Physical Chemistry Lesson of the Day: Pressure-Volume Work

In chemistry, a common type of work is the expansion or compression of a gas under constant pressure.  Recall from physics that pressure is defined as force applied per unit of area.

P = F \div A

P \times A = F

Consider a chemical reaction that releases a gas as its product inside a sealed cylinder with a movable piston.

 

Gax_expanding_doing_work_on_a_piston_in_a_cylinder

Image from Dpumroy via Wikimedia.

As the gas expands inside the cylinder, it pushes against the piston, and work is done by the system against the surroundings.  The atmospheric pressure on the cylinder remains constant while the cylinder expands, and the volume of the cylinder increases as a result.  The volume of the cylinder at any given point is the area of the piston times the length of the cylinder.  The change in volume is equal to the area of the piston times the distance along which the piston was pushed by the expanding gas.

w = -P \times \Delta V

w = -P \times A \times \Delta L

w = -F \times \Delta L

Note that this last line is just the definition of work under constant force in the same direction as the displacement, multiplied by the negative sign to follow the sign convention in chemistry.

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