Show that pressure times volume is equal to work.
Answers
Pressure times change in volume is equal to work as can be shown from the explanation and example below.
1) Let us consider a sample of gas being trapped in a cylinder with a piston on it. The force applied by the gas equals the force from outside the piston here. Volume is constant in this case.
2) Again, when we apply pressure on the piston there is change in volume and the pressure (P) of the gas exerted on the piston equals the force (F) exerted by the gas on the piston divided by the surface area (A) of the piston.
P= F/A
3) Therefore, force (F) is equal to the pressure (P) exerted on the piston times the surface area (A) of the piston.
F= P x A
4) Also we know that work done (W) is equal to the force exerted on the piston (F) times the distance (D) the piston is moved.
W= F x D
Substituting the value of F on the above equation results in the equation
W = (P x A) x D
Now, A x D equals change in volume.
Therefore, W = P x Δ V
So, Work is equal to pressure times change in volume.