Q.

For an ideal gas the instantaneous change in pressure ‘p’ with volume ‘v’ is given by the equation dpdv=ap. If p=p0 at v=0 is the given boundary condition, then the maximum temperature one mole of gas can attain is (Here R is the gas constant).

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a

ap0e  R

b

p0a  e  R

c

0

d

infinity

answer is A.

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Detailed Solution

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Given dpdv=ap

Intergrating both sides we get      P0PdpP=a0vdvln(PP0)=avp=P0eav

Using ideal gas equation pv=nRT

T=pvnR=P0veavR(n=1)

dTdv=0P0R(eav+veav(a))P0veavR{1av}=0v=1a

  Tmax=P0Rae.

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For an ideal gas the instantaneous change in pressure ‘p’ with volume ‘v’ is given by the equation dpdv=−ap. If p=p0 at v=0 is the given boundary condition, then the maximum temperature one mole of gas can attain is (Here R is the gas constant).