Question

A bicycle racer inflates their tires to 7.1 atm on a warm autumn afternoon when temperatures reached 27 °C. By morning the temperature has dropped to 5.0 °C. What is the pressure (in atm) in the tires if we assume that the volume of the tire does not change?

Answer 1

Answer:

The required pressure is 6.4866 atm.

Explanation:

The given data : -

In the afternoon.

Initial pressure of tire ( p₁ ) = 7 atm = 7 * 101.325 Kpa =  709.275 Kpa

Initial temperature ( T₁ ) = 27°C = (27 + 273) K = 300 K

In the morning .

Final temperature ( T₂ ) = 5°C = ( 5 + 273 ) K = 278 K

Given that volume remains constant.

To find final pressure ( p₂ ).

Applying the ideal gas equation.

p * v = m * R * T

$\frac{p}{T} = constant$

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

$p_{2} = \frac{T_{2} }{T_{1} } *p_{1}$  

$p_{2} = \frac{278}{300} * 709.275$  = 657.2615 Kpa = 6.486 atm