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.
• how many moles of nitrogen gas are in each tire?
• what will the tire pressure be at the peak temperature in the desert?
• will the tires burst at the peak temperature? explain.
• to what pressure should the tire pressure be reduced before starting the ride to avoid bursting of the tires in the desert heat? (assume no significant change in tire volume.)

Data
State 1 (start)
Ts = 21 °C + 273.15 = 294.15 K
Vs = 15.6 L
Ps = 249 kPa

State 2 (at the peak)

Tf = 51°C + 273.15 = 324.15 K
Vf=Vs=15.6 L

Burst ==> Pb = 269 Kpa

1) Moles of N

Ideal gas equation

pV = nRT ==> n = pV / [RT]

n = 249 kPa *1 atm/101.325KPa * 15.6L / [0.082 atm-L/K-mol * 294.15K]

n = 1.589 mol

2) Pressure at the peak

pV = nRT
p = nRT/V
p=1.589mol*0.082atm-L/K-mol*324.15K / 15.6L
p = 2.70 atm

3) Burst?

Pb = 269kPa * 1 atm /101.325  kPa = 2.65 atm

Then, given that the pressure of the tires at the peak will be greater than the burst pressure, the tires will burst.

4) Maximum initial pressure

Use the fact that the pressure is proportional to temperature, i.e. Gay-Lussac Law: Ps/Ts = Pf/Tf

The limit final pressure and temperatures are: Pf = 269 kPa, Tf=324.15 K

The limit initial pressure will be T=294.15,  Ps = [Pf/Tf]*Ts

Ps = [269 kPa/324.15K] * 294.15K = 244.10 kPa

Then, the pressure should be reduced from 249 kPa to less than 244.10 KPa before starting the ride.