Chapter21 Entropy and the Second Law of Thermodynamics

21-1 Some One – Way Processes If an irreversible process occurs in a closed system, the entropy S of the system always increase;it never decreases. There are two equivalent ways to define the change in entropy of a system: (1) In terms of the system’s temperature and the energy it gains or loses as heat (2) By counting the ways in which the atoms or molecules that make up the system can be arranged.

21-2 Change in Entropy The change in entropy of a system is To apply Eq.21-1 to the isothermal expansion Q is the total energy transferred as heat during the process

To find the entropy change for an irreversible process occurring in a closed system,replace that process with any reversible process that connects the same initial and final states.Calculate the entropy change for this reversible process with Eq.21-1.

Sample Problem 21-1 Substituting n=1.00 mol and V f /V i =2

Sample Problem 21-2 Step 1. Step 2.

Entropy as a State Function There are related by the first law of thermodynamics in differential form(Eq.19-27) Solving for dQ then leads to The entropy change is

21-3 The Second Law of Thermodynamics We can calculate separately the entropy changes for the gas and the reservoir: We can modify the entropy postulate of Section 21-1 to include both reversible and irreversible processes: If a process occurs in a closed system,the entropy of the system increases for irreversible processes and remains constant for reversible processes.It never decreases.

The second law of thermodynamics and can be written as 21-4 Entropy in the Real World: Engines A Carnot Engine In an ideal engine,all processes are reversible and no wasteful energy transfers occur due to,say, friction and turbulence.

We must have for a complete cycle Efficiency of a Carnot Engine

No series of processes is possible whose sole result is the transfer of energy as heat from a thermal reservoir and the complete conversion of this energy to work. Led to the following alternative version of the second law of thermodynamics: Stirling Engine

Sample Problem 21-3 (a) (b) (c) (d) (e)

Sample Problem 21-4 PROBLEM - SOLVING TACTICS Heat is energy that is transferred from one body to another body owing to a difference in the temperatures of the bodies. Work is energy that is transferred from one body to another body owing to a force that acts between them.

21-5 Entropy in the Real World: Refrigerators In an ideal refrigerator,all processes are reversible and no wasteful energy transfers occur due to,say, friction and turbulence. An ideal refrigerator: (coefficient of performance,any refrigerator)

The net entropy change for the entire system is No series of processes is possible whose sole result is the transfer of energy as heat from a reservoir at a given temperature to a reservoir at a higher temperature. Another formulation of the second law of thermodynamics: (coefficient of performance,Carnot refrigerator.)

21-6 The Efficiencies of Real Engines An efficiency is greater than : If Eq is true,from the definition of efficiency From the first law of thermodynamics:

21-7 A Statistical View of Entropy Extrapolating from six molecules to the general case of N molecules The basic assumption of statistical mechanics is: All microstates are equally probable Sample Problem 21-5

Probability and Entropy A relationship between the entropy S of a configuration of a gas and the multiplicity W of that configuration. The Stirling’s approximation is : Sample Problem 21-6

REVIEW & SUMMARY Calculating Entropy Change The change in entropy of a system is Q is the total energy transferred as heat during the process The entropy change is

The Second Law of Thermodynamics The second law of thermodynamics and can be written as Engines Refrigerators

Entropy from a Statistical View Extrapolating from six molecules to the general case of N molecules A relationship between the entropy S of a configuration of a gas and the multiplicity W of that configuration. The Stirling’s approximation is :