First slide

Different type of processes

Question

In an adiabatic process, R = $\frac{2}{3} C_{v}$ ,. The pressure of the gas will be proportional to:

Moderate

A

$T^{\frac{5}{3}}$
B

$T^{\frac{5}{2}}$
C

$T^{\frac{5}{4}}$
D

$T^{\frac{5}{6}}$

Solution

$R = \frac{2}{3} C_{v}$
We know, $C_{p} - C_{v} = R$
or $γ - 1 = \frac{R}{C_{v}} or R = Cv (γ - 1)$
Comparing $γ = \frac{5}{3}$
$P^{1 - γ} T^{γ} = constant = K$
or $P \propto T^{γ (γ - 1)}, Given γ = \frac{5}{3}$
$\frac{γ}{(γ - 1)} = \frac{5}{2}$
So, $P \propto T^{\frac{5}{2}}$

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