The first law of thermodynamics

Since the first law of thermodynamics is a relation between the fundamental quantities of heat and work, let us look further at their distinctions and similarities. Neither heat nor work is a property of the system. They are boundary phenomena, path-dependent, inexact differentials. Both are forms of energy in transit and have meaning when a system undergoes a change of state.

The conventional units of work are foot-pounds force; of heat, the British thermal unit. Btu was originally defined as that quantity of heat required to raise 1 lb_m of water from 59.5 to 60.5°F, which is referred to as the 60°FBtu.

To understand the first law of thermodynamics we must understand a cycle, defined as the passing of a system through a series of states but returning to its initial condition. Consider an ice-cream freezer. The ingredients, milk, eggs, sugar, etc., are contained in the system chosen. Work is transferred to the system by paddle, causing the temperature of the system to rise, but the heat resulting from the increased temperature is transferred to the surrounding brine. Work goes in; heat comes out.

What happens when all the energy added by work is extracted by the heat transfer? The system returns to its initial state, passing through a cycle. Note that for the system chosen the work is negative and the heat is negative.

The total work and heat transferred in the cycle is different from zero, i.e., * W#0, * Q#0 (3-7)

As a matter of fact, for the system in question * W<0, *Q<0 (3-18). With a little ingenuity we can measure the work and heat transferred. Equipping the input shaft with a pulley and weight will give the work, while the heat transfer can be measured by ice meltage. Before leaving this example, we should observe that more heat must be extracted than added by the work if we are to freeze the ice cream. In 1843 a British scientist, Joule, carried out a number of experiments similar to the preceding example with various configurations. In all cases, he observed that the work done on the system was directly proportional to the quantity of heat removed from the system. Mathematically, (3-19) cycle, where the proportionality constant J is the mechanical equivalent of heat the value of which depends upon the units chosen. Equation (3-19)

is the mathematical statement of the first law of thermodynamics. This law, which is the basic law of the conservation of energy, was deduced from observations. It is given the status of a law only because no contradiction to it has ever been found.

It is evident from Eq. (3-19) that work and heat can be expressed in equivalent units. Expressing work in foot-pounds force and heat in Btu, J = 778 ft-lbf/Btu. Equation (3-19) does not suggest that heat and work is the same thing, but it does establish the relationship between the two. While discussing units, recall that power is work rate, or work per unit time. Therefore, the following conversion factors will be useful 1 hp - 33,000 ft-lb_f/min = 2545 Btu/hr, 1 kw = 44,200 ft-lb_f/min = 3412 Btu/hr.

Most of our thermodynamic problems are concerned with processes rather than cycles. Systems rarely return to their initial state. Therefore, to be useful the first law should be formulated for easy application to processes.

Specific heats. If a red hot iron ingot of 20-lb_m is quenched in a 20-lb_m pail of cold water, we know intuitively that the iron will cool and the water will become hot. Experience has shown that the temperature change of the iron is not equal to the temperature change of the water. Furthermore, this is the case for all materials. This characteristic is due to a property of the material known as specific heat c. It is the amount of heat required to change the temperature of a unit mass by 1° under certain conditions.

The third law of thermodynamics. The second-law relationship for entropy can account only for changes in entropy - one state relative to another. Although this is adequate for thermodynamic calculations, it is sometimes advantageous to speak in terms of absolute entropy, which requires the third law of thermodynamics. Simply stated, it is that the entropy of a pure substance is zero at absolute zero.

In a probabilistic sense, entropy is a measure of the disorder of a system. At absolute zero there is no translational molecular activity, hence no disorder, or zero entropy.

The second law of thermodynamics. The first law of thermodynamics establishes a relationship between heat and work but places no conditions on the direction of transfer. The second law of thermodynamics is the directional law. It may be formulated thus: Heat cannot, of itself, pass form a colder to hotter body. Limitations of the first law. To illustrate the directional characteristic of the second law, let us return to the example of the ice cream freezer. We added work to the system and extracted heat. Now let us reverse the process - add heat and get work out of the system. There is no conceivable way in which a weight might be returned to its original position by reversing the process. It is impossible to fully convert all heat into work. The process is irreversible.