First slide

Thermodynamic processes

Question

A gas has molar heat capacity $C = 24.9 J / mol K$ in the process $P^{2} T = Constant$ . Then ( $R = 8.3 J / mol K$ )

Moderate

A

Gas is monoatomic
B

Gas is diatomic
C

Gas is triatomic
D

Atomicity of gas is 4

Solution

Given
Molar heat capacity $C = 24.9 J / mol K$
$\begin{array}{l} R = 8.3 J / molK \\ As P^{2} T = constant \\ \Rightarrow P^{2} (P V) = constant \\ \Rightarrow P^{3} V = constant \\ \Rightarrow P V^{1 / 3} = constant \Rightarrow (x = 1 / 3) \\ C = \frac{f R}{2} + \frac{R}{1 - x} \\ \Rightarrow 24.9 = (\frac{f}{2} + \frac{1}{1 - x}) 8.3 \\ \Rightarrow 24.9 = (\frac{f}{2} + \frac{1}{1 - 1 / 3}) 8.3 \end{array}$
$\begin{array}{l} \Rightarrow \frac{24.9}{8.3} = \frac{f}{2} + \frac{3}{2} \\ \Rightarrow f + 3 = 6 \\ ∴ f = 3 \end{array}$
After solving we get f=3
$\Rightarrow$ So the gas is monoatomic

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