Question

Describe a process in which the internal energy of some system increases as a result of work done on the system by its surroundings. Be sure to identify all objects included in your system.

Answer 1

Suppouse an isolated piston-cylinder system which has a gas at a state one and then a weight is added to the piston in order to compress the gas and taking it to a state 2.

In this case the gas will be our system and the work done by it's sorroundings is that due to the weight added on top of the piston. So using the first law of thermodynamics:

$Q-W=\Delta U$

Where Q=0 because the system is isolated and no heat changes occur with the surroundings.

The work caused by the added weight can be written as: $W=\int_{1}^{2}PdV$ and assuming constant pressure

$P_1=P_2=P$ work will be $W=P(V_2-V_1)$ so

$-P(V_2-V_1)=\Delta U$

$P(V_1-V_2)=\Delta U$

If volume 1 is bigger than volume 2 the change of internal energy is positive so the internal energy increases as a result of work done on the system by its surroundings.