Write an equation that expresses the law of thermodynamics in terms of heat and work

We write DE = q+w, where DE is the internal energy change and q and w are heat and work, respectively.

(b) Under what conditions will the quantities q and w be negative numbers?

q is negative when heat flows from the system to the surroundings, and w is negative when the system does work on the surroundings.

As an aside: In applying the first law, do we need to measure the internal energy of a system? Explain.

The absolute internal energy of a system cannot be measured, at least in any practical sense. The internal energy encompasses the kinetic energy of all moving particles in the system, including subatomic particles, as well as the electrostatic potential energies between all these particles. We can measure the change in internal energy (DE) as the result of a chemical or physical change, but we cannot determine the absolute internal energy of either the initial or the final state. The first law allows us to calculate the change in internal energy during a transformation by calculating the heat and work exchanged between the system and its surroundings.