Paper 4 Thermal Physics B Answers

Q1 Boyle law test

1. Correct reciprocal-volume values with consistent units. [1]
2. Axes and units [1]; suitable scale [1]; accurate plots [2]; best-fit straight line [1]. [5]

3. For $p=C(1/V)+p_0$, the gradient is $C=pV$. The fitted gradient is approximately $6.00\times 10^3\mathrm{kPa}\mathrm{c}{\mathrm{m}}^3$, equivalent to $6.00\mathrm{J}$. [2]
4. The vertical intercept is approximately $3.0\mathrm{kPa}$, indicating a positive sensor offset of this magnitude. [2]
5. Change volume slowly; wait for thermal equilibrium before recording; avoid warming the gas by handling; use a constant-temperature water bath. Any two. [2]
6. The trapped gas occupies the cylinder and connecting tubing, so omitting the tubing volume systematically underestimates the total $V$ used in Boyle’s law. [1]

Q2 First-law p-V data

1. Net work by gas is the area enclosed by the cycle, with sign depending on cycle direction. [1]
2. Internal energy is a state property; after a complete cycle the gas returns to its initial state, so $\Delta U=0$. [2]
3. From the first law over a cycle, net heat input equals net work done by the gas. [2]