temperature pressure volume

Question

On a cold winter morning when the temperature is –13ºC, the air pressure in an automobile tire is 1.5 atm. If the volume does not change, what is the pressure after the tire has warmed to 15ºC?

Answer 1

Hi Lindsey,

Use the Ideal gas law

PV = nRT

  P =(nR/V) T

 

P₁ = (nR/V) T₁

P₂ = (nR/V) T₂    Divide this equation by the above to get 

P₂/P₁ = T₂/T₁

 

since the volume does not change, the quantities inside the parenthesis are constant.

Change the temperature to Kelvin 

P₁ = 1.5 atm. T₁ = 273.15 + -13°C = 260 K, T₂ = 273.15 + 15°C = 288 K

P₂ =(T₂/T₁)P₁ =(288/260)*1.5 atm = 1.66 atm