We say that the water has potential energy by virtue of its elevation above the ground and that this potential energy is converted to kinetic energy as the water gathers speed in its descent. Both potential and kinetic energies are forms of mechanical energy. So in this example — known as hydroelectricity — the mechanical energy of the water is converted to mechanical energy of the rotating dynamo which in turn generates the electricity. Thus mechanical energy is converted to electrical energy.
If a waterfall is not available, but there is fuel available for burning, such as coal, gasoline or nuclear fuel, then these fuels can be burned and heat energy obtained. This heat energy can be used to drive a dynamo which would then produce electricity. So in this example — known as thermoelectricity — heat energy from the burning fuel is converted to mechanical energy in the rotating dynamo which then generates the electricity.
The obvious disadvantage of thermoelectricity is that the fuels will eventually be exhausted at some time in the future. There is also another disadvantage, and that is, in converting heat into work there is always a waste of heat energy. Not all the available heat can be converted into useful energy. And this follows from the laws of thermodynamics, which, as we shall see presently, follow from the atomic or particle nature of matter. We now turn to these laws.
The study of thermodynamics is classified under four laws: the zeroth law, the first law, the second law and the third law.
Brief explanations of these laws are laid out below:
Zeroth Law:
The zeroth law states that if two bodies are separately in thermal equilibrium with a third body, then they must be in thermal equilibrium with one another. By thermal equilibrium we mean simply that no heat flows between the two bodies. This law enables us to define the concept of temperature. Two bodies that are in thermal equilibrium with one another have the same temperature. So if body A and body B have the same temperature, and body A and body C have the same temperature, then by the zeroth law, body B and body C must have the same temperature. This means we can define temperature as an absolute quantity, regardless of the nature of the body that has the temperature. So thermometers can be built to measure the temperatures of objects having compositions totally different from that of the thermometer. We express temperature as a number. This number is commonly written using one of two common scales, Celsius and Fahrenheit. These scales are related by the formula
According to this formula 100° C = 212° F, which is the temperature at which water boils under normal atmospheric pressure.
Physicists who worked on the behavior of gases as they expanded with increase of temperature noticed that there seemed to be a lowest possible temperature which is −273.15° C. This is called Absolute Zero. One could think of Absolute Zero as the temperature of a body after all its heat has been taken away. So there is a lower limit to temperature. Since it is impossible to get colder than Absolute Zero, it makes sense to define a scale of temperature in which 0 corresponds to Absolute Zero. Such a scale is called the Kelvin or Absolute Scale.2
Exercise 3.1.
Which is colder: (a) 0° C or 0° F? (b) −20° C or −20° F? (c) −40° C or −40° F? (d) −60 ° C or −60° F?
First Law:
The first law is a statement of the conservation of energy. It states that when heat energy is given to a body, part of it goes to raise the temperature, and hence the internal energy of the body increases, and the rest goes to do external work, which is done by the expansion of the body. Since this is a law of conservation of energy, it can also be applied to a case when work is done on a gas by compressing it. In this case the gas would get heated up, and may give up some of its heat to the surroundings. Here also there is a balance of energy. No energy is created and no energy is destroyed.
If the amount of heat energy supplied to a body is ΔQ, the rise of internal energy of the body ΔU, and the external work done by the body ΔW, then the first law can be expressed as
Second Law:
The second law is a statement of irreversibility. It can be stated in many different ways. The simplest statement is that heat always flows naturally from a hotter to a cooler body.
Both the first and the second laws deal with the conversion of heat into work and work into heat. The first law tells us that heat and work are different forms of energy and that one can be converted into the other. The second law places restrictions on the conversion of heat energy into work. Heat and work (mechanical energy) are not reversible. Whereas mechanical energy can be converted entirely into heat energy, the reverse cannot take place. For example, when a meteor falls through the atmosphere, it has a large kinetic energy because of its speed, and this kinetic energy is entirely converted to heat energy as the meteor burns up in the atmosphere. When brakes are applied to a moving car, the kinetic energy of the car is entirely converted to heat energy in the wheels and the road. But the heat energy that is so generated in either of these examples cannot be converted back to kinetic energy.
Third Law:
The third law states that it is impossible to cool a body right down to absolute zero (0 K), even though it is theoretically possible to come closer to this temperature with each attempt.
All the laws of thermodynamics can be fully explained on the atomic or molecular theory of matter. Heat is a manifestation of the energies of the molecules of a body — the sum of all the kinetic and potential energies of all the molecules. Here the forces that give rise to the potential energy are not due to gravity but due to attraction and repulsion between molecules. The phenomenon of Brownian motion showed that the motion of the molecules in a liquid is erratic and random. The molecules move in all possible directions with a range of velocities that change in magnitude and direction each time a molecule collides with another or with the molecules of the walls of the container. Thus it is futile to try and follow the movements of any one molecule. The best we can do is to investigate the overall aggregate or statistical behavior of these molecules. The study of the behavior of matter in terms of the collective motion of the molecules is therefore called statistical mechanics.
3.3Statistical mechanics
Every substance — whether an element or a compound — is made up of molecules. Each molecule contains one or more atoms. The molecule of an element contains one or more atoms of the same kind. A molecule of a compound contains two or more atoms, which are not all of the same kind. Sulfuric acid has the formula H2SO4, which means a molecule of sulfuric acid contains two hydrogen atoms, one sulfur atom and four oxygen atoms. Because atoms — and molecules — are so small, there is a very large number of these particles in any observable piece of matter. A measure of this large number is Avogadro’s number NA = number of molecules present in 1 mole of any element or compound. A mole is the molecular weight expressed in grams. 1 mole of hydrogen gas (H2) has a mass of 2 grams. NA = 6.02 × 1023. So 1 gram of hydrogen gas (H2) contains about 3.01 × 1023 molecules. This means 1 hydrogen atom has a mass of about 1.7 × 10−24 grams. This is a very small quantity. 16 grams of oxygen gas (O2) contain about 3.01 × 1023 molecules. Because of the very large number of molecules present in this small mass of oxygen, we need statistical mechanics to provide a reliable description of the observable behavior of the gas.
Exercise 3.2.
(a) The formula for water is H2O. How many molecules are there in 1 gram of water?
(b) The molecular weight of a substance is the sum of the atomic weights of the atoms in a molecule of the substance. Given the following atomic weights: H = 1, O = 16, S = 32, find the molecular weight of sulfuric acid H2SO4.