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.
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Apressure exerted by the gas
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Bvolume occupied by the gas
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Ctemperature of the gas
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Dall of these
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E—
Answer
Correct Answer: all of these
Explanation
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