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Question
An ideal gas (Cp / Cv = γ) is taken through a process in which the pressure and the volume vary as p = aVb. Find the value of b for which the specific heat capacity in the process is zero.
Solution
As the process has specific heat capacity zero, the process is essentially an adiabatic process.
For an adiabatic process
PVγ = c
`=> "P" = "c"/("V"^gamma) = "c""V"^-gamma`
Comparing with eqn.
P =aVb
⇒ a=c
⇒ b = -γ
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