February/March 2026 Paper 42

The first law of thermodynamics may be written as

where $W$ is the work done on a system. State the meaning, in this equation, of the symbols $\Delta U$ and $Q$.

An ideal gas at a pressure of $2.0\times 10^5\text{ Pa}$ has an initial volume of $0.048{\text{ m}}^3$, an initial thermodynamic temperature of $560\text{ K}$, and an initial internal energy of $14.4\text{ kJ}$. The volume of the gas is reduced at constant pressure to a final volume of $0.012{\text{ m}}^3$. Show that the magnitude of the work done on the gas is $7200\text{ J}$.

Explain whether the work done on the gas is positive or negative.

Explain why the final internal energy of the gas is $3.6\text{ kJ}$.

For the reduction of the volume of the gas in 4(b), calculate $Q$. Give a unit with your answer.