Question

What is the relation between Cp and Cv for 2 moles of an ideal gas ?
PLEASE WRITE DOWN THE DERIVATION ALSO !!! And I will mark the answer as brainliest!!!
Thanks in advance !

Answer 1

Cp - Cv = R 
This is a standard relation for one mole.  For two moles the difference will be  = 2 R.

In general  Cp - Cv = n R      ---- (0)
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We know   PV = n R T,       V = (nR/P) * T   --- (1)
  At constant pressure,  ΔV/ΔT = nR/P    --- (2)

From first law of thermodynamics, we have that 
     ΔQ = ΔU + W  = ΔU + P ΔV      ---- (3)
We know that the internal energy U and the change in it ΔU, are entirely dependent on the temperature for the same amount of substance.  So it does not depend on the pressure or volume.

Cp = [ ΔQ/ΔT ]_P=const
      = [ ΔU/ΔT ]_P=const   +  P * [ ΔV/ΔT ]_P=const 
      = ΔU/ΔT + P * n R/P  = ΔU/ΔT + n R

Cv = [ ΔQ/ΔT ]_V=const
      = [ ΔU/ΔT ]_V=const + P [ ΔV/ΔT ]_V=const
      = ΔU/ΔT + 0

Hence  Cp = Cv  + n R

Answer 2

Answer:

Explanation:

H=u+pv

H=u+mrt

dh=dut+mrdt

Mcpdt=mcvdt+mrdt

Cp=cv+r

Cp-cv=r