Two heat capacities are defined: the heat capacity at constant volume (CV) and the heat capacity at constant pressure (Cp). The formal definitions of these parameters are: Cy= CP= = = aq V;N (2) (3) P;N The ratio of Cy and Cp turns out to be a very useful quantity, specially when studying thermodynamical reversible processes involving ideal gases. For instance, the speed of sound in the air (a very important parameter in aeronautical engineering) depends on this ratio. Due to its importance, the heat capacity ratio receives a special name. Some of the names that are used for this parameter are: adiabatic index, Laplace's coefficient and isentropic expansion factor. It is defined as: = Cv (4) The goal of this problem is to determine the Laplace's coefficient of an ideal monoatomic gas. 1.) Show that: Cp - Cv = = au + P T;N (VF) P:N (5) 2.) Consider an ideal monoatomic gas. What is its Cy? 3.) Deduce its Cp. 4.) Obtain the adiabatic index of an ideal monoatomic gas.