Higher November 2021 Paper 1 Q18
18. In an experiment, the volume, V, of gas in a container is inversely proportional to the pressure, P, put upon it.
At the start of the experiment, a gas has a volume of 4 m3 when the pressure put upon it is 1020 N/m2.
(a) Find the volume of this gas when the pressure put upon it is 1360 N/m2. [4]
(b) Find the pressure put upon the gas when its volume is 1·2 m3. [2]
| Scheme | Marks | Comments |
|---|---|---|
| \(V \propto \dfrac{1}{P}\) or \(P \propto \dfrac{1}{V}\) or \(V = \dfrac{k}{P}\) | B1 | si; allow e.g. \(V \propto \dfrac{k}{P}\) |
| \(4 = \dfrac{k}{1020}\) oe or \(k = 4 \times 1020\ (= 4080)\) | M1 | |
| \((V =)\ \dfrac{4 \times 1020}{1360}\) | M1 | FT ‘their \(4 \times 1020\)’ |
| \((V =)\ 3\) (m3) | A1 | CAO |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| \(P_1V_1 = P_2V_2\) oe; soi | B1 | |
| \(4 \times 1020 = V \times 1360\) seen, or implied in later working | M1 | |
| Forms \((V =)\ \dfrac{4 \times 1020}{1360}\) | M1 | FT ‘their \(4 \times 1020\)’ |
| \((V =)\ 3\) (m3) | A1 | CAO |
| Scheme | Marks | Comments |
|---|---|---|
| \((P =)\ \dfrac{4080}{1{\cdot}2}\) or \((P =)\ \dfrac{4 \times 1020}{1{\cdot}2}\) | M1 | FT ‘their \(4 \times 1020\)’ \(\div\) 1.2 |
| 3400 (N/m2) | A1 | CAO |
| (6) |