An inventor wishes to build an engine that runs off to the ambient heat of the a

Question

An inventor wishes to build an engine that runs off to the ambient heat of the atmosphere and produces energy. An ideal monoatomic gas is contained in a cylinder. First, the gas is adiabatically (or quickly) expanded by increasing the volume by a factor of 4, which decrases the temperature. Then the gas is allowed to come to thermal equilibrium with the environment, absorbing heat energy. Finally, the gas is compressed back to the original state isothermally (slowly). Will this engine produce enery? Argue your assertion. If you don't think this would produce useful work, what changs in the cycle would have to be made to produce work?

Explanation / Answer

(delta)U = Q + W (internal energy= heat absorbed + work done)

This won't produce useful work because

1st Step is adiabatic ie no heat is exchanged. But work is done W= P * (V2- V1) ----------- (V2= 4 V1 )

W= P * 3V1 = 3P * V1

2nd Step Heat energy is absorbed ie Q= something W=0

3rd Isothermal Compression To original state ie same P and V1 so work done W= -3P * V1 (negative of the original work done)

Finally from 3 steps work done =0 but heat is absorbed by the gas.

To PRODUCE WORK the 3rd step must be Adiabatic ie not heat transfer. Adiabatic Compression.

This won't allow heat to be escaped and work will be done by the gas to get decompressed thus helping the engine to produce work.

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