Relation Between Cp and Cv

Dear Ajay Tiwari,
SPECIFIC HEAT AND MOLAR HEAT CAPACITY

(1) Specific heat (or specific heat capacity)of a substance is the quantity of heat (in calories,joules, kcal, or kilo joules) required to raise the temperature of 1g of that substance through 1°C. It can be measured at constant pressure (C_p) and at constant volume (C_v).

(2) Molar heat capacity of a substance is the quantity of heat required to raise the temperature of 1 mole of the substance by 1°C.
∴ Molar heat capacity = Specific heat capacity × Molecular weight, i.e., C_v = c_v × M andC_p = c_p × M.

(3) Since gases on heating show considerable tendency towards expansion if heated under constant pressure conditions, an additional energy has to be supplied for raising its temperature by 1°C relative to that required under constant volume conditions, i.e.,
C_p > C_v or C_p = C_v + Work done in expansion, PV (= R)
where, C_p = molar heat capacity at constant pressure
C_p = molar heat capacity at constant volume.

(4) Some useful relations of C_p and C_v
(i) C_p – C_v = R = 2 calories = 8.314J
(ii) C_p = 3/2 R (for monoatomic gas) and C_v = 3/2 + x (for di and polyatomic gas), where x varies from gas to gas.
(iii) C_p / C_p = γ (Ratio of molar capacities)
(iv) For monoatomic gas, C_p = 3. calories  whereas, C_p = C_v + R = 5 calories
(v) For monoatomic gas, (γ) = C_p/C_v = 5/2R / 3/2R = 1.66
(vi) For diatomic gas (γ) = C_p/C_v = 7/2R / 5/2R = 1.40
(vii) For triatomic gas (γ) = C_p/C_v = 8R/6R = 1.33
All the Best & Good Luck !!
Hope this helped you immensely..
Please approve my answer if you liked it by clicking on "Yes" given below...

Cp - Cv = R

Cp /Cv = gamma

Dear Ajay Tiwari,
cp-cv=R(gas constant)
This is the required relation.........
All The Best........
Plz. approve my answer by clicking 'Yes' given below, if you loved it......... Plz. Plz. Plz. don't forget to do it.......Smile

Dear frnds. ...In respect of (Cp/Cv)=gamma We know that ....Cp=Cv+RThen...(Cv+R)/Cv =1+R/Cv And we also know that....Cv=fR/2Then...=1+2/fAnd it should be equal to gamma...

Cp/cv=gammacp=(f/2)R and cv=(1+f/2)R value of gamma.is 1+2/ffor monoatomic gases degree of freedom is 3 so gamma is 5/3

Dear Student

Most important relation between C_p and C_v are
(i) Cp - Cv = R

(ii) Cp /Cv = gamma

I hope this answer will help you.
Thanks & Regards
Yash Chourasiya