>>11730143Hi OP, I'm glad you ask these questions, I think most thermodynamics courses aren't very clear with what everything mens, but with a lot of thought it does all make sense. To answer:
1. The heat capacity depends on the path between the initial and final state. Most commonly the heat capacity at constant volume is what is calculated, sometimes also the heat capacity at constant pressure. For an adiabatic process you would be considering the heat capacity at constant entropy and this would in fact be 0. Since it's sort of trivial you don't usually talk about heat capacity at constant entropy.
2. In an adiabatic process, the heat is 0. Heat is a type of transfer of energy from one system to another (the other being work) so Q=0 means there is no transfer of heat energy. If Q=0 and W=0 then the change in internal energy is zero.
3. It doesn't make sense to say the heat increases or decreases after compressing a gas - heat is not a state function so a value of heat cannot be assigned to equilibrium states. Change of heat only makes sense if you mean a change in the rate of heat transfer while the system is not in equilibrium (but this is irrelevant to equilibrium thermodynamics). In this process, you do work W on the gas which increases it's internal energy, and you may or may not transfer heat to the gas as well depending on the manner in which you compress it (e.g. adiabatically, isothermally, etc). But it is the internal energy which will increase or decrease during a process; the work and heat are simply the quantities which determine what this change is.
