Chemistry - Thermodynamics - I Question with Solution | TestHub

ChemistryThermodynamics - IWorkMedium2 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 largest mass ' m ' which can be lifted through a height ' h ' in this expansion ?

Answer:

Solution:

The work done by the gas during expansion is $W = n RT ln (\frac{P _{1}}{P _{2}})$ .

This work is used to lift the mass,

so $W = m g h$ . Equating these gives $m g h = n RT ln (\frac{P _{1}}{P _{2}})$ .

For a small pressure change, $ln (\frac{P _{1}}{P _{2}}) \approx 1 - \frac{P _{2}}{P _{1}}$ .

Thus, $m = \frac{n RT}{g h} (1 - \frac{P _{2}}{P _{1}})$ .

Stream:JEESubject:ChemistryTopic:Thermodynamics - ISubtopic:Work

⏱ 2mℹ️ Source: QB

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