What do you mean by Cp and Cv. Derive the relation between Cp and Cv.

Cp is the specific heat capacity at constant pressure and Cv is the specific heat capacity at constant volume.Consider one mole of an ideal gas in a closed cylinder with a movable piston.Suppose an amount of heat is given at constant volume so that the temperature increases by Δt

                 ΔQ=Cv × Δt

Here ΔW= 0 since volume is constant            then ΔQ = ΔU                                                                                                  let the gas be now heated at constant pressure  then ΔQ' = Cp × Δt   also ΔQ' = ΔU ×PΔv      so from above equation we get     ΔQ' = ΔQ+ PΔv                                                                                                                                                           combing above  equations we get Cp× Δt= Cv × Δt PΔv                                                                                                                                                                                    By differentiating ideal gas equation for one mole we get    PΔv =RΔt

substituting this value we get Cp-Cv= R