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Mechanical Properties Of Fluids

Question
CBSEENPH11019763

An ideal gas is taken through straight A rightwards arrow straight B rightwards arrow straight C rightwards arrow straight A as shown in figure. Find the work done by gas in the process straight C rightwards arrow straight A. What is the net heat absorbed by the gas in cyclic process?

Solution
The magnitude of area under CA curve on PV diagram is, 
Area = Area of trapezium ACcaA 
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In the process straight C rightwards arrow straight A comma the gas gets compressed.
Therefore, work done by gas is negative.
Thus,
                 straight W subscript straight C rightwards arrow straight A end subscript space equals space minus 5.5 straight J 
Now by the first law of thermodynamics for cyclic process, 
       dQ subscript cyclic space equals space dW subscript cyclic 
rightwards double arrow   dQ subscript cyclic space equals space dW subscript straight A rightwards arrow straight B end subscript plus dW subscript straight B rightwards arrow straight C end subscript plus dW subscript straight C rightwards arrow straight A end subscript 
                   = Area of rectangle AbcaA + 0 + (-5.5)
                   = 10(2 - 1) -5.5  = 4.5J 
Thus the heat absorbed by gas in the cyclic process is 4.5J.