QUESTION 4 HEAT 4.1 I 90 litre cylinder is filled with nitrogen to capacity at a pressure of \( 20,11 \mathrm{kPa} \). If the cylinder enlarges, the pressure drops to 11 kPa . Calculate the increase in the volume of the cylinder.

To solve this, we can use Boyle's Law, which states that for a given mass of gas at constant temperature, the product of the pressure and volume is constant (P1V1 = P2V2). Given: - Initial pressure \( P_1 = 20.11 \, \text{kPa} \) - Initial volume \( V_1 = 90 \, \text{litres} \) - Final pressure \( P_2 = 11 \, \text{kPa} \) We need to find the final volume \( V_2 \). Using Boyle's Law: \[ P_1V_1 = P_2V_2 \] Substituting the known values: \[ 20.11 \, \text{kPa} \times 90 \, \text{litres} = 11 \, \text{kPa} \times V_2 \] Calculating \( 20.11 \times 90 = 1809.9 \, \text{kPa.litres} \): \[ 1809.9 \, \text{kPa.litres} = 11 \, \text{kPa} \times V_2 \] Now, solve for \( V_2 \): \[ V_2 = \frac{1809.9}{11} \approx 164.54 \, \text{litres} \] The increase in volume is: \[ V_2 - V_1 = 164.54 - 90 = 74.54 \, \text{litres} \] So, the increase in the volume of the cylinder is approximately \( 74.54 \, \text{litres} \).