The equation PV = constant describes which thermodynamic process?

The equation PV = constant describes which thermodynamic process?

• A. Isothermal process
• B. Adiabatic
• C. Isobaric
• D. Isochoric

Answer: (A)

The key idea is constant temperature. For an ideal gas, PV = nRT, so if the amount of gas and the gas constant are fixed, keeping PV constant means T must stay the same as the gas expands or is compressed. That is exactly what an isothermal process is: temperature remains constant while pressure and volume trade off so that their product doesn’t change. The other process types involve different relationships: in an adiabatic process, no heat is exchanged and PV^gamma remains constant; in an isobaric process the pressure stays the same while volume changes, so PV changes; in an isochoric process the volume stays the same while pressure (and temperature) can change, so PV does not stay constant.

The key idea is constant temperature. For an ideal gas, PV = nRT, so if the amount of gas and the gas constant are fixed, keeping PV constant means T must stay the same as the gas expands or is compressed. That is exactly what an isothermal process is: temperature remains constant while pressure and volume trade off so that their product doesn’t change.

The other process types involve different relationships: in an adiabatic process, no heat is exchanged and PV^gamma remains constant; in an isobaric process the pressure stays the same while volume changes, so PV changes; in an isochoric process the volume stays the same while pressure (and temperature) can change, so PV does not stay constant.