When an ideal gas at a temperature of 27 °C is suddenly compressed to one quarter of its volume, the pressure increases by a factor of 7 - AQA - A-Level Physics - Question 7 - 2020 - Paper 2

Using the ideal gas law, we can express the relationship between temperature, pressure, and volume: $\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$

Let:

• $P_1$ be the initial pressure,
• $V_1$ be the initial volume,
• $T_1$ be the initial temperature (300.15 K),
• $P_2 = 7 P_1$ (since pressure increases by a factor of 7),
• $V_2 = \frac{1}{4} V_1$ (as the volume is compressed to one quarter of its volume).

Substituting these values into the equation: $\frac{P_1 V_1}{300.15} = \frac{7 P_1 \cdot \frac{1}{4} V_1}{T_2}$

Simplifying the equation: $\frac{1}{300.15} = \frac{7 \cdot \frac{1}{4}}{T_2}$

This simplifies to: $T_2 = \frac{7 \cdot \frac{1}{4} \cdot 300.15}{1} = \frac{7 \cdot 300.15}{4}$

Calculating: $T_2 = \frac{2101.05}{4} = 525.2625 ext{ K}$

Now converting back to Celsius: $T_{new} (°C) = 525.2625 - 273.15 = 252.1125 °C$ Rounding to the nearest degree gives: 252 °C.