First slide

Different type of processes

Question

The relation between P and T for monoatomic gas during adiabatic process is $P \propto {T^C}$ . The value of C is

Easy

A

5/2
B

2/5
C

5/3
D

3/5

Solution

$P \propto {T^c} \Rightarrow P = K{T^c} \Rightarrow P{T^{ - c}} = K \to (1)$
${P^{1 - \gamma }}{T^\gamma } = K \Rightarrow P{T^{\frac{\gamma }{{1 - \gamma }}}} = K \to (2)$
comparing (1) & (2) $\frac{\gamma }{{1 - \gamma }} = - c$
$\frac{{5/3}}{{1 - 5/3}} = - c$ [for monoatomic gas γ = 5/3]
$\therefore c = \frac{5}{2}$

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