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Question

A gas expands such that its initial and final temperature are equal. Also, the process followed by the gas traces a straight line on the P-V diagram:

A
The temperature of the gas remains constant throughout
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B
The temperature of the gas first increases and then decreases
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C
The temperature of the gas first decreases and then increases
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D
The straight line has negative slope
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Solution

The correct options are
B The temperature of the gas first increases and then decreases
D The straight line has negative slope
The straight line in P-V graph P= mV + c, can have slope m>0, m=0 or m<0
For m=0, P=c increase in volume implies increase in temperature
For m>0, P and V both increase and decrease simultaneouly increase in V accompanies increase in PV which in turn means increase in T.
For m<0, applying ideal gas equation PV=nRTdP/P+dV/V=dT/TmdV/(mV+c)+dV/V=dT/TdT/dV=T(1V+c/m+1V)
m<0 c/m<0 dT/dV>0 for small V(<-c/2m) but <0 for large V(>-c/2m)
Hence temperature first increases and then decreases
So, b and d are correct options

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