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

Thermo Variables

U -- Internal Energy (really, internal motion of molecules)
Q -- Heat (in calories)
W -- Work (in Joules) Note: 1000 cal = 4186 joules

First Law of Thermodynamics --> U = Q - W

This is the standard format of the formula. Translated into English, it means that internal energy is a function of heat (Q) coming into the system (from the surroundings) and work being down by the system on the surroundings.

However, Q can be either positive or negative. If Q is positive, heat is coming into the system from the surroundings; if Q is negative heat is leaving the system and going into the surroundings.

W can also be either positive or negative. But the translation is a little less straightforward; in fact, it's pretty tricky since the negative in the standard formula means that the positive or negative value of Work can be misinterpreted.

To avoid ambiguity (and wrong answers on tests) think of the formula in two separate stages when analyzing work:

(1) U = Q - W is REALLY --------> U = Q - (+W)
In this equation Work is positive and is being done BY the system on the surroundings.

(2) U = Q + W is REALLY --------> U = Q - (-W)
In this equation Work is negative and is being done ON the system by the surroundings

The key point in analyzing whether work is positive or negative rests on a preposition: when work is done BY the system, W is pos; when work is done ON the system, W is neg.

When the work is done BY the system, the internal energy decreases; when work is done ON the system, the internal energy increases.

Along the same lines, when heat is added to the system, (Q-pos) the internal energy increases; when heat is removed (Q-neg) the internal energy decreases.

Here's a sample problem:

The internal energy of a system decreases by 200J. If 50 J or work in done BY the gas, how much energy is transfered as heat? Is the work done positive or negative?

-200 = U - 50 (answer: -150J; work done is positive.)