Heat and Work: A Definition and Explanation

[Greg Bernhardt]

Definition/Summary

Heat is the non-mechanical exchange of internal energy, $U$, between a system and its surroundings as a result of a difference in temperature.

By contrast, work, $W$, is the mechanical exchange of energy as a result of force applied across a moving surface (such as the face of a piston).

Heat is usually represented by the letter $Q$, and is measured in joules ($J$).

Equations

The first law of thermodynamics

$$\Delta U = Q + W$$

Here W is the work done on the system. Alternatively, W is often defined as the work done by the system, in which case the RHS becomes Q-W instead.

Extended explanation

Internal Energy:

We define the internal energy as the energy associated with the microscopic energies of a system, that is with the energy associated with the random motion of the molecules within a system.

So for a general fluid, the internal energy of a system is the sum of the translational kinetic energies (or thermal energy), the rotational kinetic energies, the vibrational kinetic energies and the potential energies of all the molecules in that system.

The internal energy of a system is often erroneously referred to as the heat of a system and we shall see why this is incorrect later.

One important point to note here is that the internal energy is a state variable, that is, the change in internal energy between any two states is independent of the path taken.

Energy can be external energy (due to macroscopic motion and external fields) or internal energy, $U$ (including relative motion of molecules and dipole moments and stress)

Internal energy plus pressure times volume equals enthalpy: $H\ =\ U\ +\ P\,V\text{ , or }H/V\ =\ \rho\,\epsilon\ +\ P$

$\epsilon$ is the internal energy per unit mass, or specific internal energy (s.i.e)

Temperature:

One useful definition of the temperature of a system, derived from kinetic theory, is kinetic temperature, which is a measure of the average translational kinetic energy associated with the random motion of the molecules with the system.

It should be noted that although related to internal energy, temperature is not directly proportional to internal energy since internal energy also involves the rotational and vibrational kinetic energies and the potential energies of the constituent molecules.

Work:

Well, if you're reading this I assume that you know the definition of work; in thermodynamics work is usually associated with a mechanical transfer of internal energy into or out of a system.

Work, outside of thermodynamics, is also associated with mechanical transfer of external energy, due to macroscopic motion (motion of the system as a whole), which is unconnected with temperature.

An example of work specific to thermodynamics is the application of a force through a piston, whose movement compresses the gas within a cylinder, thus doing work on the gas.

Since work is being done on the gas the W term in the usual expression would be positive. If we assume that the walls of the cylinder are adiabatic (no heat transfer) then all the work done is converted to internal energy. Suppose that after we have compressed the piston, we release it. Intuitively, we expect the piston to recoil back, and this is exactly what happens; the gas expands and does [an equal amount of] work on the piston against atmospheric pressure. In this case, since it is the gas that is doing work, our W term would be negative.

Heat:

So, we come to the definition of heat. If we examine the first law of thermodynamics, we can see that we can increase the internal energy of a system either by doing work on it, or adding heat to it.

Consider a piston and a cylinder filled with gas, we can increase the internal energy of the system by either compressing the gas by applying a force to the piston (work) or by fixing the piston and placing the cylinder in a flame (heat). We can compress and heat the gas in such a way that after the operation all the macroscopic properties (pressure, volume & temperature) are identical, that is the two cylinders are in identical states. Suppose we take two identical cylinders (but not necessarily in identical initial states) filled with a gas at 373K, one of which we compress and the other of which we heat such that both cylinders are at 473K and all their macroscopic quantities are identical, that is the final states of the two cylinders are identical. If we were to now examine the final states of the two cylinders, we have no way of knowing which was compressed and which was heated; the only conclusion we can draw is that their internal energies have increased. In this way we can consider heat as the microscopic analogy of work (macroscopic). I therefore, offer you a formal definition of heat:

"Heat is the non-mechanical exchange of energy between the system and surroundings as a result of a difference in temperature"
​

Both work and heat can be considered as methods of transferring energy within or between systems. It should now be apparent why the statement "a body posses heat" is nonsensical. To say that a body possesses heat is analogous to stating that a "body has work", which you must agree is utter rubbish. Rather, one transfers energy to a body by doing work on that body and one transfers energy to a body by heating or adding heat to that body. Similarly, it is incorrect to state that a body's heat has increased, rather its internal energy has increased.

A note about Thermal Energy:

Some texts make use of the term "thermal energy" to describe the "translational kinetic energy" of the molecules, I personally find that the term "thermal energy" only serves to confuse discussions further.

- original written by Hootenany

* This entry is from our old Library feature. If you know who wrote it, please let us know so we can attribute a writer. Thanks!

 

[AaronS]

This is a great explanation of the concepts of heat, work, and internal energy. It's well written and easy to understand. The concept of heat being the non-mechanical exchange of energy is clearly explained, as well as the equations used to describe the thermodynamics involved. The example of compressing a piston is also helpful in understanding the concept. The discussion at the end about thermal energy is also useful in helping to clear up any confusion. Thanks for posting this!