Question

The pressure inside an automobile tire is 44.0 pounds per square inch (psi) on a very warm summer day (40.0 °C). Calculate the tire pressure in the same tire on a very cold winter day (-35.0 °C) five months later, assuming that no air escapes from the tire. Hint: you will need to make another reasonable assumption that is not stated here.

Answer 1

Answer:

The tire pressure will be 33.5 psi.

Explanation:

Considering the ideal gas equation as:

$PV=nRT$

where,  

P is the pressure

V is the volume

n is the number of moles

T is the temperature  

R is Gas constant having value = 0.0821 L.atm/K.mol

Thus, at constant volume and number of moles, Pressure of the gas is directly proportional to the temperature of  the gas.

P ∝ T

Also,  

$\frac {P_1}{T_1}=\frac {P_2}{T_2}$

Given ,  

P₁  = 44.0 psi

P₂ = ?

T₁ = 40.0  °C

T₂ = -35.0  °C

The conversion of T( °C) to T(K) is shown below:

T(K) = T( °C) + 273.15  

So,  

T₁ = (40.0 + 273.15) K = 313.15 K  

T₂ = (-35.0 + 273.15) K = 238.15 K  

Using above equation as:

$\frac{44.0}{313.15}=\frac{P_2}{238.15}$

$P_2=\frac{44\cdot \:238.15}{313.15}\ psi=33.5\ psi$

The tire pressure will be 33.5 psi.