For ideal gases, temperature is the average kinetic energy of the molecules. We measure temperature with a thermometer. A thermometer is an object that expands as it gets hot. We have to say this, as every quantity in physics must be defined in terms of what we have to do to measure it.

 

Heat is energy that flows from a hot object (high temperature) to a cool object (low temperature).

 

The very confusing thing about heat is that it is not a state quantity. A state quantity is something that describes the system the way it is, but does not depend on how the system got there. For example, temperature and pressure are state quantities. The temperature does not depend on if it was hot and cooled down or cold and heated. The temperature is whatever is measured with the thermometer. The internal energy, which is the sum of the energies of all the molecules, is a state vector.

 

Heat is not a state vector. Say we heat a gas by adding Q1 joules, and then the gas expanded and did work. This is how a steam engine works. Then we cool the gas, causing the system to lose Q2 joules. Q1= Work + Q2. This shows that the heat lost is less than the heat initially added. This means that it makes a difference whether we measure the heat before it did work or after, and so it cannot be a state vector.

 

Since this is so very confusing, I am going to repeat it. If we measure the heat before the gas does work, we get Q1 joules. If we measure the heat after it did work, i.e., the heat lost, we get Q2 joules. Heat does not describe the system.

 

We like to feel that adding heat changes something, and we would like to find a state quantity that is changed by adding heat. It can be shown that if we add ΔQ joules at a constant temperature T, the quantity ΔQ/T is a state vector. After the gas did work, although the heat lost is less than the heat gained, the temperature was also smaller. We define entropy as

 

ΔS = ΔQ/T

 

The units of entropy are joules/°. The entropy is the same before the gas did work and after. It describes the state of the gas.

 

The next very confusing thing is what does entropy describe. 

 

SEE THE BOOK FOR MORE DETAILS.