Which equation relates pressure, volume, and temperature for a fixed amount of gas when conditions can change, i.e., the combined gas law?

Which equation relates pressure, volume, and temperature for a fixed amount of gas when conditions can change, i.e., the combined gas law?

• A. PV = nRT
• B. P = nRT/V
• C. P1V1/T1 = P2V2/T2
• D. P1V1 = P2V2

Answer: (C)

For a fixed amount of gas, pressure, volume, and temperature are all linked as the gas changes state. The two-state form P1V1/T1 = P2V2/T2 captures this relationship by comparing an initial state to a final state while the amount of gas remains the same. It comes from the ideal gas law PV = nRT with n constant, so PV/T is constant between states. The other forms are single-state relations or apply only when temperature or volume is held constant. PV = nRT or P = nRT/V describe pressure, volume, and temperature at one state, not how they change from one state to another. Boyle’s law (P1V1 = P2V2) assumes temperature is constant, which isn’t the general changing-condition case described here.

For a fixed amount of gas, pressure, volume, and temperature are all linked as the gas changes state. The two-state form P1V1/T1 = P2V2/T2 captures this relationship by comparing an initial state to a final state while the amount of gas remains the same. It comes from the ideal gas law PV = nRT with n constant, so PV/T is constant between states.

The other forms are single-state relations or apply only when temperature or volume is held constant. PV = nRT or P = nRT/V describe pressure, volume, and temperature at one state, not how they change from one state to another. Boyle’s law (P1V1 = P2V2) assumes temperature is constant, which isn’t the general changing-condition case described here.