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

• -14

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

• 10

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

• 6
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