A tire contains air at a pressure of 2.8 bar at 10C. If the tire’s volume is unchanged, what will the air pressure in it be when the tire warms up to 35C as the car is driven?
P2=P1*T2/T1 so change the temps to Kelvins, and calculate P2
To determine the air pressure inside the tire when it warms up, we need to use the ideal gas law. The ideal gas law equation is:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = gas constant
T = temperature
In this case, we have the initial conditions (P1 = 2.8 bar and T1 = 10°C) and we want to find the final pressure (P2) when the temperature changes to T2 = 35°C. We can assume that the volume (V) remains constant.
To solve for P2, we need to rearrange the ideal gas law equation:
P1V1/T1 = P2V2/T2
Since the volume (V) is constant, we can simplify the equation:
P1/T1 = P2/T2
Substituting the values we have:
(2.8 bar)/(10 + 273.15 K) = P2/(35 + 273.15 K)
First, we need to convert the initial temperature from Celsius to Kelvin by adding 273.15.
(2.8 bar)/(283.15 K) = P2/(308.15 K)
To solve for P2, we cross-multiply:
P2 = (2.8 bar) * (308.15 K) / (283.15 K)
P2 ≈ 3.05 bar
Therefore, the air pressure in the tire will be approximately 3.05 bar when the tire warms up to 35°C.