First Law of Thermodynamics for AP Physics B

Practice problems for these concepts can be found at:

Thermodynamics Practice Problems for AP Physics B

Before you start this lesson, be sure you understand the difference between heat and internal energy. Furthermore, remember that mechanical work is done whenever a force is applied through a distance.

The first law of thermodynamics is simply a statement of conservation of energy.

U is the internal energy of the gas in question. Q is the heat added to the gas, and W is the work done on the gas when the gas is compressed.

The signs of each term in the first law are extremely important. If heat is added to the gas, Q is positive, and if heat is taken from the gas, Q is negative. If the gas's internal energy (and, thus, its temperature) goes up, then ΔU is positive; if the gas's temperature goes down, then ΔU is negative.

The sign of W is more difficult to conceptualize. Positive W represents work done on a gas. However, if a gas's volume expands, then work was not done on the gas, work was done by the gas. In the case of work done by a gas, W is given a negative sign.

Define the variables in the first law, being careful of signs: Here Q = +2500 J. We're pushing the piston down; therefore, work is done on the gas, and W is positive. We remember that work = force × distance; so, the work done on the gas here is 1800 N·1 m, or +1800 J. Now plug into the first law of thermodynamics: the answer is +4300 J.

Practice problems for these concepts can be found at:

Thermodynamics Practice Problems for AP Physics B