## Laws of Thermodynamics

### Zeroth Law of Thermodynamics

Any two objects in equilibrium have the same temperature.

### First Law of Thermodynamics

The First Law is a restatement of the Principle of Conservation of Energy, written in terms of energy appropriate to thermodynamics, that is heat and thermal (or internal) energy. It can be best illustrated using the example of a balloon. If heat is added to the air inside a balloon then
• The air inside the balloon expands. To do so it has to push away the air surrounding the balloon, and this takes work.
• The temperature of the air inside the balloon increases. Since the temperature is a measure of the average kinetic energy of the molecules, a rise in temperature means an increase in the average, and hence total, kinetic energy of the molecules. This total kinetic energy is called the thermal or internal energy
• Both of these occur
Conservation of energy requires that the heat transferred to the balloon plus the energy that is added by doing work on the balloon must equal the rise in its internal energy

 Q = DU + W

#### Sign convention in the first law

In the equation above any one of the three quantities can be either positive or negative. In all three cases the signs are important

 positive negative Heat (Q) heat is being added heat is being extracted Work (W) work is done by the system (in our example the balloon expands ) work is done on (or against) the system (in our example the balloon is made to contract) Change in internal energy (DU) The temperature rises or Change of phase by melting or evaporating The temperature falls or Change of phase by freezing or condensing

#### Calculations using the first law

• If 60 J of heat is added, and 40 J of work is done to expand the gas, what is the change in internal energy?
• DU = Q + W = 60 J + (-40 J) = 20 J
• since the change in internal energy is positive the temperature must have risen.

### Second Law of Thermodynamics

There is more than one way of stating the second law. All are equivalent, in that one statement can be used to derive the others.
1. Heat, by itself will always flow from a region of high temperature to one of lower temperature
2. No heat engine can convert heat into work with 100 % efficiency
3. No refrigerator can be made to move heat from one region to one of higher temperature without the input of work (from some external energy source such as the electrical system of your house.)
4. For an isolated system, the entropy will always tend to increase.

#### Second Law of Thermodynamics - first statement

Heat, by itself will always flow from a region of high temperature to one of lower temperature. As an example, consider a hot cup of coffee left on the kitchen table. Since the water in the cup and the air in the kitchen are at different temperatures there will be an exchange of heat between them. The first law of thermodynamics only requires that the heat moved from one is the same as the heat added to the other. It is satisfied if heat passes from the water to the air or if heat passes from the air to the water. However, experience tells us that the coffee always cools down, it never gets hotter. The second law tells is the direction of heat flow, it must pass from the hot water to the cooler air.
Conversely if a glass of iced water is left on the kitchen table then the air is now warmer than the water, and so the heat will now flow from the air to the water. As experience tells us, the ice will melt, and the water temperature rises.

#### Second Law of Thermodynamics - second statement

No heat engine can convert heat into work with 100 % efficiency. By definition, heat engines convert heat into work (see the first law) without changing the internal energy. The second law states that not all of the heat can be converted to work, some must be exhausted from the heat engine as waste heat.

#### Second Law of Thermodynamics - third statement

No refrigerator can be made to move heat from one region to one of higher temperature without the input of work. The first statement prohibits heat moving from one region to a hotter region by itself. However there is no such restriction on heat being made to move from one region to a hotter region. Any device which accomplishes this is known as a refrigerator. This third statement of the second law states that any such refrigerator must have an external source of energy to make it work. Unplug your kitchen refrigerator and the food stored inside it will start to warm up to the kitchen temperature.

#### Second Law of Thermodynamics - fourth statement

For an isolated system, the entropy will always tend to increase. The really important phrase here is the first one. An isolated system is one which does not interact at all with its surroundings. There is no heat exchange with any other system, nor is there any means of doing work.
Entropy is a mathematical concept which can be most accurately translated as disorder in everyday language. For example, in your living room to place all of the air molecules into one half of the room would require a lot of organization. It is much more likely that the molecules are uniformly distributed, half of them in one half of the room, and half in the other half of the room. That is the condition which corresponds to the maximum entropy, and that is the situation which actually exists.

### Third Law of Thermodynamics

There is a lowest possible temperate, absolute zero. The question is "Can we ever reach it?" The third law of thermodynamics answers this question - no. In order to cool anything down we need a refrigerator. As the temperature gets colder and colder the ability of the refrigerator to cool further, its efficiency if you like, is steadily reduced, eventually becoming zero. You can potential cool as close to absolute zero as you like, but you can never reach it. You can never remove that last little bit of heat.