Problem 1. A truck, driven in the winter, when the temperature was -5°C, hit the

Question

Problem 1. A truck, driven in the winter, when the temperature was -5°C, hit the curb with its right front tire, which suddenly decreased the volume of this tire by 20%. a) b) What was the temperature of the air in the tire immediately after the hit? What was the pressure at this moment, if the initial pressure in the tire was 3 atmospheres? The same truck was outside for few days in the same temperature and its loading area was slowly filling with snow. The weight of snow deformed the tire so its volume was reduced by 20%. c) What was the resulting pressure in the tire?

Explanation / Answer

given To = -5 C = 268.15 K

initial tyre voilume = V

final tyre volume = 0.8 V

a. assuming this to be an adiabatic change

PV^gamma = constant

Pi = 3 atm

also from ideal gas equation

PV = nRT

hence

PiV = nRTi

3V/268.15 = Pf*0.8V/Tf

Tf = Pf*71.50666

now,

3*V^1.4 = Pf*(0.8V)^1.4

Pf = 4.1 atm

hence

Tf = 293.185 K = 20.03 C

b. Pf = 4.1 atm

c. this change is isothermal ( as it is slow)

hence

PiVi = PfVf

Pf = PiVi/Vf = 3*1/0.8 = 3.75 atm

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