Question

A car tire contains 0.0380m3 of nitrogen at a gauge pressure of 2.20×105N/m2 (about 32 psi). How much more internal energy does this gas have than the same volume has at zero gauge pressure (which is equivalent to normal atmospheric pressure)? (Use Eint=52NkT for the internal energy of nitrogen, a diatomic gas.)

a) 1.15×10⁵ J
b) 2.30×10⁵ J
c) 3.45×10⁵ J
d) 4.60×10⁵ J

Answer 1

To determine the increased internal energy in nitrogen gas inside a car tire at high pressure compared to atmospheric pressure, one must use the internal energy formula for a diatomic gas and Ideal Gas Law to calculate the number of moles and thus the number of molecules in the given volume.

Step-by-step explanation:

The question asks how much more internal energy does nitrogen gas have in a car tire at a gauge pressure of 2.20×105 N/m2 (approximately 32 psi) compared to the same volume of gas at zero gauge pressure (atmospheric pressure). To find this, we can use the formula for the internal energy of a diatomic gas, which is U = (5/2)NkT, where N is the number of molecules, k is the Boltzmann constant, and T is the temperature in Kelvin.

First, we'll have to find the number of moles of nitrogen using the Ideal Gas Law, PV = nRT, where P is the absolute pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.

The gauge pressure does not include atmospheric pressure, so the absolute pressure is the gauge pressure plus the atmospheric pressure (1.013×105 N/m2). Once we have n, we can find the number of molecules by multiplying n by Avogadro's number, NA. With the number of molecules, we can then calculate the internal energy at the tire's pressure and compare it to the internal energy at atmospheric pressure to find the difference.