The equation notes a change in Energy as work is done from heat in a system
However, I am a bit confused with this equation...
Because you are subtracting the energy for work from the amount of heat, the deltaE that is calculated seems to be just Left over Energy
I don't really seem to understand how this equation figures a change in energy. If anything the energy for the work itself is the actual change in energy and the deltaE you get is just Energy left over
Am I wrong in this? What am I overlooking?
Internal energy, which I'm going to call U (you called it E, but I'm trying to make a point here that we're really talking about a more precise quantity called "internal energy" rather than just a nebulous "energy"), represents the total energy of a system at any time as a result of kinetic and potential energy on a molecular scale. In other words, if my system is a balloon of air and I move the balloon from the floor to the ceiling, the internal energy of the system hasn't changed because gravitational potential energy is a macroscopic, not microscopic (molecular) phenomena.
There are two ways, and only two ways, to transfer energy to/from a system. They are heat (q) and work (W). So, from conservation of energy (the first law of thermodynamics), you can write deltaU = q + W
q is positive when heat is absorbed into the system (when the system gains energy)
W is positive when work is done on the system (when the system gains energy)
If we add the stipulation that pressure is constant, we can say that W = P delta V. Now, let's combine this into the conservation of energy equation we have above:
deltaU = q + P(deltaV)
But there's a problem here. If our system consists of gas, and it is compressed, delta V is negative. This would make the second term above, which represents work, negative. But we know that when we compress a gas, an external force is doing work on the gas. Work is being done on the system (our gas), yet the equation we have results in saying that negative work happened. This is inconsistent with the sign convention I defined above, where work on a system is positive.
To fix this problem, we rewrite the equation with a sign change:
deltaU = q - P(deltaV) (general eqn for change of internal energy of the
system with
const P)
Other than the fact that what I called U, you called E, this is the equation you have. You are interpreting the negative sign there as meaning that the difference between those two quantities represents some physically meaningful "left over energy" when that is not the case. Hopefully the way I explained this will make it clear that the only reason that negative sign is there is to keep the convention for what is called positive and negative work consistent.
