Define molar specific heat capacities.

Explanation

(a) Linear molecule :
Energy of one mole ` = ( 7)/(2 ) kT xx N_(A) = (7)/(2) RT `
` C_V = ( dU )/(dT ) = ( d )/(dT ) [ 7/2 RT ]`
`C_v =7/2 R `
`C_p = C_v + R = 7/2 R+R =(9R )/(2)`
` therefore gamma = ( C_p )/( C_(V )) = ((9)/(2)R )/((7)/(2)R) = 9/7 = 1.28 `
(b ) Non linear molecule :
Energy of a mole `=6/2 kT xx N_(A) = 6/2 RT = 3RT `
`C_V = (dU )/(dT ) = 3R `
`C_p = C_v +R = 3R +R = 4R `
` therefore gamma = (c_p )/(C_(v)) = ( 4R) /( 3R ) = (4)/(3 ) = 1.33`
Note that according to kin e tic theory model of gases the specific heat capacity at constant volume and constant pressure are independent of temperature. But in reality it is not sure. The specific heat capacity varies with the temperature.