What is an example of the first law of thermodynamics practice problem?

Temperature Variables

Q: Heat (in calories); W: Work (in Joules); U: Internal Energy (actually, internal motion of molecules); Note: 1000 Cal = 4186 Joules.

Thermodynamics' First Law: U = Q - W

In English, this formula's standard format means that internal energy is a function of heat (Q) entering the system (from the environment) and work (W) that the system puts out on the environment.

On the other hand, Q can be either positive or negative. In the former case, heat is entering the system from outside; in the latter case, heat is exiting the system and entering the surroundings.

W may also be positive or negative, but the translation is a little trickier to understand as the negative in the standard formula implies that the value of Work, whether positive or negative, can be misunderstood.

When evaluating work, consider the formula in two stages to avoid ambiguity and incorrect test answers:

(1) In this equation, work is positive and is being done by the system on the environment. U = Q - W is actually --------> U = Q - (+W).

(2) In this equation, work is negative and is being done ON the system by the environment. U = Q + W is REALLY --------> U = Q - (-W).

The preposition "by" is crucial in determining whether a work is positive or negative: W is positive when it is performed BY the system, and W is negative when it is performed ON the system.

Internal energy increases when work is done ON the system, and decreases when work is done BY the system.

Similarly, the internal energy of the system increases (Q-pos) when heat is added, and decreases (Q-neg) when heat is removed.

Observe this example problem:

A system's internal energy decreases by 200J. If the gas performs 50 J of work, how much of that work is transferred as heat, and is that work positive or negative?

-200 = U - 50 (response: -150J; positive work done)

An example of a first law of thermodynamics practice problem is:

A gas in a piston-cylinder system undergoes a process where 500 J of heat is added to the system, and 300 J of work is done on the system. Determine the change in internal energy of the system.