First slide

Thermodynamic processes

Question

The ratio of the slopes of P-V graphs of adiabatic and isothermal process is(in terms of specific heat ratio $γ$ )

Moderate

A

$γ$
B

$1 + γ$
C

$\frac{1}{γ}$
D

$1 - γ$

Solution

In isothermal process ${(\frac{dP}{dV})}_{Isotherm} = \frac{-P}{V} ---(1)$
In adiabatic process ${(\frac{dP}{dV})}_{Adiabatic} = \frac{-γP}{V} ---(2)$
From equation (2) divided by equation(1 )
$\Rightarrow R a t i o = \frac{s l o p e o f a d i a b a t i c p r o c e s s}{s l o p e o f i s o t h e r m a l p r o c e s s} \Rightarrow R a t i o = \frac{\frac{- γ P}{V}}{\frac{- P}{V}} \Rightarrow R a t i o = γ$

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