State Variables of a Perfect (Ideal) Gas — Which Variables Govern Its Physical Properties? Identify the set of variables that control the thermodynamic state and physical properties of a perfect (ideal) gas in equilibrium.

Introduction / Context:
State description for a simple compressible substance (such as an ideal gas) requires identifying independent variables that uniquely fix the state. For ideal gases, the classic triad is pressure, volume, and temperature.

Given Data / Assumptions:

• Simple, single-phase ideal gas.
• Equilibrium (no significant gradients).
• Fixed composition (molar mass constant).

Concept / Approach:
The ideal-gas equation p * V = m * R * T relates pressure p, volume V, and temperature T for a fixed mass m and gas constant R. Any two independent variables determine the third. Together, they govern density, specific volume, internal energy (through T), and other derived properties.

Step-by-Step Solution:
Recognize the equation of state: p * V = m * R * T.For fixed m and R, two independent variables among p, V, T determine the state.Hence, the full set p, V, and T control the gas’s physical state and properties.

Verification / Alternative check:
Experimental P–V–T surfaces for gases confirm that specifying two variables (e.g., p and T) fixes specific volume v via v = R * T / p.

Why Other Options Are Wrong:
Each of A, B, or C alone is incomplete; all three together constitute the governing variables.

Common Pitfalls:
Using Celsius rather than Kelvin for ideal-gas calculations; forgetting composition must be fixed for R to be constant.

Final Answer:
all of these