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A cycle followed by an engine is shown in the figure. Find heat exchanged by the engine, with the surroundings for each section of the cycle considered C_{v} = \left (\frac{3}{2} \right )R.

AB: constant volume

BC: constant pressure

CD: adiabatic

DA: constant pressure

Answers (1)

For any process

dQ=dV+dW

? known AB is isochoric

So, dw=0

dQ=dV

dQ=CvdT

Q=∫dQ=∫BACvdT

=C_{V} [T]_{A}^{B} = C_{V} (T_{B}- T_{A})

=C_{V} [\frac{P_{B}V_{B}}{R} - \frac{P_{A}V_{A}}{R}]

= \frac{3}{2}R [\frac{P_{B}V_{B} - {P_{A}V_{A}}}{R}]                               [\because V_{A} = V_{B}]

= \frac{3}{2} [{P_{B} - {P_{A}}}] V_{A}

The correct option is C \frac{3}{2}(P_{B}- P_{A}) V_{A}.

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