The pressure of air in a tire is \(22.5Nm^{-2}\) at 27°C. If the air in the tyre heats up to 47°C, calculate the new pressure of the air, assuming that no a...

Answer Details

The relationship between pressure, volume, and temperature of a gas is given by the ideal gas law: PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the universal gas constant, and T is the temperature in Kelvin. Assuming that the volume of the tire remains constant and no air leaks out, we can use the ideal gas law to calculate the new pressure of the air in the tire when the temperature increases from 27°C to 47°C. First, we need to convert the temperatures from Celsius to Kelvin by adding 273 to each temperature: Initial temperature, T1 = 27°C + 273 = 300K Final temperature, T2 = 47°C + 273 = 320K Next, we can set up the following equation using the ideal gas law: P1V = nRT1 Since the volume and the number of moles of air remain constant, we can rearrange this equation to solve for the initial pressure, P1: P1 = (nR / V) * T1 Similarly, we can use the ideal gas law to calculate the final pressure, P2: P2V = nRT2 P2 = (nR / V) * T2 Since the volume and the number of moles of air remain constant, we can simplify this equation to: P2 = P1 * (T2 / T1) Substituting the values we know: P1 = 22.5 Nm^(-2) T1 = 300 K T2 = 320 K P2 = 22.5 * (320 / 300) = 24 Nm^(-2) Therefore, the new pressure of the air in the tire is 24 Nm^(-2) when the temperature increases from 27°C to 47°C. Therefore, the correct option is: - \(24Nm^{-2}\)