College Physics I: BIIG problem-solving method

Created Feb. 7, 2024 by C N Hiremath

Thermodynamics

  • Thermodynamics the study of heat transfer and its relationship to doing work.

 

Mechanical Equivalent of Heat

  • It is possible to change the temperature of a substance by doing work.

Work can transfer energy into or out of a system.

  • Heat is a form of energy.

1 kcal   =   4186 J

Heat added or removed from a system changes its internal energy and thus its temperature.

Work done on the system or by the system can also change the internal energy of the system.

 

Heat Transfer Methods

  • Heat transfer takes place by only three methods:

  • Conduction is heat transfer through stationary matter by physical contact.

  • Convection is the heat transfer by the macroscopic movement of a fluid.

  • Heat transfer by radiation occurs when microwaves, infrared radiation, visible light, or another form of electromagnetic radiation is emitted or absorbed.

  • The quantitative relationship between heat transfer and temperature change contains all three factors:

            Q   =   m c ΔT

where, Q is the symbol for heat transfer, m is the mass of the substance, and ΔT is the change in temperature, and c stands for specific heat and depends on the material and phase.

  • The specific heat c is a property of the substance; its SI unit is J/(kg K) or J/(kg ºC).

 

The First Law of Thermodynamics

  • The first law of thermodynamics applies the conservation of energy principle to systems where heat transfer and doing work are the methods of transferring energy into and out of the system.

  • The first law of thermodynamics states that the change in internal energy of a system equals the net heat transfer into the system minus the net work done by the system.

            ΔU   =   Q − W

where, ΔU is the change in internal energy U of the system, Q is the net heat transferred into the system, and W is the net work done by the system.

  • Sign conventions:  if Q is positive, then there is a net heat transfer into the system;

if W is positive, then there is net work done by the system.

 

Internal Energy

  • The internal energy U of a system is the sum of the kinetic and potential energies of its atoms and molecules.

  • It is the sum of atomic and molecular mechanical energy.

  • Consider a system going from State 1 to State 2.  The system has internal energy U1 in State 1, and

it has internal energy U2 in State 2, no matter how it got to either state. So the change in internal energy

ΔU   =   U2 − U1

is independent of what caused the change.

  • ΔU is independent of path.  Both Q and W depend on path, but ΔU does not.

  • Problem (E15.1):  Suppose there is heat transfer of 40.00 J to a system, while the system does 10.00 J of work. Later, there is heat transfer of 25.00 J out of the system while 4.00 J of work is done on the system. What is the net change in internal energy of the system?                                                                        ( 9.00 J )

Heat Engines

  • One of the most important things we can do with heat transfer is to use it to do work for us.

Such a device is called a heat engine.

  • Car engines and steam turbines that generate electricity are examples of heat engines.

  • It is impossible to devise a system where Qout = 0, That is, in which no heat transfer occurs to the environment.

 

Reversible Processes

  • A reversible process is one in which both the system and its environment can return to exactly the states they were in by following the reverse path.

  • Real macroscopic processes are never exactly reversible.

  • If there are any energy-dissipating mechanisms, such as friction or turbulence, then heat transfer to the environment occurs.

  • For example, heat transfer occurs spontaneously from hot to cold and never spontaneously the reverse.

 

Irreversible Process

  • Many processes occur spontaneously in one direction only, they are irreversible, under a given set of conditions. An irreversible process is one that depends on path.

  • If the process can go in only one direction, then the reverse path differs fundamentally and

the process cannot be reversible.

 

The Second Law of Thermodynamics

  • (First form): Heat transfer occurs spontaneously from higher- to lower-temperature bodies but never spontaneously in the reverse direction.

  • (Second form): It is impossible in any system for heat transfer from a reservoir to completely convert to work in a cyclical process in which the system returns to its initial state.

 

Efficiency

  • We define conversion efficiency Eeff to be the ratio of useful work output to the energy input.

            Eeff   =   W / Qh

where,  W is the net work output, and Qh is heat transfer to the engine.

  • Since the net work done by the system is

            W   =   Qh  −  Qc

  • The efficiency is given by

            Eeff   =    ( Qh  − Qc ) / Qh    =    1  −  ( Qc / Qh )

  • Note, an efficiency of 1, or 100%, is possible only if there is no heat transfer to the environment (Qc = 0 ).

  • Problem (E15.3):  A coal-fired power station is a huge heat engine. It uses heat transfer from burning coal to do work to turn turbines, which are used to generate electricity. In a single day, a large coal power station has 2.50 × 1014 J of heat transfer from coal and 1.48 × 1014 J of heat transfer into the environment. What is the efficiency of the power station?                                                                                          ( 40.8 % )  

 

Carnot Engine

  • Any heat engine employing the Carnot cycle is called a Carnot engine.

What is crucial to the Carnot cycle is that only reversible processes are used.

  • The second law of thermodynamics (third form):  A Carnot engine operating between two given temperatures has the greatest possible efficiency of any heat engine operating between these two temperatures.

  • Furthermore, all engines employing only reversible processes have this same maximum efficiency when operating between the same given temperatures.

  • What Carnot found was that for a perfect heat engine, the ratio Qc / Qh equals the ratio of the absolute temperatures of the heat reservoirs.

            Qc / Qh   =   Tc / Th

Therefore, the maximum or Carnot efficiency Eeffc   is given by

Eeffc   =   1  -   ( Tc / Th )

where, Tc and Th are in kelvins.

  • Problem (E15.4):  A nuclear power reactor has pressurized water at 300 ºC. Steam, produced in the steam generator, is used to drive the turbine-generators. Eventually the steam is condensed to water at 27 ºC and then heated again to start the cycle over. Calculate the maximum theoretical efficiency for a heat engine operating between these two temperatures.                                                                                            ( 50 % ) 

 

Heat Pumps

  • Transferring heat energy from a cold reservoir to a hot reservoir is called a heat pump.

Opposite of the natural direction!  Examples:  Air conditioners, refrigerators,

  • Heat does not spontaneously flow from cold to hot. Heat energy is transferred from a cold reservoir to a hot reservoir by doing work.

  • Coefficient of performance for heating is defined as

CPH  =   Qh / Win   =   Qh / ( Qh – Qc )   =    1 / Eeff

                    =   Th / ( Th – Tc )

  • Problem (E15.5):  A heat pump is used to warm a home. What is the best coefficient of performance possible for such a heat pump, if it has a hot reservoir temperature of 45.0 ºC and a cold reservoir temperature of −15.0 ºC?                                                                                                                 ( 5.30 ) 

  • The maximum possible coefficient of performance of a heat pump used for cooling is related to the temperatures of the hot and cold reservoirs as

CPC   =   QC / Win          =   TC / (TH - TC )

 

Entropy

  • The entropy of a system is a measure of its disorder and of the unavailability of energy to do work.

  • The change in entropy ΔS for a reversible process,

ΔSrev   =    Q / T

where, Q is the heat transfer, which is positive for heat transfer into and negative for heat transfer out of, and T is the absolute temperature at which the reversible process takes place.

  • The SI unit for entropy is joules per kelvin (J/K).

  • Entropy is a property of state. Thus the change in entropy ΔS of a system between state 1 and state 2 is the same no matter how the change occurs.

  • Problem (E15.6):  Spontaneous heat transfer from hot to cold is an irreversible process. Calculate the total change in entropy if 4000 J of heat transfer occurs from a hot reservoir at 327 ºC to a cold reservoir at −23 ºC, assuming there is no temperature change in either reservoir.                                                 ( 9 J/K ) 

  • The second law of thermodynamics stated in terms of entropy (Fourth form):  The total entropy of a system either increases or remains constant in any process; it never decreases.


BIIG: Problems & Solutions


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