Rankers Physics

Thermal Physics: Practice Problem & Solution

In an adiabatic change, the pressure and temperature of a monoatomic gas are related as $P \propto T^C$ where $C$ equals: (1994)
$\frac{3}{5}$
$\frac{5}{3}$
$\frac{2}{5}$
$\frac{5}{2}$

Solution Explained:

To solve this problem, we apply the core principles of Thermal Physics. Understanding the underlying formula is key to arriving at the correct answer below:

From $P^{1-\gamma} T^\gamma = \text{constant}$, we get $P \propto T^{\frac{\gamma}{\gamma-1}}$. For a monoatomic gas, $\gamma = 5/3$, so $C = \frac{5/3}{5/3 - 1} = \frac{5}{2}$.

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