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Chapter 12 The Laws of Thermodynamics. Heat and work Thermodynamic cycle. Heat and work Work is done by the system: Work is done on the system :. The first law of thermodynamics Work and heat are path-dependent quantities

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Chapter 12 The Laws of Thermodynamics

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Chapter 12 the laws of thermodynamics

Chapter 12

The Laws of Thermodynamics


Chapter 12 the laws of thermodynamics

Heat and work

Thermodynamic cycle


Chapter 12 the laws of thermodynamics

  • Heat and work

  • Work is done by the system:

  • Work is done on the system :


Chapter 12 the laws of thermodynamics

  • The first law of thermodynamics

  • Work and heat are path-dependent quantities

  • Quantity Q + W = ΔEint(change of internal energy) is path-independent

  • 1st law of thermodynamics: the internal energy of a system increases if heat is added to the system or work is done on the system


Chapter 12 the laws of thermodynamics

  • The first law of thermodynamics

  • Adiabatic process: no heat transfer between the system and the environment

  • Isochoric (constant volume) process

  • Free expansion:

  • Cyclical process:


Chapter 12 the laws of thermodynamics

Chapter 12

Problem 18

Consider the cyclic process depicted in the figure. If Q is negative for the process BC and ΔEint is negative for the process CA, what are the signs of Q, W, and ΔEint that are associated with each process?


Chapter 12 the laws of thermodynamics

  • Work done by an ideal gas at constant temperature

  • Isothermal process – a process at a constant temperature

  • Work (isothermal expansion)


Chapter 12 the laws of thermodynamics

  • Work done by an ideal gas at constant volume and constant pressure

  • Isochoric process – a process at a constant volume

  • Isobaric process – a process at a constant pressure


Chapter 12 the laws of thermodynamics

  • Molar specific heat at constant volume

  • Heat related to temperature change:

  • Internal energy change:


Chapter 12 the laws of thermodynamics

  • Molar specific heat at constant pressure

  • Heat related to temperature change:

  • Internal energy change:


Chapter 12 the laws of thermodynamics

Free expansion of an ideal gas


Chapter 12 the laws of thermodynamics

  • Time direction

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


Chapter 12 the laws of thermodynamics

  • Configuration

  • Configuration – certain arrangement of objects in a system

  • Configuration for N spheres in the box, with n spheres in the left half


Chapter 12 the laws of thermodynamics

  • 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


Chapter 12 the laws of thermodynamics

  • Multiplicity

  • Multiplicity ( W ) – a number of microstates available for a given configuration

  • From statistical mechanics:


Chapter 12 the laws of thermodynamics

Multiplicity


Chapter 12 the laws of thermodynamics

Multiplicity


Chapter 12 the laws of thermodynamics

Multiplicity


Chapter 12 the laws of thermodynamics

Multiplicity


Chapter 12 the laws of thermodynamics

  • 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

  • isolatedsystems


Chapter 12 the laws of thermodynamics

  • 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 tendencyto increase in open systems


Chapter 12 the laws of thermodynamics

  • Entropy in open systems

  • In open systems entropy can decrease:

  • Chemical reactions

  • Molecular self-assembly

  • Creation of information


Chapter 12 the laws of thermodynamics

  • Entropy in thermodynamics

  • In thermodynamics, entropy for open systems is

  • For isothermal process, the change in entropy:

  • For adiabatic process, the change in entropy:


Chapter 12 the laws of thermodynamics

  • 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


Chapter 12 the laws of thermodynamics

Nicolas Léonard

Sadi Carnot

(1796–1832)

  • Engines

  • In an ideal engine, all processes are reversible and no wasteful energy transfers occur due to friction, turbulence, etc.

  • Carnot engine:


Chapter 12 the laws of thermodynamics

  • Carnot engine (continued)

  • Carnot engine on the p-V diagram:

  • Carnot engine on the T-S diagram:


Chapter 12 the laws of thermodynamics

  • Engine efficiency

  • Efficiency of an engine (ε):

  • For Carnot engine:


Chapter 12 the laws of thermodynamics

  • 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


Chapter 12 the laws of thermodynamics

  • Gasoline engine

  • Another example of an efficient engine is a gasoline engine:


Chapter 12 the laws of thermodynamics

Chapter 12

Problem 31

In one cycle, a heat engine absorbs 500 J from a high-temperature reservoir and expels 300 J to a low-temperature reservoir. If the efficiency of this engine is 60% of the efficiency of a Carnot engine, what is the ratio of the low temperature to the high temperature in the Carnot engine?


Chapter 12 the laws of thermodynamics

  • Heat pumps (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 :


Chapter 12 the laws of thermodynamics

  • 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


Chapter 12 the laws of thermodynamics

Questions?


Chapter 12 the laws of thermodynamics

Answers to the even-numbered problems

Chapter 12

Problem 36

6.06 kJ/K


Chapter 12 the laws of thermodynamics

  • Answers to the even-numbered problems

  • Chapter 12

  • Problem 56

  • −4.9 × 10−2 J

  • 16 kJ

  • 16 kJ


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