Question

You inflate the tires of your car so the pressure is 30 psi, when the air inside the tires is at 20 degrees c. After driving on the highway for a while, the air inside the tires heats up to 38 c. Which number is closest to the new air pressure?.

Answer 1

32 psi

Step-by-step explanation:

First, when doing any engineering problem, we define our knowns. When working with temperatures, we should always be using absolute temperature in units of Kelvin (K).

Knowns:

• Inflated Pressure = P1 = 30 psi
• Inflated Temperature = T1 = 20 °C = 293 K
• New Pressure = P2 = ? (What we're solving for)
• New Temperature = T2 = 38 °C = 311 K

The following is the relevant equation we'll be using. This is the Ideal Gas Law.

PV = nRT

We know that the only variables that are changing are Pressure and Temperature, so we can isolate all constant variables on one side of the equation and all the changing variables on the other side.

P / T = nR / V

We can then use Ideal Gas Law to determine the new Pressure, P2.

P1 / T1 = P2 / T2

Substitute all known variables into the equation and solve for P2.

30 psi / 293 K = P2 / 311 K

P2 = (30 psi / 293 K) * 311 K = 32 psi