GATE ME 2024 Set 1 — Question 46
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Thermodynamics → Laws & Properties → Ideal & Real Gas Behaviour
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Question
A piston-cylinder arrangement shown in the figure has a stop located above the base. The cylinder initially contains air at and and the piston is resting in equilibrium at a position which is above the stops. The system is now cooled to the ambient temperature of . Consider air to be an ideal gas with a value of gas constant .The absolute value of specific work done during the process is________ (rounded off to decimal place)
Correct answer
58 to 61
Solution
1.Initial State (1):
- Pressure
- Temperature
- Height of piston
- The piston is in equilibrium, so as long as it moves freely, the pressure remains constant at .
- The piston will move down as the air is cooled until it hits the stops at .
- Using the ideal gas law for a constant pressure process:
- The final temperature is .
- Since , the piston will rest on the stops, and the volume remains constant from state 2 to state 3.
- Specific work from 1 to 2 (constant pressure):
- Specific work from 2 to 3 (constant volume):
- Total specific work
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