Consider a tire at 35 Celcius filled with 32 psig of O2 instead of N2. Calculate the pressure in the tire at -18 celcius?

Thanks!

I assume this problem wants you to use the van der Waals equation. Solve for n, then use the same equation to solve for the new pressure at the new conditions.

To calculate the pressure in the tire at -18 degrees Celsius, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

First, let's convert the temperature from Celsius to Kelvin. The conversion formula is: T(K) = T(°C) + 273.15.

So, for the initial temperature of 35°C:
T1 = 35°C + 273.15 = 308.15 K

For the final temperature of -18°C:
T2 = -18°C + 273.15 = 255.15 K

Now, let's convert the initial pressure of 32 psig to absolute pressure in Pascals (Pa). The conversion factor is 1 psi = 6894.76 Pa.

P1 = 32 psig * 6894.76 Pa/psi = 220630.72 Pa

Now, let's calculate the number of moles of O2 in the tire. We can use the ideal gas law equation and solve for n:

PV = nRT

n1 = (P1 * V) / (R * T1)

Where:
P1 = Initial pressure in Pa (220630.72 Pa)
V = Volume of the tire (assumed constant)
R = Ideal gas constant (8.314 J/(mol·K))
T1 = Initial temperature in Kelvin (308.15 K)

Now, we can solve for n1:

n1 = (220630.72 Pa * V) / (8.314 J/(mol·K) * 308.15 K)

To calculate the pressure at the final temperature, we can use the same equation but solve for P2:

P2 = (n1 * R * T2) / V

Substituting the known values:

P2 = (n1 * 8.314 J/(mol·K) * 255.15 K) / V

The final pressure in the tire at -18 degrees Celsius will depend on the volume of the tire. If you provide the volume, we can calculate the final pressure for you.

I hope this explanation helps you understand the process of calculating the pressure in the tire at a different temperature using the ideal gas law equation.