Question

The pressure in an automobile tire is 2.0 atm at 27°C. At the end of a journey on a hot summer day the pressure has risen to 2.2 atm. What is the temperature of the air in the tire? a. 272.72 K b. 330 K c. 0.014 K d. 175 K

Answer 1

Hey there!

For this we can use the combined gas law:

`(P_(1)V_(1) )/(T_(1)) = (P_(2)V_(2) )/(T_(2))`

We are only working with pressure and temperature so we can remove volume.

`(P_(1) )/(T_(1)) = (P_(2) )/(T_(2))`

P₁ = 2 atm

T₁ = 27 C

P₂ = 2.2 atm

Plug these values in:

`(2atm)/(27C) = (2.2atm)/(T_(2))`

Solve for T₂.

`2atm = (2.2atm)/(T_(2))*27C`

`2atm * T_(2)={2.2atm}*27C`

`T_(2)={2.2atm}/2atm*27C`

`T_(2)=1.1*27C`

`T_(2)=29.7C`

Convert this to kelvin and get 302.85 K, which is closest to B. 330 K.

Hope this helps!