Question

1. A mountain biker goes for a ride in the desert. The air temperature is 21°C at the start of the ride, but the temperature in the desert will reach a peak of 51°C. The tires on the bike hold 15.6 L of nitrogen gas at a starting pressure of 249 kPa. The tires will burst when the internal pressure (Pb) reaches 269 kPa. Answer the following questions and show your work.

Answer 1

Assuming that we need to find the maximum temperature so that the tires will not burst. And assuming constant volume. Use Gay-Lussac's Law:

T1 = 21 C
T2 = ?

P1 = 249 kPa
P2 = 269 kPa

From the ideal gas law, PV = nRT

P/T = constant

P1/T1 = P2/T2

so,

249 kPa/(21+273)K = 269 kPa/ (T2 +273) K

T2 = 44.61 C