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Question

The given figure shows an isochoric process, an isothermal process, an adiabatic process and two isobaric processes (one for monoatomic gas and other for diatomic) on a work done (W) versus heat supplied(Q) curve. The initial states of both gases are the same and the scales for the two axes are same.



Which of the following statements is incorrect?

A
Straight line 1 corresponds to an isochoric process.
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B
Straight line 2 corresponds to an isobaric process for diatomic gas.
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C
Straight line 4 corresponds to an isothermal process.
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D
Straight line 1 corresponds to an isothermal process.
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Solution

The correct option is D Straight line 1 corresponds to an isothermal process.

From the first law of thermodynamics
Q=W+ΔU
For an isobaric process
W=PΔV=nRΔT
Q=nCPΔT=n(f+22)RΔT
WQ=2f+2
where f is the number of degrees of freedom, (WQ) represents the slope of WQ graph.
For monatomic gas f=3 and for diatomic gas f=5.
WQ=25 (for monatomic gas)
& WQ=27 (for diatomic gas)
Hence, for both the gases, isobaric curve will be straight line passing through origin and slope represented by value of their (WQ).

For an isochoric process,
W=0,WQ=0
The straight line 1 corresponds to an isochoric process because slope of WQ is zero.

For adiabatic process Q=0, hence line 5 represents adiabatic process.

For isothermal process, ΔU=0, hence W=Q
slope=tanθ=WQ=1
The isothermal process will have a straight line with highest slope compared to other processes.
Straight line 4 corresponds to isothermal process.
Option (d) is incorrect.

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