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Thermodynamic Processes

An ideal gas ...

Question

An ideal gas is taken from state 1 to state 2 through optional path A, B , C & D as shown in P-V diagram. Let Q, W and U represent the heat supplied, work done & internal energy of the gas respectively. Then

A

Q_{B} - W_{B} > Q_{C} - W_{C}

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B

Q_{A} - Q_{D} = W_{A} - W_{D}

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C

W_{A} < W_{B} < W_{C} < W_{D}

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D

Q_{A} > Q_{B} > Q_{C} > Q_{D}

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Solution

The correct options are
B $Q_{A} - Q_{D} = W_{A} - W_{D}$
D $Q_{A} > Q_{B} > Q_{C} > Q_{D}$
Work done is equal to the area under the P-V curve.
From the graph, area under path A is the largest whereas under path c is the smallest.
Thus $W_{A} > W_{B} > W_{C} > W_{D}$ ............(1)
From Ist law of thermodynamics, $Q = Δ U + W$ ........(2)
As $Δ U$ is a state function, thus $Δ U$ is same for all paths.
From (1) & (2), $Q_{A} > Q_{B} > Q_{C} > Q_{D}$
Also for path A and D, $Q_{A} = Δ U + W_{A}$ and $Q_{D} = Δ U + W_{D}$
Subtracting these two, $⟹ Q_{A} - Q_{D} = W_{A} - W_{D}$
Similarly, $Q_{B} - W_{B} = Q_{C} - W_{C}$

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