THE FIRST LAW OF THERMODYNAMICS

The First Law Of Thermodynamics

We have seen that heat is just a form of energy. A system can be given energy either by supplying heat to it (by placing it in contact with a hotter object) or by doing mechanical work on it. consider an ideal gas in a cylindrical container fitted with a piston (figure 2.1). Suppose the piston is fixed in its position and the walls of the cylinder are kept at a temperature higher than that of the gas. The gas molecules strike the wall and rebound. The average kinetic energy of a wall molecule is larger than the average kinetic energy of a gas molecule. Thus, on collision, the gas molecules receive energy from the wall molecules.This increased kinetic energy is shared by other molecules of the gas and in this way the total internal energy of the gas increases.

Figure 2.1

Next, consider the same initial situation but now the walls are at the same temperature as the gas. Suppose the piston is pushed slowly to compress the gas. As a gas molecule collides with the piston coming toward it, the speed of the molecule increases on collision (assuming elastic collision, v2 + v1 +2u in figure 2.2). This way the internal energy of the molecules increases as the piston is pushed in.

Figure 2.2

We see that the total internal energy of the gas may be increased because of the temperature difference between the walls and the gas (heat transfer) or because of the motion of the piston (work done on the gas).

In a general situation both modes of energy transfer may go together. As an example, consider a gas kept in a cylindrical can fitted with a movable piston. If the can is put on a hot stove, heat is supplied by the hot bottom to the gas and the piston is pushed out to some distance. As the piston moves out, work is done by the gas on it and the gas loses this much amount of energy. Thus the gas gains energy as heat is supplied to it and it loses energy as work is done by it.

Suppose, in a process, an amount ∆Q of heat is given to the gas and an amount ΔW of work is done by it. The total energy of the gas must increase by ΔQ - ∆W. As result, the entire gas together with its container may start moving (systematic motion) or the internal energy (random motion of the molecules) of the gas may increase. If the energy does not appear as a systematic motion of the gas then this net energy ΔQ - ∆W must go in the form of its internal energy. If we denote the change in internal energy by ∆U, we get.

ΔU = ∆Q - ∆W

or.      ΔQ = ∆U + ∆W ...........(2.3) 

equation (2.3) is the statement of the first law of thermodynamics. In an ideal monatomic gas, the internal energy of the gas is simply translational kinetic energy of all its molecules. In general the internal energy may get contributions from the vibrational kinetic energy of molecules, rotational kinetic energy of molecules as well as from the potential energy corresponding to the molecular forces. Equation (2.3) represents a statement of conservation of energy and is applicable to any system, however complicated.