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An ideal gas (Cp // CV = (gamma) is take...

An ideal gas `(C_p // C_V = (gamma)` is taken through a process in which the pressure and the volume vary as `P = aV^b`. Find the values of (b) for which the specific heat capacity of the gas for the process is zero.

Text Solution

Verified by Experts

Given that `P = a V^(b)`
or `PV^(-b) = a`
Comparing with `PV^(r )` = constant, we have
`r = -b`
We know that `C = C_(v) - (R )/(r - 1)`
Here `C = 0 = C_(V) - (R )/(gamma - 1)`
`:. O = (R )/(gamma - 1) - (R )/(- b - 1)`
or `b = - gamma`
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