In Section 11.3, we will define the ratio of Cp to CV as given by the number γ. We will also show that Cp=CV+R, where the heat capacities here are per mole. Show that these definitions lead to
CV=(γ−1)R.(9.50)
Starting with the formulae CV=CV′+CV′′ and κ=(25CV′+CV′′)η, show that if CV′/R=23, then
κ=41(9γ−5)ηCV,(9.51)
which is Eucken's formula. Deduce the value of γ for each of the following monatomic gases measured at room temperatures.
[table — see PDF]
Deduce what proportion of the heat capacity of the molecules is associated with the translational degrees of freedom for these gases. (Hint: notice the word ``monatomic''.)