Source: QB

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