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# Work from expansion

How a system can do work by expanding. Created by Sal Khan.

## Want to join the conversation?

• In these types of problems, you'll hear the term adiabatic used. What is an adiabatic process and how do you know if the system is adiabatic?
• adiabatic process is a process where no transfer of heat is exchanged with the outside the system is isolated, you will know if the problem tells you,
• while piston moving upwards by removing small weight over the piston, there is change in volume and pressure also. but why the change in pressure is not considered
• Remember, we are talking about very small changes here. In order to be a 'quasi-static' process all changes are small and slow. Therefore the change in pressure is 'infinitesimal'.
• When Volume increases, pressure must decrease, that was in the first lesson on thermodynamics.

P1 x V1 = P2 x V2 (assuming there was no exchange of energy from outside).
Here Volume increases by very small number and Pressure decreases also by very small number as seen in the pictures by Sal.

Here we are assuming (as I have read some comments below), that changes in pressure are so infinitesimally small in quasistatic process that we can take pressure initial to the equation. But hey, I'm very confused now, because it seems illogical to me that volume isn't infinitesimly small also. Either both of them change or none of them changes(in my opinion).

Please, is there any logical explanation?? Otherwise I can't accept this equation, for me this is Work = (change in Pressure)x(change in Volume) .

But if Pressure x Volume haven't change has Internal Energy risen?

Thank you for your kindness and please explain this to me :-)
• Why change in volume is not infinitesimal but change in pressure is ?
• That's a good question. I do think that here the changes in pressure and volume are (or should be) both considered infinitesimal since they are taking place in a quasistatic process if I'm not wrong.
• why do the molecules produce pressure when they bump into a surface
• Take your hand and tap against a door that can swing, did it move? No? Tap it harder, did it move? Yes? Well you exerted pressure by your kinetic energy.

Now tape it a few billion times per second and you have the pressure caused by molecules.
• Is PV work the only kind of work a system can do?
• It's the only type of work that a system such as this (piston-cylinder) can achieve. There are many different forms of Work, such as electrical work (dW=Current*Voltage*dt), rotational work (dW=Torque*Angular Acceleration*dt), and many other situations. Basically, anything that has Power (noted as W_dot, which means P=dW/dt) contains the capacity to do work and must be able to do work over time by it's definition.
• why are heat and work not state functions?
• Because work and heat are concepts that deal with the "transfer" of energy. It is not a property of the macro-states. You cannot say "the work inside this system is..." or "the heat inside this system is...". Rather you may state "the work done by the system unto this object is...and the head added to the system is...". So pretty much work and heat are not properties rather the change in properties.
• At when Sal defines the pressure and force, why does he assume that the force applied on the ceiling of the piston is constant? As the volume increases by the force pushing the ceiling a distance "x", shouldn't the pressure decrease? If the pressure decreases in this process, why doesn't the force also decrease?
• Because x is assumed to be a very small number. And over a very small displacement the pressure is assumed to be as good as constant.
The math of that is explained in the videos on finding the area under a curve in the calculus section (Riemann sums and definite integration)
• The pressure of the air in the system changes. Which value of pressure should I use and why?