Integrating Factor of Quasi-Static Displacement Work

Integrating factor is a mathematical tool used in solving differential equations. For quasi-static displacement work, the integrating factor is given by:

1/P, where P is the pressure

Explanation:

Quasi-static processes are processes that occur very slowly, allowing the system to remain in thermal equilibrium throughout the process. These processes are usually reversible and can be analyzed using thermodynamics.

Displacement work is the work done by a system when it changes its volume. In quasi-static processes, the pressure remains constant, and the work done can be calculated using the formula:

W = PΔV

Where W is the work done, P is the pressure, and ΔV is the change in volume.

To solve the differential equation for quasi-static displacement work, we need to multiply both sides of the equation by an integrating factor. The integrating factor is a function that makes the equation easier to solve.

In this case, the differential equation is:

dW = PdV

To solve this equation, we need to multiply both sides by an integrating factor, which is given by:

1/P

Multiplying both sides by 1/P, we get:

dW/P = dV

Integrating both sides, we get:

W/P = V + C

Where C is the constant of integration.

Therefore, the integrating factor of quasi-static displacement work is 1/P.