A piston-cylinder device is used to compress a gas by pushing the piston with an external force.

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A piston-cylinder device is used to compress a gas by pushing the piston with an external force. During the compression process, heat is transferred out of the gas in such a manner that the stored energy in the gas remains unchanged. Also, the pressure is found to be inversely proportional to the volume of the gas.
(a) Determine an expression for the heat transfer rate in terms of the instantaneous volume and the rate of change of pressure of the gas.
(b) At a given instant, when the gas occupies a volume of 0.1 m3, the rate of change of pressure is found to be 1 kPa/s. Determine the rate of heat transfer.
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