The molar heat capacity for an ideal gas

The molar heat capacity has the general definition 

$\mathrm{C}=\frac{1}{\mathrm{n}}\cdot \frac{\mathrm{\Delta Q}}{\mathrm{\Delta T}}$

where $n =$ number of moles, $\mathrm{\Delta Q}=$hat absorbed by the gas and $∆T=$ rise in temperature of gas. It is possible to obtain almost any set of values for$∆Q$ and $∆T$ by proper selection of a process. 

$C_v=\frac{fR}{2} and C_p=\frac{(f+2)R}{2}$