Question

The 1st Law of Thermodynamics can be written in the differential form dQ = dU + PdV . i) By expressing dU in terms of dT and dV, show that dQ/dT = (partial U / partial T)_V + [(partial U / partial V)_T + P] dV/dT . ii) Hence show that for one mole of an ideal gas, the heat capacities CP and CV differ by the Gas Constant, R. iii) Show that CP - CV can be also be expressed as CP - CV = -T (partial V / partial T)_P^2 (partial P / partial V)_T = (TV eta^2) / kappa

          The 1st Law of Thermodynamics can be written in the differential form
dQ = dU + PdV .

i) By expressing dU in terms of dT and dV, show that

dQ/dT = (partial U / partial T)_V + [(partial U / partial V)_T + P] dV/dT .

ii) Hence show that for one mole of an ideal gas, the heat capacities CP and CV differ by the Gas Constant, R.

iii) Show that CP - CV can be also be expressed as CP - CV = -T (partial V / partial T)_P^2 (partial P / partial V)_T = (TV eta^2) / kappa

The 1st Law of Thermodynamics can be written in the differential form
dQ = dU + PdV .

i) By expressing dU in terms of dT and dV, show that

dQ/dT = (partial U / partial T)V + [(partial U / partial V)T + P] dV/dT .

ii) Hence show that for one mole of an ideal gas, the heat capacities CP and CV differ by the Gas Constant, R.

iii) Show that CP - CV can be also be expressed as CP - CV = -T (partial V / partial T)P^2 (partial P / partial V)T = (TV eta^2) / kappa

Added by Enrique C.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Shaiju T

05/10/2022

Step 1

The 1st Law of Thermodynamics can be expressed as dQ = dU + PdV, where dQ is the differential heat added to the system, dU is the differential change in internal energy, and PdV is the work done by the system. Show more…

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The 1st Law of Thermodynamics can be written in the differential form dQ = dU + PdV. i) By expressing dU in terms of dT and dV, show that dQ/dT = (partial U/partial T)_V + [(partial U/partial V)_T + P] dV/dT. ii) Hence show that for one mole of an ideal gas, the heat capacities Cp and Cv differ by the Gas Constant, R. iii) Show that Cp - Cv can be also be expressed as Cp - Cv = -T (partial V/partial T)^2_P (partial P/partial V)_T = (TVeta^2)/kappa.