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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: molar heat capacity
Forum Index -> Thermal Physics like the article? email it to a friend.  
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umang (229)

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if for an ideal gas in a process P=kV (k=const.) then prove that C = Cv + R/2
 
i am really stuck at this!!
pls help !!!

Umang
    
abhishekray07 (224)

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P=kV
PV-1=K
so now n=-1
 
now
C=Cv+ R/(1-n) for polytropic process
C=Cv+R/2
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umang (229)

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can u pls derive that formula ???
i am stuck at that formula !!!
i cant derive it !!!

Umang
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abhishekray07 (224)

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PV^{x}=k\\

\int dW=W=\int pdV\\
=k\int_{V_1}^{V_2} \frac{dV}{V^{x}}\\
solving\ this \ we \ get\\
\ W=\frac{{P_2}{V_2}-{P_1}{V_1}}{1-x}}\\

\ W= \frac{nR\Delta T}{1-x}\\
\ now \\
\ \Delta Q= \Delta U + \Delta W\\

\ C=C_v+ \frac{\Delta W}{n\Delta T}\\
\ C=C_v+ \frac{R}{1-x}\\
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NAKEWL (38)

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no need 4 all this...
just remember...specific heat
C= Cv + (P/n)dV/dT *
where P=pressure, n= no. of moles of gas,
dV/dT can be found 4rm the relation P=KV....substitute value of P wid nRT/V and find dV/dT...
put it in *...and there u get ur answer.....
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karthik2007 (3349)

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Will nip in at times to solve problems :)
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karthik2007 (3349)

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Please ask if you have doubts

edit - I am dividing throughout by ndT, and not nT

Will nip in at times to solve problems :)
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karthik2007 (3349)

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Always go from first principles for such problems, you'll never go wrong

Will nip in at times to solve problems :)
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anchitsaini (4290)

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this might help

http://www.goiit.com/posts/list/heat-thermodynamics-molar-capacity-43950.htm#217049

Impossible To be Impossible is Impossible
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umang (229)

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hey guys !
thanks for answering !
doubt cleared !!!

Umang
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