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Question

If a gas is taken from A to C through B, then heat absorbed by the gas is 8 J. Heat absorbed by the gas in taking it directly from A to C is


A
+8 J
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B
+9 J
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C
+5 J
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D
+7 J
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Solution

The correct option is B +9 J
When the gas is taken through process ABC,
Work done is during the process is given by
W=WAB+WBC
But, WBC=0 [isochoric process]
Thus,
W=PΔV=10×[400200]×[103×106]=2 J
According to first law of thermodynamics,
Heat absorbed ΔQ=ΔU+W
From the data given in the question,
8=ΔU+W
8=ΔU+2
ΔU=6 J
Here initial state is A and final state is C
Thus ΔU=UCUA=+6 J .....(1)

Now, when directly taken from A to C, by applying first law of thermodynamics, we get
ΔQ=W+ΔU
Using(1),
ΔQ=W+6 ......(2)
Here W is area under process AC.
So, W=(12[(20+10)×103][(400200)×106])
W=+3 J
Substituting this in (2) we get,
ΔQ=6+3=+9 J
Thus, option (b) is the correct answer.

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