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An ideal gas has adiabatic exponent gamm...

An ideal gas has adiabatic exponent `gamma`. It expands according to the law `P = alpha`V, where is `alpha` constant. For this process, the Bulk modulus of the gas is

A

Molar heat capacity of gas in the process is `(R(gamma+1))/(2(gamma-1))`

B

Work done by the gas is `15V_(o)^(2)(alpha)/2`

C

Change in internal energy of gas is `15V_(o)^(2)(alpha)/2`

D

Both `B` and `C` are correct

Text Solution

Verified by Experts

The correct Answer is:
A, B
A. `P=alphaV`
`PV^(-1)=alpha`
We know for polytropic process
`PV^(x)=` constant
`:.x=-1`
We know `C=C_(v)-R/(x-1)`
`C=C_(v)+R/2`
`C=R/(gamma-1)+R/2`
`C=(R(gamma+1))/(2(gamma-1))`
B. `dW=-PdV`
`dW=-alpha VdV`
On integrating above equation. ltbgt `W=-alpha[((4V_(o))^(2))/2-(V_(o)^(2))/2]`
`W=-(alpha)/2[16V_(o)^(2)-V_(0)^(2)]`
`W=-15V_(o)^(2) (alpha)/2`
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