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Ayush Kumar from Don Bosco Academy, asked a question
Subject: Physics , asked on 17/10/12

i want derivation of cp and cv for monoatomic, diatomic, triatomic..... plz answer fast its urgent 2morrow is my exam..

EXPERT ANSWER

Hansraj Rai , Meritnation Expert added an answer, on 8/11/12
306 helpful votes in Physics

Dear Student!!

Please refer the answer posted by Aman. 

Similarly you can for diatomic and tri atomic gas gases.

Diatomic gas has 5 degrees of freedom and tri atomic gas has 6 degrees of freedom.  

@ Aman - Good effort keep it up!!

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Aman Kumar , added an answer, on 28/1/12
7 helpful votes in Physics

For Monoatomic gases

No of degrees are 3.All Three are translational energies

Hence the total internal energy for 1 mole of gas is

U=(1/3KBT+. 1/3KBT+1/3KBT)NA               (Acc to law of equipartition law)(K=boltzman constant)

U=3/2KBTNA  

diff. it both sides w.r.t. T

=dU/dT=3/2R                         (R=KBNA)

but dU/dT=Cv

therefore Cv =3/2R

hence Cp=CV+R

Cp=3/2R+R

CP=5/2R

Similarly you can solve for Diatomic gases but it has 5 degree of freedom.

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Abhinav Dwivedi From Saraswati Vidya Mandir Uchchtar, added an answer, on 18/1/12
3 helpful votes in Physics

By definition of Specific heat

  Cv =dQ/(µ+dT)

by first law of thermodynamics

  dQ=dU+dW

at constant volume (dW=0) then

  dQ=dU

But U=fµRT/2, so that

dU/dT=fµR/2

Then molar specific heat at constant volume,

  Cv=dU/µdT

Here

  Cv=fR/2

Here  Cp-Cv=R

then

  Cp=Cv+R

Hence

  Cp=(f/2+1)R

now, rate of molar specific heat,

Cp/Cv=Γ  (Γ is gamma)

then

Γ=[(f/2+1)R]/(f/2)r

█ For monoatomic gas (f=3)

Cv=3R/2

Cp=5R/2

Γ=5/3

█ For diatomic gas  (f=5)

Cv=5R/2

Cp=7R/2

Γ=7/5

█ For Triatomic gas

▄Linear Structural  (f=7)

Cv=7R/2

Cp=9R/2

Γ=9/7

▄non-linear structural  (f=6)

Cv=3R

Cp=4R

Γ=4/3

Hence Proved.

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Vineeta From Pragati Vidya Peeth, added an answer, on 18/1/12
37 helpful votes in Physics

thanxxx  sir

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