Relation Between Cp and Cv

Ajay Tiwari, 12 years ago

Grade:

6 Answers

Godfrey Classic Prince

633 Points

12 years ago

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..
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KARAN ACHARYA

52 Points

12 years ago

Cp - Cv = R

Cp /Cv = gamma

Ashwin Sinha

520 Points

12 years ago

Dear Ajay Tiwari,
cp-cv=R(gas constant)
This is the required relation.........
All The Best........
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Anurag

19 Points

7 years ago

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...

Gambhir sudhakar

11 Points

6 years ago

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

Yash Chourasiya

askIITians Faculty 256 Points

3 years ago

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