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Heat, Internal Energy and Work

Let us now discuss how this temperature concept is related to heat, internal energy and work.

Heat flows from the body at a higher temperature to the one at lower temperature. The flow stops when the temperatures will be equal and the two bodies are then in thermal equilibrium.

Heat is energy that flows between a system and its environment by virtue of a temperature difference between them.

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.

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 and can be denoted as U. The internal energy U is simply a macroscopic variable of the system.

The internal energy depends only on the state of the system, and not on how that state was achieved.

Internal energy U of a system is an example of a thermodynamic ‘point or 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 values of pressure, volume and temperature. It does not depend on how this state of the gas came about.

Gas molecules in motion is not only translational it also includes rotational and vibrational motion of the molecules.

What are the ways of changing internal energy of a system?
Consider a system of gas contained in a cylinder with a movable piston. There are two ways, we can change the state of the gas and hence its internal energy.
  1. Put the cylinder in contact with a body at a higher temperature 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.
  2. Push the piston down i.e. to do work on the system, which again results in increasing the internal energy of the gas.
If the surroundings are at a lower temperature, heat would flow from the gas to the surroundings.

Similarly, the gas could push the piston up and do work on the surroundings.

In short, heat and work are two different modes of altering the state of a thermodynamic system and changing its internal energy.
Heat is a form of energy, but more in general it is energy in transit.

The state of a thermodynamic system is characterized 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 'a 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 statements 'a certain amount of heat is supplied to the system' or 'a certain amount of work was done by the system' are perfectly meaningful.

Finally we can say that 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.

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