the air in a steel belted tire is at a gauge pressure of 29.8 psi at a temperature of 20 degrees celsius. After the tire is driven out fast on a hot road, the temperature in the tire is 48 degrees celsius. What is the tires new gauge pressure.
Can someone please explain this step by step for me? thank you =)
but do you have to do something special since its gauge?
Use (V1/T1) = (V2/T2)
Don't forget T must be in Kelvin.
I don't have the slightest idea why I wrote that formula. There is no volume to be found but I stuck volume in the equation. I should have written
P1/T1 = P2/T2.
Since the problem starts with psig and ends with psig, I don't think the units should be changed.
To solve this problem, we can use the ideal gas law, which states that the pressure (P), volume (V), and temperature (T) of a gas are related as follows:
PV = nRT
where:
P = pressure
V = volume
n = number of moles of gas
R = ideal gas constant
T = temperature (in Kelvin)
First, let's convert the temperatures from Celsius to Kelvin:
Initial temperature: T1 = 20°C + 273.15 = 293.15 K
Final temperature: T2 = 48°C + 273.15 = 321.15 K
Next, let's consider the fact that the number of moles of gas and the volume of the tire remain constant. This means that n is constant, and we can rewrite the ideal gas law as:
P1/T1 = P2/T2
where P1 is the initial pressure and P2 is the final pressure.
Now, let's substitute the given values into the equation:
P1 = 29.8 psi (given)
T1 = 293.15 K (calculated)
T2 = 321.15 K (calculated)
P1/T1 = P2/T2
29.8 psi / 293.15 K = P2 / 321.15 K
To find P2, we can cross-multiply and solve for P2:
29.8 psi * 321.15 K = P2 * 293.15 K
P2 = (29.8 psi * 321.15 K) / 293.15 K
P2 ≈ 32.64 psi
Therefore, the tire's new gauge pressure is approximately 32.64 psi.