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For an ideal gas the equation of a proce...

For an ideal gas the equation of a process for which the heat capacity of the gas varies with temperatue as `C=(alpha//T(alpha)` is a constant) is given by

A

`VlnT=constant`

B

`VT^(1//(gamma-1))_(e)^(alpha//RT)`=constant

C

`V^(1)/(gamma-1)T^(alpha//RT)`=constant

D

`V^(gamma-1)T`=constant

Text Solution

Verified by Experts

The correct Answer is:
B
`DeltaQ=dU+PdV`
`rArr(alpha)/(T)dT=C_(V)dT+PdV rArr(alpha)/(T)dT=C_(V)dT+(RT)/(V)dV`
`alpha(dT)/(T)=(R )/(gamma-1)dT+RT(dV)/(V)`
`rArr(alpha)/(R )(dT)/(T_(2)=(1)/(gamma-1a)(dT)/(t)+(dV)/(V)`
On integrating and soliving
`VT^(1//(gamma-1)_(e)^(alpha//(RT)`=constant
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