Different Versions of the Work Equation

[Dahlia Kirov 3A]

Hey!

Would someone mind explaining where these different variants to the work equation come/are derived from? I think the terms relate to the ideal gas law, but I'm not sure how to go from the gas law to here.

w = -PΔV

w = -ΔnRT

[Abhay Mahajan 3D]

Hey!

Would someone mind explaining where these different variants to the work equation come/are derived from? I think the terms relate to the ideal gas law, but I'm not sure how to go from the gas law to here.

w = -PΔV

w = -ΔnRT

Work is the energy required to move an object a certain distance (Force * Distance). In the case where we are talking about ideal gases, you can think about the force as the pressure applied over a certain area (like my hand pushing down on a piston to compress a container of gas —> pressure of hand * surface area of piston pushing down).

This leads to the equation w= Pressure * Area* Distance ( as opposed to simply Force * Distance from before). You may realize that, the area x distance = change of volume (area of base of object * distance or change in length of the object).

This link has a good visualization of the volume change: https://qph.cf2.quoracdn.net/main-qimg- ... a4fbfd0-lq

This means that work= Pressure * change in volume , and since that change in volume is negative due to the container being compressed, it becomes w= -PΔV.

using the ideal gas equation: PV=nRT, we may be told that the pressure is held constant, which in that case, P, R, and T, will be constants. That means that when V changes, n changes as well (directly proportional). This means that w=-P ΔV can also be written as w=-ΔnRT because: P ΔV = Δn*RT