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Question

An ideal gas can be expanded from an initial state to a certain volume through two different processes: (i) PV2 = constant and (ii) P=KV2, where K is a positive constant. Then:

A
Final temperature in (i) will be greater than in (ii).
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B
Final temperature in (ii) will be greater than in (i).
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C
Heat supplied in process (ii) is less than heat supplied in process (i).
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D
Heat supplied in process (ii) is greater than heat supplied in process (i).
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Solution

The correct option is D Heat supplied in process (ii) is greater than heat supplied in process (i).
Pictorial representation of the two processes is shown in the figure below.
Let the two processes be represented by AC and AB.


Given, VC=VB [final volumes same]
From the graph, we can deduce that
PC<PB
Using PV=nRT, we can say that TB>TC
TBTA>TCTA

Also, WAB>WAC
[from area under the PV graph]

So, from the 1st law of thermodynamics,
Q=ΔU+W
We can say that,
QAB=f2R ΔTAB+WAB
QAC=f2R ΔTAC+WAC
QAB>QAC
[(ΔT)AB>(ΔT)AC and WAB>WAC]

Hence, options (B) and (D) are the correct answers.

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