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

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Detailed 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) and (2)

$\frac{\gamma }{{1 - \gamma }} = - c$

For monoatomic gas $γ = \frac{5}{3}$

$\frac{{5/3}}{{1 - 5/3}} = - c$

$\therefore c = \frac{5}{2}$

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