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Question

# One mole of ideal monotonic gas is taken through process AB given by p=α−βv2 where α and β are +ve constants as shown in the P-V diagram. Which of the following are the correct statements regarding the process

A
Temp is maximum at V=α3β
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B
Temp is minimum at V=α3β
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C
Rate of increse of temp of gas with volume is maximum at A
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D
Rate of increase of temp of gas with volume in maximum at V=α3β
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Solution

## The correct options are A Temp is maximum at V=√α3β B Rate of increse of temp of gas with volume is maximum at AGiven: p=α−βv2For one mole of an ideal gas, pv=RTRT=(α−βv2)v⟹T=αv−βv3RFor extrimas, dTdv=0α−3βv2R=0⟹v=√α3βAlso, d2Tdv2=−6βvR<0Thus at v=√α3β Temp is maximum.Also as vA<vB⟹dTdv is max at A

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