# Restriction on the value of adiabatic exponent

My instructor stated in his lecture that the maximum value of the adiabatic exponent, $$\gamma$$, can be 5/3 which is that of a monoatomic gas and that it cannot go below 1, but why is this so?

He also stated that this can be found from the first law of thermodynamics? How is this so? I know that gamma is defined as Cp/Cv which can be thought to be heat exchanged at constant pressure / heat exchanged at constant volume

• Are you familiar with the definition of gamma in terms of the molar heat capacities at constant volume and pressure? – Chet Miller Aug 20 '19 at 19:46
• Yes....gamma is defined as Cp/Cv – Schwarz Kugelblitz Aug 20 '19 at 19:58
• Using the enthalpy version of the First Law, namely, $H=U+PV$ - I'll leave it to you to prove it - if you differentiate the enthalpy with respect to $T$, then the answer to your first question follows from the definitions $C_{P}$ and $C_{V}$ - and the value $C_{V}$ for a monoatomic gas - and the Ideal Gas Law. – Cinaed Simson Aug 20 '19 at 21:42
• Good. And how is Cv related to the number of degrees of freedom? What is the minimum degrees of freedom that a molecule can have? – Chet Miller Aug 20 '19 at 21:58
• The minimum degrees of freedom are 3 which are translational...CV=fR/2 where f is degree of freedom – Schwarz Kugelblitz Aug 21 '19 at 12:44