Answer to Question #138520 in Physical Chemistry for Martina

Question

A person, living in Canada in the winter, pumps their car tires in the morning with a pressure of 35 psi. The temperature in the morning is 20°C. By the evening, the temperature has dropped to 0°C and the tire pressure monitoring system in the car starts indicating low pressure with a warning light. What pressure will the tires have in the evening that made the warning light from the pressure monitoring system turn on?

Answer 1

The pressure of a gas $p$ is related to its temperature $T$, volume $V$ and its quantity $n$ through the ideal gas law:

$pV=nRT$ .

For the gas in the car tires, the volume and the number of the moles of the gas are constant:

$V,n = const$ .

Therefore, the ratio of pressure and temperature should be kept constant, too:

$\frac{p}{T} = const$.

Remember that the temperature should be experssed in kelvin and not in celsius. Therefore, 20°C is 293.15 K and 0°C is 273.15 K:

$\frac{p_{morning}}{T_{morning}}=\frac{p_{evening}}{T_{evening}}$

$\frac{35}{293.15} = \frac{p_{evening}}{273.15}$

$p_{evening}=\frac{35}{293.15}\cdot273.15=32.6$ psi.

Answer: the tires have a pressure of gas of 32.6 psi in the evening.