A tire contains air at a pressure of 2.8 bar at 10 degrees Celsius. If the tires volume is unchanged, what will the air pressure in it be when the tire warms up to 35 degrees Celsius as the car is driven?
To solve this question, we can use the ideal gas law, which states that the product of pressure and volume is directly proportional to the product of the number of gas molecules, the ideal gas constant, and the temperature in Kelvin. The formula for the ideal gas law is:
PV = nRT
Where:
P is the pressure
V is the volume
n is the number of moles of gas
R is the ideal gas constant
T is the temperature in Kelvin
Now, let's proceed step by step to solve the problem:
Step 1: Convert the initial temperature from Celsius to Kelvin.
The initial temperature is 10 degrees Celsius. To convert it to Kelvin, add 273 to the Celsius temperature:
T1 = 10 + 273 = 283 K
Step 2: Calculate the initial pressure in Pascals (Pa).
The initial pressure is 2.8 bar. We need to convert it to Pascals since the ideal gas law requires pressure to be in SI units:
1 bar = 100,000 Pa
P1 = 2.8 x 100,000 = 280,000 Pa
Step 3: Convert the final temperature from Celsius to Kelvin.
The final temperature is 35 degrees Celsius. Convert it to Kelvin using the same procedure as before:
T2 = 35 + 273 = 308 K
Step 4: Use the combined gas law to find the final pressure.
Since the volume is unchanged, we can use the combined gas law to find the final pressure by rearranging the ideal gas law formula:
P1V1 / T1 = P2V2 / T2
Since V1 and V2 are the same, we can simplify the equation to:
P1 / T1 = P2 / T2
Plugging in the values:
P1 / 283 = P2 / 308
Solve for P2:
P2 = (P1 x T2) / T1
P2 = (280,000 x 308) / 283
Step 5: Calculate the final pressure.
Calculate the final pressure using the formula from Step 4:
P2 = (280,000 x 308) / 283 = 304,560 Pa
Therefore, when the tire warms up to 35 degrees Celsius, the air pressure in it will be approximately 304,560 Pa.