Question

A tire with a volume of 11.41 L reads 44 psi (pounds per square inch) on the tire gauge. What is the new tire pressure if you compress the tire and its new volume is 10.6 L?

Answer 1

Given:

The volume of the tire = 11.4 L

Pressure of the tire on the tire gauge = 44 psi = 2.99 atm ...... [∵ 1 psi = 0.068 atm]

New Volume of the tire after compressing = 10.6 L

To find:

The new tire pressure

Solution:

According to the Ideal Gas Law, we have

$\boxed{\bold{PV = nRT}}$

We know that if the temperature of the gas remains constant, then on changing the volume, the pressure of the enclosed gas also changes inversely. This is known as the Boyle's Law.

$\boxed{ PV = constant}$ ....... when the temperature remains constant

So, we can rewrite the formula as,

$\boxed{P1V1 = P2V2}$

where

P1 = initial pressure

V1 = initial volume

P2 = final pressure

V2 = final volume

Now, on substituting the given values in the formula, we get

2.99 * 11.4 = P2 * 10.6  

⇒ P2 =   $\frac{2.99 \:*\:11.4 }{10.6}$

⇒ P2 =   $\frac{34.086 }{10.6}$

⇒ P2 = 3.215 atm

converting again into psi  by multiplying with 14.696, since the reading of the tire is seen on the tire gauge

⇒ P2 = 47.24 psi

Thus, the new tire pressure after compressing the tire is 47.24 psi.

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