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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 JWhen 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×[400−200]×[103×10−6]=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=UC−UA=+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][(400−200)×10−6]) ⇒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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