A tire contains air at a pressure of 2 bar at 15 degrees Celsius. If the tires volume is unchanged, what will the air pressure in it be when the tire warms up to 40 degrees Celsius as the car is driven?
To determine the air pressure in the tire when it warms up to 40 degrees Celsius, you can use the Ideal Gas Law, which states:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles of gas
R = Gas constant
T = Temperature
In this case, the volume of the tire is assumed to be unchanged, so V remains constant. The number of moles of gas (n) also remains constant.
First, we need to convert the temperatures given from Celsius to Kelvin, as the Ideal Gas Law requires temperature in Kelvin:
Temperature in Kelvin = Celsius temperature + 273.15
Initial temperature in Kelvin = 15 + 273.15 = 288.15 K
Final temperature in Kelvin = 40 + 273.15 = 313.15 K
Now, let's assign the values we know:
P1 = 2 bar (initial pressure)
T1 = 288.15 K (initial temperature)
T2 = 313.15 K (final temperature)
We can rearrange the equation to solve for P2:
P2 = (P1 * T2) / T1
Substituting the known values:
P2 = (2 * 313.15) / 288.15
P2 = 627.3 / 288.15
P2 ≈ 2.176 bar
Therefore, when the tire warms up to 40 degrees Celsius, the air pressure will be approximately 2.176 bar.