second law

second law of thermodynamics

1. M Sc Engineering in Energy Systems Planning and Management I/I THERMO-FLUID ENGINEERING Second Law of Thermodynamics

2. Why Second Law of Thermodynamics? First law of thermodynamics explains thermodynamic processes with reference to mass conservation and energy conservation. It deals with the quantitative aspect of the energy and gives the only condition that any process is possible provided that the total energy remains constant. But some processes in nature cannot occur although energy conservation principle is satisfied. In this regard, second law of thermodynamics deals with quality or nature of energy and defines the direction of the process in which the system can proceed. THERMO-FLUID ENGINEERING

3. Example 1 According the first law of thermodynamics, for a cyclic process net heat transfer is equal to net work transfer. But any real device, even operating on a cycle, cannot convert heat supplied to it completely into output work. Hence, the second law of thermodynamics explains why any real engine cannot operate without heat loss. Example 2 THERMO-FLUID ENGINEERING

4. Example 3 Work always produces some heat itself. But the reverse process i.e., the self conversion of heat to work (without any device) cannot occur. The second and third examples discussed above present the basic nature or inherent tendency of a system (or a process); that most of the processes in nature proceed in only direction. Such directional feature of the processes cannot be explained only with the first law of thermodynamics. THERMO-FLUID ENGINEERING

5. Entropy The main feature of the second law of thermodynamics is that it defines the directions of the processes. Second law of thermodynamics defines the direction of the process with reference to the system property called entropy . System itself tends to undergo a process from less uncertain or less random state to more uncertain or more random state. But the reverse direction is not possible. High grade of energy (work) itself get converted into low grade of energy (heat) and the reverse direction is not possible (without nay device) The property of a system which gives a measure of molecular randomness, disorder or uncertainty existing in a system is called entropy. It is an extensive property and is denoted by S . THERMO-FLUID ENGINEERING

6. Second Law of Thermodynamics for an Isolated System Entropy of an isolated system always increases or may remain constant (in an ideal process). Any isolated system can proceed in the direction in which its randomness or uncertainty i.e., entropy increases. This feature of the isolated system can be stated as the second law of thermodynamics as THERMO-FLUID ENGINEERING The difference between entropies at the final state and the initial state during any process is called entropy production or entropy generation and is denoted by  S gen .

7. THERMO-FLUID ENGINEERING According to second law of thermodynamics, during any real process net entropy change is always greater than or equal to zero, i.e , for any process between state 1 and state 2, Reversible and Irreversible Processes During any process if S 2 = S 1 ; the reverse process is also possible because entropy is same for both forward and reverse direction. Hence the process is called reversible process . S 2  S 1 During any process, if S 2 > S 1 , i.e., entropy increases in forward direction, then the reverse direction is not possible because any real process can not result in decrease in entropy. Hence the process is called an irreversible process . We can rewrite the above Equation in equivalent from to avoid inequality sign as

8. THERMO-FLUID ENGINEERING A process is said to be a reversible process if the initial conditions of both the system and surroundings can be restored by the reverse action such that net change in entropy is zero for both forward and reverse process. A process is said to be an irreversible process , if the initial conditions of both the system and surroundings cannot be restored (certain effects are left either on the system or on the surroundings) by the reverse action. In this case entropy of the system increases in forward process and therefore reverse direction is not possible.

9. THERMO-FLUID ENGINEERING Entropy Relations Applying state postulate, we can determine the internal energy of a system if its volume and entropy are given as U = U (S,V) The change in internal energy during any process is then given as The first partial derivative is equal to the temperature and the second partial derivative is equal to the negative of the pressure, i.e., Substituting T and P in the above Equation, ……… Gibbs Equation

10. THERMO-FLUID ENGINEERING Rearranging Gibbs equation, we can get the expression for the change in entropy as The control mass formulation of the second law of thermodynamics gives the expression for the change in entropy of the control mass because of heat transfer and work transfer. Control Mass Formulation of Second Law of Thermodynamics For this formulation, we first find out the effects of heat transfer and work transfer separately on the entropy of the control mass and then we can develop the general expression and statement for the second law of thermodynamics for a control mass.

11. THERMO-FLUID ENGINEERING Contribution of Heat Transfer on Entropy To determine the effect of heat transfer on entropy, we consider a system having infinite heat capacity such that its temperature is unaffected by the heat transfer. Such an idealized system which can interact with its surroundings only by heat transfer (but not work transfer) is called a reversible heat transfer reservoir and is specified by its temperature T i .

12. THERMO-FLUID ENGINEERING Substituting W = PdV = 0 into Gibbs Equation, we get Applying first law of thermodynamics, we get Substituting dU into the above Equation, we get an expression for the change in entropy due to a reversible heat transfer process as It shows that entropy of a system increase if heat is supplied to it and decrease if it loses heat.

13. THERMO-FLUID ENGINEERING Contribution of Work Transfer on Entropy To determine the effect of work transfer on entropy, we consider a system having infinite work capacity such that its pressure is unaffected by the work transfer. Such an idealized system which can interact with its surroundings only by work transfer (but not heat transfer) is called a reversible work transfer reservoir and is specified by its pressure P i . Applying first law of thermodynamics for a reversible work transfer reservoir, we get Substituting dU into Gibbs Equation, we get an expression for the change in entropy due to a reversible work transfer process as

14. THERMO-FLUID ENGINEERING It shows that work transfer does not have any contribution on the entropy of the system. Since the total change in entropy of the isolated system is given by the sum of the change in entropy of the control mass, the change in entropy of the reversible heat transfer reservoirs and the change in entropy of the reversible work transfer reservoirs, i.e., Control Mass Formulation Now, applying second law of thermodynamics for the isolated system

15. THERMO-FLUID ENGINEERING If (  Q i ) RHTRS is the heat supplied to the reservoir at temperature T i , that is supplied by the control mass, therefore, The above Equation reduces to With reference to the above Equation, second law of thermodynamics for a control mass can be stated as, The change in entropy of a control mass is greater than or equal to the sum of heat transfers divided by the corresponding boundary absolute temperatures.

16. THERMO-FLUID ENGINEERING The above can also be expressed in terms of entropy generation to avoid inequality sign as The above Equations can also be expressed in terms of rate as

17. THERMO-FLUID ENGINEERING Control Volume Formulation of Second Law of Thermodynamics Control volume formulation of second law of thermodynamics gives the expression for the change of entropy of a control volume due to mass transfer as well as energy transfer. The effect of mass transfer on the entropy can be determined by evaluating properties of working substance at the inlet and outlet. The effects heat transfer and work transfer on the entropy of the control volume is similar to that for the control mass. Therefore, we can state the second law of thermodynamics for a control volume as The change in entropy of a control volume minus the net entropy change of working substance due to mass transfer is greater than or equal to the sum of heat transfers divided by the corresponding boundary absolute temperatures.

18. THERMO-FLUID ENGINEERING The above Equation can also be expressed in terms of entropy generation to avoid inequality sign as

19. THERMO-FLUID ENGINEERING Isentropic Efficiency of Steady Flow Devices The process occurring in any steady flow device will be isentropic if it does not involve any kind of losses (frictional loss, heat loss, etc) therefore isentropic process is an ideal process. But the process occurring in any real device involves losses and the real process differs from the idealized isentropic condition. The performance of the real device is compared with the idealized device (isentropic) with reference to isentropic efficiency. Isentropic Efficiency of a Turbine In case of work producing device real work is always less than the isentropic work output because of losses. Hence, the isentropic efficiency of a turbine is defined as the ratio of work output from a real turbine and the work that would have been produced when the turbine operates under isentropic condition, i.e.,

20. THERMO-FLUID ENGINEERING Isentropic Efficiency of a Pump/Compressor In case of work consuming device real work is always more than the isentropic work input because we have to increase work input to overcome the losses to get the same desired output effect. Hence, the isentropic efficiency of a pump or compressor is defined as the ratio of the work that would have been required when the pump/compressor operates under isentropic condition to work required for the real pump/compressor and, i.e., Isentropic Efficiency of a Nozzle Similarly, the isentropic efficiency of a nozzle is defined as the ratio of the kinetic energy of the fluid at the real nozzle exit to the kinetic energy value at the exit of an isentropic nozzle for the same inlet state and exit pressure, i.e.,