Topic Summaries: Thermal Physics

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Introduction
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Heat & Temperature

Temperature

Energy
- The energy due to the coordinated motion (kinetic energy) and average position (potential energy) of a large collection of particles is usually known as its mechanical energy, but is sometimes called its external energy.
- The sum of the energies due to the random motion (kinetic energy) and local position (potential energy) of a large collection of particles is known as its internal energy.
  - Two regions that can exchange internal energy are said to be in thermal contact.
  - The net transfer of internal energy between two regions in thermal equilibrium is zero.
  - Heat is the net transfer of internal energy from one region to another.
Temperature
- Temperature can be defined informally as the measure of a region's "hotness".
  - A region which is "hot" has a higher temperature than one that is "cold".
- Two regions have the same temperature when there is no net exchange of internal energy between them.
  - Heat flows from one region to another due to a difference in temperature. (Heat flows from "hot" to "cold".)
  - No heat flows between two regions with the same temperature.
- The symbol for temperature is T.
A device that can be used to measure temperature is called a thermometer.
- All thermometers measure the value of some thermometric variable that responds to changes in temperature.
- Thermometers can be classified according to the thermometric variable measured.
A temperature scale is built from …
- at least two fixed points (an upper fixed point and a lower fixed point) corresponding to the temperatures of a pair of reproduceable experiments and …
- a fundamental interval or span of numbers between the two fixed points.
The SI unit of temperature is the kelvin [K].
- Symbology
  - In current usage, the kelvin is always written in lowercase letters without a degree symbol [K].
  - In some early Twentieth Century sources it was common to see degree Kelvin [°K], but this is no longer considered acceptable.
- The kelvin is a fundamental unit; that is, it cannot be reduced to any simpler units.
- By definition, the kelvin is 1/273.16 of the thermodynamic temperature of the triple point of water; therefore …
  - the triple point of water is the upper fixed point,
  - absolute zero is the lower fixed point, and
  - 273.16 is the fundamental interval of the kelvin temperature scale.

The degree Celsius [°C] is an acceptable non SI unit.

Symbology
- Use degrees Celsius [°C] for temperatures (T).
- Use Celsius degrees [C°] for temperature intervals (ΔT).
The current definition of the degree Celsius is 1/273.16 of the thermodynamic temperature of the triple point of water like the kelvin, but …
- the triple point of water is assigned the value 0.1°C and
- absolute zero is assigned the value −273.15 °C.
The original definition of the degree Celsius is still approximately valid with …
- the normal boiling point of water as the upper fixed point,
- the normal freezing point of water as the lower fixed point, and
- 100 °C as the fundamental interval

The degree Celsius and kelvin have the same size, but assign zero to different values.

ΔT	[K]	=	ΔT	[°C]
T	[K]	=	T	[°C]	+ 273.15
T	[°C]	=	T	[K]	− 273.15

Sensible Heat
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Latent Heat

All phase changes …
- take place at a specific temperature.
- take place without a change in temperature. (There is no temperature change during a phase change.)
- involve changes in internal potential energy.
- release or absorb latent heat.
  - Endothermic phase changes absorb heat from the environment. (They are cooling processes.)
  - Exothermic phase changes release heat to the environment. (They are warming processes.)
The specific latent heat (L) of a material …
- is a measure of the heat energy (Q) per mass (m) released or absorbed during a phase change.
- is defined through the formula Q = mL.
- is often just called the "latent heat" of the material.
- uses the SI unit joule per kilogram [J/kg].
There are three basic types of latent heat each associated with a different pair of phases.

	solid-liquid	liquid-gas	solid-gas
latent heat of …	fusion	vaporization	sublimation
endothermic phase changes	melting, liquefaction*	boiling, evaporation, vaporization	sublimation
exothermic phase changes	crystallization, freezing, fusion, solidification	condensation, liquefaction*	deposition
temperature	melting point, freezing point	boiling point, dew point	sublimation point, frost point
* Use of the word liquefaction should be avoided since the starting phase is ambiguous.

Phase Diagrams
- Equilibrium can be used to describe two very different situations.
  - Static equilibrium occurs whenever the components of forces and torques acting in one direction are balanced by the components of forces and torques acting in the opposite direction.
    - A system in static equilibrium will have a constant translational and angular velocity.
  - Dynamic equilibrium occurs whenever a change in the statistical behavior of a large group of particles is balanced by an opposite change in the statistical behavior of a similarly large group of different particles.
    - A system in dynamic equilibrium will have a constant mass, pressure, temperature, and volume.
    - Dynamic equilibrium is a state where no macroscopic change is observed.
  - Phase changes occur whenever a large group of particles is out of dynamic equilibrium.
- The dynamic equilibrium phase plotted on a pressure-temperature graph is called a phase diagram.
  - Each substance has its own characteristic phase diagram.
  - The lines separating phases on a phase diagram are known as phase boundaries.
    - liquid-gas
      - The liquid-gas phase boundary is known as the vaporization curve or vapor pressure curve.
      - The value of the liquid-gas phase boundary at a given pressure is a boiling point.
      - The value of the liquid-gas phase boundary at atmospheric pressure is the normal boiling point
      - The liquid-gas phase boundary terminates at a critical point with a critical pressure and critical temperature.
        
        A gas cannot be liquefied by compression if it is hotter than its critical temperature. It will remain a gas.
    - solid-liquid
      - The solid-liquid phase boundary is known as the fusion curve or melting curve.
      - The value of the solid-liquid phase boundary at a given pressure is a melting point (or freezing point).
      - The value of the solid-liquid phase boundary at atmospheric pressure is the normal melting point (or normal freezing point).
    - solid-gas
      - The solid-gas phase boundary is known as the sublimation curve.
      - The value of the solid-gas phase boundary at a given pressure is a sublimation point.
      - The value of the solid-gas phase boundary at atmospheric pressure is the normal sublimation point.
  - The point where three phase boundaries meet is a triple point.
    - All three phases exist in dynamic equilibrium when a substance is at its triple point.
    - A gas cannot be liquefied by cooling if the pressure is less than the triple point pressure. It will go directly to the solid phase.
Thermal Expansion
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Gas Laws

The basic gas law relationships …
- The pressure of a gas is inversely proportional to its volume when temperature is constant.
  - This relationship is known as Boyle's law or Mariotte's law.
- The volume of a gas is directly proportional to its temperature when pressure is constant.
  - This relationship is known as Charles' law or Gay-Lussac's law.
- The pressure of a gas is directly proportional to its temperature when volume is constant.
  - This relationship is not associated with any particular scientist.

Combine these relationships into one law, which can be written in two different ways …


functional thermodynamics version				statistical thermodynamics version
PV = nRT				PV = NkT
where …
		P =	absolute pressure
		T =	absolute temperature
		V =	volume
and …				or …
n =	number of moles			N =	number of particles
R =	gas constant = 8.315 J/mol·K			k =	Boltzmann's constant = 1.382 J/K

Thermodynamic changes with special names …
- An isobaric process is one that takes place without any change in pressure.
- An isochoric process is one that takes place without any change in volume.
- An isothermal process is one that takes place without any change in temperature.
  - Isothermal processes are often described as "slow".
  - The pressure of a gas is inversely proportional to its volume only if the change takes place isothermally.
- An adiabatic process is one that takes place without any exchange of heat.
  - Adiabatic processes are often described as "fast".
  - The pressure of a gas is not inversely proportional to its volume if the change takes place adiabatically.

Heat Transfer

Conduction
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Convection

Convection is the transfer of heat by the flow of a fluid.
Spontaneous convection …
- is caused by the boyancy differences between
  - warmer, less dense fluid and
  - cooler, more dense fluid
- is also caused by differences in surface tension between
  - hotter regions with less surface tension and
  - cooler regions with more surface tension
- can be summarized in two simple rules
  - hot fluid rises
  - cold fluid sinks
- will result in the formation of closed loops of circulating fluid called convection cells

Forced convection …

is aided by fans, blowers, impellers, lungpower, etc.

is described by newton's law of cooling


P =	dQ	= hA (T − T₀)
P =	dt	= hA (T − T₀)

where …

P = dQ/dt is rate at which heat is transferred
h = convection heat-transfer coefficient (or film coefficient or film conductance)
A = exposed surface area
T = temperature of the immersed object
T₀ = temperature of convecting fluid

heat-transfer coefficients are determined experimentally

Radiation
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Statistical Mechanics
1. Kinetic-Molecular Theory
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2. Pressure
3. Temperature
4. Diffusion

Thermodynamics

Heat & Work
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Pressure-Volume Diagrams
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Engines
- A heat engine (often just called an engine) is a device for transforming heat into mechanical energy.
- An electric motor (often just called a motor) is a device for transforming electrical energy into mechanical energy.

Refrigerators

A refrigerator is any kind of enclosure (like a box, cabinet, or room) whose interior temperature is kept substantially lower than the surrounding environment.
Types of Refrigerators
- non-mechanical
  - for example: ice box, root cellar, wine cellar
  - are not often considered true refrigerators
- mechanical
  - vapor compression
  - vapor absorption
  - multievaporator, cascade
  - gas cycle, air cycle
  - pulse tube
  - thermoacoustic
- electronic
  - thermoelectric
  - magnetic, magneto-calorific
An air conditioner is a mechanical system in a room, building, or vehicle for controlling …
- temperature (by providing cool air),
- humidity (by providing dry air),
- and ventilation (by providing fresh air).
A heat pump is a device for moving heat mechanically.
- A heat pump can move heat against the temperature gradient (from cold to hot).
- Refrigerators and air conditioners are examples of heat pumps.
- In common usage, the tem heat pump often refers to air conditioners that can be run …
  - "forward" to cool a building in summer by extracting heat from the building and depositing it in the environment (refrigerating the building and heating the environment) or
  - "backward" to warm a building in winter by extracting heat from the environment and depositing it in the building (refrigerating the environment and heating the building).
Energy is conserved in the operation of a heat pump.
- The heat extracted from the cold reservoir (Q_c) plus the work done by the system (W) is equal to the heat deposted in the hot reservoir (Q_h).
The coefficient of performance (COP) is the ratio of the useful energy output of a system to the mechanical work required to operate it.
- The COP is a measure of the effectiveness of a mechanical device or system at performing some task.
- The COP of a heat pump used as …
  - an air conditioner or refrigerator is the ratio of the heat extracted to the mechanical work required to operate it.
  - a heater is the ratio of the heat deposited in the room to the mechanical work required to operate it.

	conservation of energy	coefficient of performance
air conditioner and refrigerator	Q_c + W = Q_h	COP = Q_c ∕ W
heat pump used for heating	Q_c + W = Q_h	COP = Q_h ∕ W

Energy & Entropy
- Entropy is
  - the degree to which energy is dissipated
  - a measure of the unavailability of heat energy for work
  - a measure of disorder
  - the number of identical microstates
  - information
Absolute Zero
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