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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.
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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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