Rankers Physics

Thermodynamics: Practice Problem & Solution

At a given volume and temperature, the pressure of a gas :
varies inversely as its mass
varies inversely as the square of its mass
varies directly as its mass
is independent of its mass

Solution Explained:

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

At constant volume and temperature, the ideal gas law is:

\[
PV = nRT
\]

Since \( n = \frac{\text{mass}}{\text{molar mass}} \), we can rewrite the equation as:

\[
P \propto \frac{\text{mass}}{M}
\]

Thus, for a given volume and temperature, the pressure \( P \) varies directly with the mass of the gas.

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