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:

$\frac{P_{1}V_{1} }{T_{1}} = \frac{P_{2}V_{2} }{T_{2}}$

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

$\frac{P_{1} }{T_{1}} = \frac{P_{2} }{T_{2}}$

P₁ = 2 atm

T₁ = 27 C

P₂ = 2.2 atm

Plug these values in:

$\frac{2atm}{27C} = \frac{2.2atm}{T_{2}}$

Solve for T₂.

$2atm = \frac{2.2atm}{T_{2}}*27C$

$2atm * T_{2}={2.2atm}*27C$

$T_{2}={2.2atm}\div2atm*27C$

$T_{2}=1.1*27C$

$T_{2}=29.7C$

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

Hope this helps!