Question

3. An equation for the average thermal energy per gas molecule (monoatomic or diatomic) is given by where f is the number of degrees of freedom accessible to the gas molecules. (a) How many degrees of freedom does a diatomic molecule have at low temperatures, medium temperatures, and high temperatures (consult Figure 20.11). (b) Describe what degrees of freedom are accessible (e.g., "translational but nothing else," "trans- lational + vibrational but nothing else," etc.) to the gas molecules in each of three three temperature regions (low, medium and high). Again, the discussion surrounding Figure 20.11 will be useful. (c) Is room temperature considered low, medium, or high temperature? Remember, the horizontal scale in Figure 20.11 is logarithmic.

Answer 1

DOF is temperature-dependent.

a)Diatomic molecule : 3 DOF at low temp

5 DOF at medium temp

7 DOF at a high temp

b) low temperature:: Translational(3) but nothing else so only 3 DOF

Medium temperature: translational(3) + vibrational (2)but nothing else so Total 5 DOF

high temperature : Translational(3) + Vibrational(2) +rotational(2) so total 7 DOF

c) room temperature is medium temperature

Note : Model we use on a molecule is dependent on its temperature. At low energy ( i.e at low temp ) there is minimum vibrational effect so we can treat the molecule as if a RIGID ROTATOR.however at high energies (i.e high temp) vibrational effects are involved so we should treat the molecule as SPRINGY DUMBBELL so that it can vibrate