Entropy and the Second Law of Thermodynamics Chapter 20 Entropy and the Second Law of Thermodynamics

Time direction Irreversible processes – processes that cannot be reversed by means of small changes in their environment

Configuration Configuration – certain arrangement of objects in a system Configuration for N spheres in the box, with n spheres in the left half

Microstates Microstate – one of the ways to prepare a configuration An example of 4 different microstates for 4 spheres in the box, with 3 spheres in the left half

Multiplicity Multiplicity ( W ) – a number of microstates available for a given configuration From statistical mechanics:

Multiplicity

Multiplicity

Multiplicity

Multiplicity

Entropy For identical spheres all microstates are equally probable Entropy ( S ), see the tombstone:

Entropy For identical spheres all microstates are equally probable Entropy ( S ), see the tombstone: For a free expansion of 100 molecules Entropy is growing for irreversible processes in isolated systems

Entropy Entropy, loosely defined, is a measure of disorder in the system Entropy is related to another fundamental concept – information. Alternative definition of irreversible processes – processes involving erasure of information Entropy cannot noticeably decrease in isolated systems Entropy has a tendency to increase in open systems

Entropy in cosmology In modern cosmology, our universe is an isolated system, freely (irreversibly) expanding: total entropy of the universe increases and gives time its direction The evolution equation of the universe (the Friedman equation) has two solutions (positive t and negative t) – entropy is increasing in two time directions from a minimum point

Entropy in open systems In open systems entropy can decrease: Chemical reactions Molecular self-assembly Creation of information

Entropy in thermodynamics In thermodynamics, entropy for open systems is The change in entropy is For isothermal process, the change in entropy: For adiabatic process, the change in entropy:

Entropy as a state function First law of thermodynamics for an ideal gas: For irreversible processes, to calculate the change in entropy, the process has to be replaced with a reversible process with the same initial and final states or use a statistical approach

The second law of thermodynamics In closed systems, the entropy increases for irreversible processes and remains constant for reversible processes In real (not idealized) closed systems the process are always irreversible to some extent because of friction, turbulence, etc. Most real systems are open since it is difficult to create a perfect insulation

Engines In an ideal engine, all processes are reversible and no wasteful energy transfers occur due to friction, turbulence, etc. Carnot engine: Nicolas Léonard Sadi Carnot (1796–1832)

Carnot engine (continued) Carnot engine on the p-V diagram: Carnot engine on the T-S diagram:

Engine efficiency Efficiency of an engine (ε): For Carnot engine:

Perfect engine Perfect engine: For a perfect Carnot engine: No perfect engine is possible in which a heat from a thermal reservoir will be completely converted to work

Stirling engine Another example of an efficient engine is the Sterling engine: Robert Stirling (1790 - 1878)

Refrigerators In an ideal refrigerator, all processes are reversible and no wasteful energy transfers occur due to friction, turbulence, etc. Performance of a refrigerator (K): For Carnot refrigerator :

Perfect refrigerator Perfect refrigerator: For a perfect Carnot refrigerator: No perfect refrigerator is possible in which a heat from a thermal reservoir with a lower temperature will be completely transferred to a thermal reservoir with a higher temperature

Answers to the even-numbered problems Chapter 20: Problem 6 2.75 mol

Answers to the even-numbered problems Chapter 20: Problem 22 (a) 31%; (b) 16 kJ

Answers to the even-numbered problems Chapter 20: Problem 34 (a) 49 kJ; (b) 7.4 kJ

Answers to the even-numbered problems Chapter 20: Problem 52 (a) 93.8 J; (b) 231 J