Which formula relates work to pressure and volume at constant pressure?

Which formula relates work to pressure and volume at constant pressure?

• A. w = PΔV
• B. w = -PΔV
• C. ΔU = q + w
• D. ΔH = q_p

Answer: (B)

When a system changes its volume against a constant external pressure, the work is given by W = -PΔV. The negative sign is tied to the convention: work done on the system is positive, while work done by the system on the surroundings is negative. So if the gas expands (ΔV > 0), the system does work on the surroundings and W is negative; if the gas is compressed (ΔV < 0), the surroundings do work on the system and W is positive. This formula assumes the external pressure remains constant during the process and that P represents that constant pressure. This is the right relation for linking work to pressure and volume at constant pressure. The other expressions describe different thermodynamic ideas: W = PΔV would imply the opposite sign for expansion work under the usual convention; ΔU = q + w is the first law of thermodynamics (energy balance for the system), and ΔH = q_p relates enthalpy change to heat added at constant pressure, not the direct PV work.

When a system changes its volume against a constant external pressure, the work is given by W = -PΔV. The negative sign is tied to the convention: work done on the system is positive, while work done by the system on the surroundings is negative. So if the gas expands (ΔV > 0), the system does work on the surroundings and W is negative; if the gas is compressed (ΔV < 0), the surroundings do work on the system and W is positive. This formula assumes the external pressure remains constant during the process and that P represents that constant pressure.

This is the right relation for linking work to pressure and volume at constant pressure. The other expressions describe different thermodynamic ideas: W = PΔV would imply the opposite sign for expansion work under the usual convention; ΔU = q + w is the first law of thermodynamics (energy balance for the system), and ΔH = q_p relates enthalpy change to heat added at constant pressure, not the direct PV work.