1. Thermodynamics of Ideal Processes P M V Subbarao Professor Mechanical Engineering Department Entropy View of Theoretical Processes …..

2. Reversible Cycle & Origin of Thermodynamic Entropy

3. Temperature- Entropy Diagram

4. Temperature-Entropy Change -- Equations For a control mass containing a pure compressible substance undergoing a reversible process (no change in KE & PE) dU=  Q rev -  W rev = TdS - pdV TdS = dU + pdV, or Tds = du + pdv ( per unit mass)  This is the famous Gibbsian equation Eliminate du by using the definition of enthalpy h=u+pv dh = du + pdv + vdp, thus du + pdv = dh - vdp Tds = du + pdv, also Tds = dh - vdp Important: these equations relate the entropy change of a system to the changes in other properties: dh, du, dp, dv. Therefore, they are independent of the processes.

5. Entropy change of an incompressible substance For most liquids and all solids, the density is not changed as pressure changes, that is, dv=0. Gibbsian equation states that Tds=du+pdv=du, du=CdT. For an incompressible substance C p =C v =C is a function of temperature only. Integrating from state 1 to state 2 Where, C avg is the averaged specific heat over the given temperature range.

6. Entropy change during change of Phase Consider steam is undergoing a phase transition from liquid to vapor at a constant temperature. For a change from saturated liquid to saturated vapor

7. The Thermodynamics of Temperature Creation The Gibbsian equation,defines the change in specific entropy of any substance during any reversible process. Consider a control mass executing a constant volume process: The relative change in internal energy of a control mass w.r.t. change in entropy at constant volume is called as absolute temperature.

8. The Thermodynamics of Temperature Creation Consider a control volume executing a reversible constant pressure process: The relative change in enthalpy of a control volume w.r.t. change in entropy at constant pressure is called as absolute temperature.

9. Entropy change of an ideal gas From the Gibbsian equations, the change of entropy of a substance can be expressed as For an ideal gas, u=u(T) and h=h(T), du=c v (T)dT and dh=c p (T)dT and Pv=RT By Integration, the change in the entropy is or

10. Ideal Gas with constant specific heats When specific heats are constant (calorically perfect gas), the integration can be simplified: If a process is isentropic (that is adiabatic and reversible), ds=0, s 1 =s 2,

11. Isentropic Process by an idea gas with constant propeties or Are the reversible Process practicable? 100% perfection is possible but may not ne practicable..!?!!?!