Measurements have been made of the ultrasonic absorption and the velocity of propagation in a number of liquefied gases at temperatures from 0 to 50°C and over the frequency range 1 to 50 Mc/s. The observations in liquid carbon dioxide cover the major part of a relaxation region, centred about a frequency of approximately 10 Mc/s, and a full analysis is therefore possible in this case. The results are adequately described in terms of a relaxation of the total vibrational specific heat associated with a single relaxation time. For sulphur hexafluoride, nitrous oxide,
cyclo
propane and methyl chloride it was not possible to cover a substantial part of the relaxation region. In each case, however, the results are consistent with the assumption that the observed non-classical absorption is entirely due to vibrational relaxation and that the total vibrational specific heat relaxes with a single relaxation time. The corresponding characteristic frequencies are calculated and fall within the range 60 to 250 Mc/s. Comparisons are made between the values of the product, density (
ρ
) times relaxation time at constant temperature (ז
T
), in the gaseous and liquid states for the above substances and for others, where adequate data is available. It is found that for a given temperature the ratio (
ρז
T
)
liquid
(
ρז
T
)
gas
is greater than, but close to, unity. It is concluded that vibrational transitions in liquids which are not highly associated occur by the mechanism of binary collisions between molecules. The quantity (
ρז
T
√
T
)
–1
, which can be taken as a measure of the collision efficiency, increases with increasing temperature for non-polar liquids, but appears to depend very little on temperature for highly polar ones.
Finite-size scaling and bulk critical behavior of a quantum spherical model with a long-range interaction: entropy, internal energy and specific heat
