When is this equation used?
Functions involving work totally throw me off.
Also, What rules apply to the question of whether or not work is done by a system?
i think its better to understand this in terms of balancing units. of course, it sounds ridiculous because all the units are the same. however, the basic thing to remember is that it takes energy to do work. you raise a dumb bell, you did work, but you got the energy from ATP. 1 mol of ATP yields something like ~30 kJ energy? raising a 1 kg dumbell 1 meter requires 1m*1kg*10 m/s^2 of energy, 10J. assuming 50%, or even 100% efficiency of ATP, how many moles are needed to raise the dumb bell?
on the flip side, a gas expands, doing work on the surroundings. where did that energy come from? from the internal energy of the gas (kinetic energy aka temperature). if some internal energy was used to do work on the enviroment, then the internal energy of the gas is now lower. hence, when a balloon or piston expands against constant external pressure, its temperature will be lower afterwards. you can also flip it, and see what happens when the surroundings do work on a gas. the gas increases in internal energy/temperature.
then you have adiabatic expansion, in which there is no heat exchange, so dE=W. then there is reversible and irreversible expansions to consider and what not. isovolumetric, isobaric, isothermal expansion/compression. you can look up all of these, the corresponding changes in entropy, dU, work done, etc. however, the main thing to keep in mind is that it takes energy to do work, and you can transform work into energy (rather heat into work into energy as is the case in steam driven turbines in power plants). heat is just a form of energy, so is work. you can use one to do the other.
