driving on a hot day causes tire pressure to rise. what is the pressure inside an automobile tire at 288, if the tire has a pressure of 30 psi at 318k? Assume that the volume and amount of air in the tire remain constant
Use Charle's law:
P1/T1=P2/T2
P V = n R T
V and n and R are constant
so
P/T = constant = 30/318
P = 288 (30/318)
To find the pressure inside an automobile tire at 288K, given that the tire has a pressure of 30 psi at 318K, you can use the ideal gas law equation:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles of gas
R = Ideal gas constant
T = Temperature in Kelvin
Since the volume and amount of air in the tire remain constant, we can rearrange the equation as:
P1 / T1 = P2 / T2
Where:
P1 = Initial pressure (30 psi)
T1 = Initial temperature in Kelvin (318K)
P2 = Final pressure (what we want to find)
T2 = Final temperature in Kelvin (288K)
Now we can substitute the values into the equation and solve for P2:
P1 / T1 = P2 / T2
30 psi / 318K = P2 / 288K
To solve for P2, cross multiply and divide:
30 psi * 288K = P2 * 318K
8640 psi*K = 318P2
Divide both sides by 318K:
8640 psi * K / 318K = P2
27.17 psi = P2
Therefore, the pressure inside the automobile tire at 288K would be approximately 27.17 psi.