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For an ideal gas the instantaneous chang...

For an ideal gas the instantaneous change in pressure 'p' with volume 'v' is given by the equation `(dp)/(dv)` =-ap If p = `p_(0)` 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)

A

`(ap_0)/(eR)`

B

Infinity

C

`0^@C`

D

`(p_0)/(a eR)`

Text Solution

Verified by Experts

The correct Answer is:
D
`(dP)/(dV)=-aP`
`overset(P)underset(P_0)(int) (dP)/(P)=- overset(v)underset(0)(int) adV implies In (P)/(P_0)=-aV`
`P=P_0e^(-aV)`
Now, `PV=RT` (as n=1)
`P+V(dP)/(dV)=R(dT)/(dV)` [for maximum T, `(dT)/(dV)=0`]
`P-aPV=0 implies V=1/a`
Thus, `T=(PV)/(R)=(P_0e^(-1))/(Ra)=(P_0)/(eRa)`.
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