Question

.An automobile tire contains 0.033 m3 of air at a gauge pressure of 3.46 × 105 N/m2. The composition of air is about 78% nitrogen (N2) and 21% oxygen (O2), 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

To calculate the internal energy of the air in the tire, use the equation U = NKT, where U is the internal energy, N is the number of moles of gas, K is the Boltzmann constant, and T is the temperature in kelvin. The number of moles of gas can be calculated using the ideal gas law equation PV = nRT. Given the composition of air, the number of moles of nitrogen and oxygen in the tire can be determined. Finally, plug the values into the equation U = NKT to calculate the internal energy.

Step-by-step explanation:

The internal energy of the air in the tire can be calculated using the equation U = NKT, where U is the internal energy, N is the number of moles of gas, K is the Boltzmann constant, and T is the temperature in kelvin. Since the air in the tire has a gauge pressure of 3.46 × 105 N/m2, it can be assumed that the temperature remains constant and the volume of the tire does not change. The number of moles of gas can be calculated using 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. Given that the volume of the tire is 0.033 m3 and the pressure is 3.46 × 105 N/m2, we can solve for n. Assuming air is 78% nitrogen and 21% oxygen, we can calculate the number of moles of nitrogen and oxygen in the tire by multiplying the total number of moles by their respective percentages. Finally, we can calculate the internal energy using the equation U = NKT.