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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


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

  • 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


  • 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

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?


  • Work done by an ideal gas at constant temperature

  • Isothermal process – a process at a constant temperature

  • Work (isothermal expansion)


  • 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


  • Molar specific heat at constant volume

  • Heat related to temperature change:

  • Internal energy change:


  • Molar specific heat at constant pressure

  • Heat related to temperature change:

  • Internal energy change:


Free expansion of an ideal gas


  • 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:

  • For a free expansion of

  • 100 molecules

  • Entropy is growing for

  • irreversible processes in

  • isolatedsystems


  • 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


  • 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

  • For isothermal process, the change in entropy:

  • For adiabatic process, the change in entropy:


  • 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


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:


  • 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


  • Gasoline engine

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


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?


  • 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 :


  • 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


Questions?


Answers to the even-numbered problems

Chapter 12

Problem 36

6.06 kJ/K


  • Answers to the even-numbered problems

  • Chapter 12

  • Problem 56

  • −4.9 × 10−2 J

  • 16 kJ

  • 16 kJ


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