2) A diatomic molecule which consists of two atoms can have translational, rotational, and vibrational degrees of freedom because the molecule can translate, rotate, and vibrate. However, it is known that just because a molecule is capable of rotating or vibrating does not mean that there is enough energy available to do so. The temperature has to be high enough to enable different types of motion. In that case, we say that the degree of freedom is active if the temperature is high enough or inactive if it is not. How many degrees of freedom are active in a hydrogen molecule, H2, at 500 K? 3) Write an expression for the internal energy U of a gas of N particles (that is, atoms or molecules) at temperature T in terms of N and T and any required constants, when the gas consists of a. Ne (neon atoms) b. N2 (nitrogen molecules), assuming all degrees of freedom are active. 4) Calculate the internal energy U of a liter of helium at room temperature and atmospheric pressure. Then repeat the calculation for a liter of air. 5) The equipartition theorem allows us to write U = ¤NKT, where the constant a is the number of (active) degrees of freedom per molecule and k is Boltzmann's constant. Write an expression for the change in internal energy AU. 6) What does the expression for AU from the previous problem say about AU if the temperature is constant?

2) A diatomic molecule which consists of two atoms can have translational, rotational, and vibrational degrees of freedom because the molecule can translate, rotate, and vibrate. However, it is known that just because a molecule is capable of rotating or vibrating does not mean that there is enough energy available to do so. The temperature has to be high enough to enable different types of motion. In that case, we say that the degree of freedom is active if the temperature is high enough or inactive if it is not. How many degrees of freedom are active in a hydrogen molecule, H2, at 500 K? 3) Write an expression for the internal energy U of a gas of N particles (that is, atoms or molecules) at temperature T in terms of N and T and any required constants, when the gas consists of a. Ne (neon atoms) b. N2 (nitrogen molecules), assuming all degrees of freedom are active. 4) Calculate the internal energy U of a liter of helium at room temperature and atmospheric pressure. Then repeat the calculation for a liter of air. 5) The equipartition theorem allows us to write U = ¤NKT, where the constant a is the number of (active) degrees of freedom per molecule and k is Boltzmann's constant. Write an expression for the change in internal energy AU. 6) What does the expression for AU from the previous problem say about AU if the temperature is constant?