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Challenge: Problem 2

When dealing with the ideal gas, we assume that its particles have only translational kinetic energy, with three corresponding degrees of freedom. In producing the result that U = /NT, where N is the number of particles, we seem to have /T energy for each separate degree of freedom (we have a total of 3N such degrees). When we have a molecule we would also expect there to be two extra degrees of freedom, because of the movement of each atom of a pair around the other (see fig. 8.7). Then U = /NT and the specific heat is = /N, which for one gram molecule is /R cal mole deg

Consider the graph (fig. 8.8) of experimental values of for hydrogen (H). Only around room temperature does show the expected value of /Rcal mole deg. What happens in regions A and B?

Find those items on the RESPONSE ARRAY which you would bring into your thinking about (i) region A, and (ii) region B. Which items can you then find which represent assumptions you would call into question?

1
break up of material particles into smaller particles 2
momentum or velocity space 3
energy cells that accommodate only one particle at a time 4
number of arrangements corresponding to the distribution of energy 5
mass of particles

6
translational kinetic energy 7
average thermal energy of a particle is an integral multiple of 1/2 kT 8
number of particles possible in a particular energy cell 9
internal energy states of particles 10
at absolute zero, entropy is zero

11
state of greatest probability 12
number of degrees of freedom for thermal energy 13
rotational energy 14
intrinsic structure of energy cells, such as their size and the "separation" betweeen them 15
= ( 1 / kT )

16
zero point energy of a system 17
vibrational energy 18
effective continuum of energy states 19
internal energy is the sum of the energies of the particles 20
thermal equilibrium entails maximum entropy