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In an article on tire maintenance, it is stated that tires lose air over time, and pressure losses as high as 90 kPa (13psi) per year are measured. The article recommends checking tire pressure at least once a month to avoid low tire pressure that hurts fuel efficiency and causes uneven thread wear on tires. Taking the beginning tire pressure to be 220 kPa (gage) and the atmospheric pressure to be 100 kPa, determine the fraction of air that can be lost from a tire per year.

Respuesta :

Answer:

0.28125

Explanation:

Given:

Loss in the tire pressure = 90 kPa

Gage pressure = 220 kPa

Atmospheric pressure = 100 kPa

Now,

the absolute pressure is given as:

[tex]P_{abs}=P_{gage}+P_{atm}[/tex]

on substituting the values, we get

the initial absolute pressure of the tire as, P₁:  220 + 100 = 320 kPa

also, we know

P×V = nRT

where,

V represents the volume of air in the tire

n is the number of moles of gas in the tire

R is the gas constant

and, T represents temperature

now, the volume and temperature for both cases remains the same

thus, for the initial pressure, we have

P₁V = n₁RT

or

320 × V = n₁RT

now for case 2 we have

P₂ = 320 kPa - 90 kPa = 230 kPa

thus,

P₂V = n₂RT

or

230 × V = n₂RT

now, by dividing 1 by 2, we get

[tex]\frac{320}{230}=\frac{n_1}{n_2}[/tex]

or

[tex]\frac{n_2}{n_1}=0.71875[/tex]

thus,

fraction of air lost is 1 - 0.71875 = 0.28125

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