Thermodynamics

The first law of thermodynamics is the law of conservation of energy written for a system that can exchange energy with its surroundings in only two ways: as heat and as work. Divide the world into a system (the gas in a cylinder, say) and everything else, and the energy stored inside the system is its internal energy $U$. Give the system an amount of heat $Q$ and let it do work $W$, and the first law states that the heat supplied equals the gain in internal energy plus the work done:

$$Q = \Delta U + W, \qquad \Delta U = Q - W.$$

The two forms are the same equation rearranged, which is why the paper accepts either. The sign convention is the part to fix firmly in the mind: $Q$ is positive when heat is absorbed and $W$ is positive when the gas does work on its surroundings, so a gas that absorbs heat and expands uses part of that heat to push the piston and stores only the remainder.

The reason the law matters is that internal energy is a state function while heat and work are not. A system can reach the same final state by many routes, and each route splits the energy differently between $Q$ and $W$, but $\Delta U$ is fixed by the initial and final states alone. Energy is never created or destroyed, only moved or transformed. The examples the examiner uses are ordinary: metabolism turns the chemical energy of food into heat and the mechanical work of muscles, rubbing the hands together converts work into internal energy and warms them, and shaking an insulated flask of tea does mechanical work on the liquid, raising both its kinetic energy and its temperature. The opposite case is a free expansion, where a gas rushes into a vacuum: no heat crosses the wall and no work is done because there is nothing to push against, so the internal energy and the temperature both stay put.