Prove that cp-cv=r with help of first law of thermody
Answers
To answer this question, let us assume an isobaric expansion of a gas from a temperature T1 to T2. Let T2-T1 = ∆T.
We know that for a process, change in internal energy is ∆U = n(Cv)∆T.
Work done by the gas in this process would be P∆V. But by the ideal gas law, PV=nRT.
=> P∆V = nR∆T (the other terms are constant).
Now by the definition of Cp, the heat supplied to the gas is Q=n(Cp)∆T.
By the first law of thermodynamics,
Q = ∆U + W
Substituting the values,
n(Cp)∆T = n(CV)∆T + nR∆T
=> Cp = Cv + R
=> Cp - CV = R.
Since R is a positive number, Cp - Cv > 0 or Cp > Cv.
Answer:
the heat supplied to the gas is Q=n(Cp)∆T. => Cp - CV = R. Since R is a positive number, Cp - Cv > 0 or Cp > Cv. The first law of thermodynamics states that energy can neither be created nor destroyed, only transferred.