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

The tire pressure will be 33.5 psi.

Step-by-step 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:

`(44.0)/(313.15)=(P_2)/(238.15)`

`P_2=(44\cdot \:238.15)/(313.15)\ psi=33.5\ psi`

The tire pressure will be 33.5 psi.