Question

(20%) Problem 5: An SUV tire contains 0.037 m? of air at a gauge pressure of 2.67 10 N/m? The composition of air is about 78% nitrogen (N) and 21% oxygen (O), both diatomic molecules How much more internal energy, in joules, does the air in the tire have than the same volume of air has at zero gauge pressure outside the tire?

Answer 1

the change in internal energy (ΔU) will be zero, and the air in the tire will have the same internal energy as the same volume of air at zero gauge pressure outside the tire.

Step-by-step explanation:

To solve this problem, we need to calculate the internal energy difference between the air inside the tire and the air outside the tire.

First, we need to calculate the number of moles of nitrogen and oxygen in the tire. Let's assume that the volume of the tire remains constant at 0.037 m^3.

The molar mass of nitrogen (N2) is 28 g/mol, and the molar mass of oxygen (O2) is 32 g/mol.

The mass of nitrogen in the tire can be calculated as follows:

Mass of nitrogen = volume of air * percentage of nitrogen * molar mass of nitrogen

= 0.037 m^3 * 0.78 * (28 g/mol)

= 0.8172 g

Similarly, the mass of oxygen in the tire can be calculated as follows:

Mass of oxygen = volume of air * percentage of oxygen * molar mass of oxygen

= 0.037 m^3 * 0.21 * (32 g/mol)

= 0.25152 g

Next, we need to calculate the number of moles of nitrogen and oxygen in the tire.

The number of moles can be calculated using the formula:

Number of moles = mass of substance / molar mass

Number of moles of nitrogen = mass of nitrogen / molar mass of nitrogen

= 0.8172 g / (28 g/mol)

= 0.029186 mol

Number of moles of oxygen = mass of oxygen / molar mass of oxygen

= 0.25152 g / (32 g/mol)

= 0.007860 mol

Now we can calculate the change in internal energy. The change in internal energy (ΔU) can be calculated using the formula: ΔU = (ΔUnitrogen + ΔUoxygen) Where ΔUnitrogen and ΔUoxygen are the changes in internal energy for nitrogen and oxygen, respectively.

The change in internal energy for a gas can be calculated using the formula:

ΔU = (3/2 * n * R * ΔT)

Where n is the number of moles, R is the ideal gas constant (8.314 J/(mol·K)), and ΔT is the change in temperature.

Since the temperature remains constant in this case, the change in internal energy for both nitrogen and oxygen will be zero. This is because the temperature inside and outside the tire is assumed to be the same.

Therefore, the change in internal energy (ΔU) will be zero, and the air in the tire will have the same internal energy as the same volume of air at zero gauge pressure outside the tire.