Heat, Work and Internal Energy

Internal Energy:

What is meant by Internal Energy of a System?

The internal energy of a system is the sum of molecular kinetic and potential energies in the frame relative to which the centre of mass of the system is at rest. The intermolecular potential energy of a real gas is a function of its volume. The internal kinetic energy of a gas is a function of its temperature.

The kinetic energy does not include overall kinetic energy of the system .It includes only the disordered energy associated with random motion of the molecules. It is denoted as “U”. Internal energy can be described as the sum of kinetic and potential energies of individual molecules in the material. But in thermodynamics one should keep in mind that “U” is simply a macroscopic variable of the system. “U” is thermodynamic state variable and its value depends only on the given state of the system and not on path taken to arrive the state.

Transfer of heat and performance of work are two mean of adding or subtracting energy from a system. On transfer of energy, system is said to have undergone a change in internal energy. Thus the sum of heat put into the system plus work done on the system equals increase in internal energy of the system for any process. Here heat and work are the state 1 and state 2 of internal energy.

a) Internal energy U of a gas is the sum of the kinetic and potential energies of its molecules when the box is at rest. Kinetic energy due to various types of motion

(translational, rotational, vibrational) is to be included in U. (b) If the same box is moving as a whole with some velocity, the kinetic energy of the box is not to be included in U.

If U₁ is internal energy of state 1 and U₂ is internal energy of state 2 than change in internal energy would be

ΔU = U₂ - U₁ ------ (1)

If W is the work done by the system on its surroundings then -W would be the work done on the system by the surroundings.

If Q is the heat put into the system then,

Q + (-W) = ΔU ------ (2)

usually written as

Q = ΔU+W ------ (3)

Equation (3) is known as first law of thermodynamics and it can be applied when Q, W and U are expressed in same units.
Some Important stuffs are given as follows:

(1) Q is positive when heat is given to the system and Q is negative when heat is taken from the system

(2) W is positive when system expands and does work on surroundings

Hence when a certain amount of heat Q is given to the system then some part of it is used in increasing internal energy ΔU of the system while remaining part leaves the system in form of work done by the system on its surroundings. From equation (3) it is observed that first law of thermodynamics is a statement of conservation of energy stated as: ' The energy put into the system equals the sum of the work done by the system and the change in internal energy of the system'

If the system undergoes any process in which ΔU = 0 i.e., charge in internal energy is zero then from equation (3)

Q = W

that is heat supplied to the system is used up entirely in doing work on the surroundings. Stability and nature of the internal energy of an ideal gas and system:

· Internal energy of a system is a thermodynamic “stable variable”

· Internal energy of an ideal gas is purely “kinetic in nature”.

Two Ways of Changing the Internal Energy of a System:

Heat and work are two distinct modes of energy transfer to a system that results in change in its internal energy. (a) Heat is energy transfer due to temperature difference between the system and the surroundings. (b) Work is energy transfer brought about by means (e.g. moving the piston by raising or lowering some weight connected to it) that do not involve such a temperature difference.

The system to be a certain mass of gas contained in a cylinder with a movable piston. This shows there are two ways of changing the state of the gas (and hence its internal energy). One way is to 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. 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. Both these 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.

Hence heat and work are two different modes of altering the state of a thermodynamic 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 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.

Are Heat and Work State Variable?

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. In ordinary language, we often confuse heat with internal energy. The distinction between them is sometimes ignored in elementary physics books. For proper understanding of thermodynamics, however, the distinction is crucial.

Sign Conversion used in the Measurement of Heat, Work and Internal energy:

· Heat absorbed by the system is positive and heat given out by the system is negative.

· Work done by a system is positive and work done on a system is negative.

· The increase in internal energy of a system is positive and the decrease in internal energy of a system is negative.

Difference between Heat and Work:

Heat	Work
It is a mode of energy transfer due to temperature difference between the system and the surroundings.	Work is the mode of energy transfer brought about by means that do not involve temperature difference.
When heat is supplied to a gas, its molecule move faster in all direction at random.	When a piston compresses a gas to do work on it, it forces the molecule to move in the direction of piston’s motion.
So heat is a mode of energy transfer that produces random motion.	So work may be regarded as the mode of energy transfer that produces organized motion.