The Zorth Low of Thermodynamics led us to the concept of temperature that agree with our commonsense notion. Temperature is a maker of the 'hotness' of a body It determine the direction of flow of heat when two bodies are placed in thermal contact. Heat flow from the body at a higher temperatures to the one at lower temperatures. The flow stops when the temperatures equalise; the two bodies are then in thermal equilibrium.
We saw in some detail how to construct temperature scales to assign temperatures to different bodies. We now describe the concepts of heat and other relevant quantities like internal energy and work.
The concept of internal energy of a system is not difficult to understand. We know that every bulk system consists of a large number of molecules. Internal energy is simply the sum of the kinetic energies and potential energies of these molecules. We remarked earlier that in thermodynamics, the kinetic energy of the system, as a whole, is not relevant. Internal energy is thus, the sum of molecular kinetic and potential energies in the frame of reference relative to which the centre of mass of the system is at rest. Thus, it includes only the (disordered) energy associated with the random motion of molecules of the system. We denote the internal energy of a system by U.
Through we have invoked the molecular picture to understand the meaning of internal energy, as far as thermodynamics is concerned, U is simply a macroscopic variable of the system. The important thing about internal energy is that it depends only von the state of the system, not on how that state was achieved. Internal energy U of a system iscan example of a thermodynamics 'state variable' - its value depends only on the given state of the system, not on history i.e. not on the 'path' taken to arrive at that state.
Thus, the internal energy of a given mass of gas depends on its state. described by specific value of pressure, volume and temperature. It does not depend on how this state of the gas came about. Pressure, volume, temperature and internal energy are thermodynamics state variables of the system (gas). If we neglect the small intermolecular force in a gas, the internal energy of a gas various random motions of its molecules.
What are the way of changing internal energy of a system?
Consider again, for simplicity, the system to be a certain mass of gas contained in a cylinder with a movable piston. Experience shows there are two ways of changing the state of the gas. (and hence it's internal energy). One way is to put the cylinder in contact with a body at a higher temperatures than that of the gas. The temperature difference will cause a flow of energy (heat) from the hotter body to the gas, thus increasing the internal energy of the gas.
The other way is to push the piston down i.e. to do work on the system, which again results in increasing the internal energy of the gas. Of course, both theses things could happen in the reverse direction. With surroundings at a lower temperature, heat would flow from the gas to the surroundings. Likewise, the gas could push the piston up and do work on the surroundings. In short, heat and work are two thermodynamics system and changing its internal energy.
The notion of heat should be carefully distinguished from the notion of internal energy. Heat is certainly energy, but it is the energy in transit. This is not just a play of words. The distinction is of basic significance. The state of va thermodynamics system is characterised by its internal energy, not heat. A statement like 'a gas in a given state has a certain amount of heat' is as meaningless as the statement that 'gas in a given state has a certain amount of work'. In contrast, 'a gas in a given state has a certain amount of internal energy' is a perfectly meaningful statement. Similarly, the statement 'a certain amount of heat is supplied to the system or 'a certain amount of work was done by the system' are perfectly meaningful.
To summarise, heat and work in thermodynamics are not state variables. They are modes of energy transfer to a system resulting in change in its internal energy, which ,as already mentioned, is a state variable.
