Law of Conservation of Energy

In thermochemistry we decide on the boundaries of the problem.  In other words, we define the system.  We could define a system as only a piston, as the engine, the car, the car in the garage or the entire universe.  Obviously, the smaller the system, the easier the problem will be.  Anything not IN the system is considered surroundings. If energy is lost to a system (exothermic), that means that the surroundings have gained the energy (endothermic).

There are 3 basic types of systems:

• open systems allow for the exchange of both matter and energy
• closed systems allow energy to move but not matter
• isolated systems cannot exchange matter nor energy with their surroundings

Now the Law of Conservation of Energy makes more sense- 

The amount of energy in the universe is constant, 

therefore energy is neither created nor destroyed, just converted.  

That means that energy could be lost to a system, BUT it will be gained by the surroundings.  Energy can also convert from one type to another.  For instance mechanical energy could be converted into heat energy through friction.

We use the term internal energy to mean the total amount of energy in a system- kinetic, potential, heat, work, ...  Although we can't calculate the exact amount of internal energy, it is possible to determine the CHANGE in internal energy or ∆E.  

In science we always calculate a change (∆) by subtracting the FINAL - INITIAL values. We must define the way we subtract because it will determine the sign of the value.  The the final value is larger than the initial value, the change will be positive- for Energy that means ∆E>0 or endothermic.  If the final value is smaller than the initial value, the change will be negative- ∆E<0 or exothermic.

The change in internal energy to a system is the sum of the the heat (q) added to the system and the work (w) done on a system.  

∆E = q + w

While the math is very simple, the problem is interpreting the signs of the values of heat and work.  Refer to the chart for hints.  Remember compressed or decreased volume is positive (work done ON the system), expand or increase volume is negative (work done BY the system).