Consider 1.5 mol of pure nitrogen gas N2 which we will treat as a diatomic ideal gas. From 100 K to 1000 K, the gas has three translational and two rotational degrees of freedom. Above 1000 K, there are two additional vibrational degrees of freedom. The molar mass of N2 is 0.028 kg/mol. a. If the nitrogen molecules have an rms translational molecular speed of 511 m/s, what is the temperature of the gas? b. What is the internal energy U of the nitrogen gas at the temperature from part a? c. If the nitrogen gas has a pressure of 1.2 atm, what volume (in liters) does it occupy at the temperature from part a? d How much heat would be required to raise the temperature of the gas from 1500 K to 1800 K, at a constant volume? Remember that vibrational degrees of freedom are active at these temperatures.

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Maxwell speed distribution

Maxwell-Boltzmann distribution or commonly known as Maxwell speed distribution, explains the division of the energy levels of the molecules of an ideal gas on the basis of the statistical theory. In 1859, Scottish physicist James Clerk Maxwell established the context for the distribution of molecular velocities for random molecules moving in a closed environment. This theory was generalized in 1871 by German physicist Ludwig Boltzmann. He improvised the theory to express the distribution of energy levels among different molecules.