First slide

Different type of processes

Question

Which of the following relations does not give the equation of an adiabatic process, where terms have their usual meaning?

Easy

A

$P^{1 - γ} T^{γ} = constant$
B

$P V^{γ} = constant$
C

$T V^{γ - 1} = constant$
D

$P^{γ} T^{1 - γ} = constant$

Solution

$For an adiabatic process, P V^{γ} = constant ......(i) A c c o r d i n g t o i d e a l g a s e q u a t i o n P V = n R T \Rightarrow P = \frac{n R T}{V} P u t t i n g (i), w e g e t \frac{n R T}{V} V^{γ} = constant ∴ T V^{γ - 1} = constant A g a i n f r o m t h e i d e a l g a s e q u a t i o n P u t t i n g (i), w e g e t P {(\frac{n R T}{P})}^{γ} = constant P^{1 - γ} T^{γ} = constant$

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