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He concluded the mathematical relationships of the temperature Cv and Cp

He concluded the mathematical relationships of the temperature Cv and Cp
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Answer #1

To prove that Cp - Cv = R

Where Cp = Heat capacity of constant pressure

Cv = Heat capacity at constant volume

R = Gas constant

If n = 1 mole, then from first law of thermodynamics, we have,

dQ = dU + PdV –(1)

taking V = constant , then dV = 0

then from equation (1), we have

(dQ)v = (dU)v

Dividing both sides by dT and taking V as constant

Then from equation (1) we have

dQ = dU + PdV

Dividing both sides by dT and taking P as constant

Then from equation (4) we have

From one mole of gas equation , we have

PV = nRT

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