Here in the above question #'n'# is considered and being denoted for "degrees of freedom". In some of the cases we also use #'f'# for denoting the degrees of freedom.
For an ideal gas,
#C_V=(dU)/(dT)=[(n)/(2)]R=(R)/(gamma-1)#which is considered as equation#1#.
From the relation #C_P-C_V=R#
we rewrite it as#rArr C_P=C_V+R#, consider as equation#2#
Now the ratio of #C_P# and #C_V# is given by
#rArr gamma=(C_P)/(C_V)#
Substituting equation#1# and equation#2# in #'gamma'#, we get
#rArr gamma=(C_V+R)/(C_V)=(C_V/C_V)+(R/C_V)#
#=1+(R/C_V)#
From Equation#2#, we have
#rArr gamma=1+{R/[(n/2)R]}#
#=1+{cancel(R)/[(n/2)cancel(R)]}=1+(2/n)#
#:.gamma=1+2/n#
#NOTE:# Here #'n'# is degrees of freedom .
