Thermodynamics I

Thermodynamics I

Temperature

• Thermal Equilibrium and Temperature. Temperature scales

• Absolute Temperature Scale. The Ideal-Gas Law

• The Kinetic Theory of Gases. Pressure and Temperature

Heat

• Heat. Heat capacity and Specific Heat

• Change of Phase and Latent Heat

• Thermal expansion and Phase Diagrams

• Heat Transfer

• Transport Laws

References: Tipler; wikipedia, Britannica

References: Tipler; wikipedia,…

Thermodynamics II

The First Law of Thermodynamics

• Heat and Work. First Law of Thermodynamics

• Heat and Work on Quasi-Static Processes for a Gas.

The Second Law of Thermodynamics

• Heat Engines and the Second Law of Thermodynamics

• Refrigerators and the Second Law of Thermodynamics

• The Carnot Engine

• Heat Pumps

• Irreversibility and disorder. Entropy

Temperature Thermal Equilibrium and Temperature.

Temperature scales

References: Tipler; Britannica

A thermometer is any of class of instrument that measures the temperature. Temperature is the physical magnitude that is measured by thermometers.

A physical property that changes with the temperature is called a thermometric property- most solids an liquids expand when they are heated- electrical resistance change when is heated- in a gas pressure and volume change when it is heated - radiation from the surface of a body depends on the surface temperature-……

Our sense of touch can usually tell us if an object is hot or cold. Usually we need get in touch –physical contact- to appreciate if a body is hot or cold.

But our perception is very subjective.

Temperature: measure of hotness and coldness in terms of any arbitrary scales and indicating the direction which energy spontaneously flows (from a hotter body to a colder one)

Temperature


Thermal contact: Heat energy is transferred between the bodies in thermal contact

Thermal equilibrium: When the thermometric properties of the bodies in thermal contact do not change

If two objects are in thermal equilibrium with a third, then they are in thermal equilibrium each other (Zeroth Law of thermodynamics)

Two objects are defined to have the same temperature if they are in thermal equilibrium with each other. Temperature may be defined as the property of a system that determines whether it is in thermal equilibrium with other system.

Temperature is one of the seven basic physical quantities in term of which all other physical quantities are defined. It is an “intensive” property, as pressure or density. Length, mass are “extensive”

Thermodynamics. Temperature

• Temperature scalesCalibration of a thermometer: Reproducibility and Reliability.

When the thermometric property changes lineally with the temperature, two fixed points can be used to calibrate the thermometer.

Ice point temperature (normal freezing point of water)

Steam-point temperature : normal boiling point of water

Centigrade Temperature Scale (Celsius scale) Fahrenheit Temperature Scale Absolute Temperature Scale

Derive and check the above expressions to convert Fahrenheit degrees temperature to centigrade degrees temperature and the inverse relationship. The same to convert Kelvin scale to centigrade. Apply to obtain the Fahrenheit normal human temperature if it is 36.5 Celsius degrees

)32t(t

32tt

F9

5C

C5

9F

15.273 CtT

Thermodynamics. Absolute Temperature Scale. Kelvin Scale.

It is possible to define a temperature scale in a independent way of the used thermometric substance

A constant-volume gas thermometer

Temperature of the boiling point of sulfur measured with constant-volume gas thermometers . P100 is the pressure of the gas at 100ºC

Plot of pressure versus temperature for a gas, as measured by a constant-volume gas thermometer. When extrapolated to zero pressure, the plot intersects the temperature axis at the showed value of - 273.25 ºC

The ideal-gas temperature scale is defined so that the temperature of the triple point state is 273.16 kelvins, K.

The triple point of water is the unique temperature and pressure at which water, water vapor and ice coexist in equilibrium. [0.01 ºC and 4.58 mmHg]T

Thermodynamics. Ideal Gas Law

The properties of gas samples that have low densities led to the definition of the ideal-gas temperature scales. The behavior of gases at this low densities was described (1) by Boyle´s Law (1661)

PV = constant (for a constant temperature)

(2) by Charles and Gay-Lussac Law (about 1800)

P = C1 T (for a constant volume)

V = C2 T (for a constant pressure) T absolute temperatures; C1 and C2 constants

Ideal Gas-Law

TRnPV

n = amount of gas expressed in moles

R : Universal gas constant

R = 8.314 J/(mol • K) = = 0.082 atm • L/(mol • K)The temperature of 0º (273.15 K) and the pressure of 1 atm are often referred as standard condition.

Equation of state of ideal gas

A mole (mol) of any substance is the amount of substance that contains the Avogadro number, NA, of atoms or molecules, defined as the number of carbon atoms in 12 g of 12C.

Thermodynamics. Dealing with the Ideal Gas Law

Ideal Gas-LawTRnPV n = m/ M [mass of the substance in g/molecular mass] mol R = 8.314 J/(mol • K) = 0.082 atm • L/(mol • K)

Equation of state of ideal gas

density

TRM

TRP

What is the density of dry air at standard conditions of pressure and temperature?. The same at 20ºC; The same at 20ºC and 933 mb. Molecular mass of dry air: 28.97 g.

A gas has a volume of 2 L, a temperature of 30ºC, and a pressure of 1 atm. When the gas is heated to 60ºC and compressed to a volume of 1.5 L, what is the new pressure

The mass per mole of a substance is called its molar mass. (The terms molecular mass or molecular weight are sometimes used

An automobile tire is filled to a gauge pressure of 200 kPa when its temperature is 20ºC. After the car has been driven at high speeds, the tire temperature increases to 50ºC. (a) Assuming that the tire volume does not change, find the gauge pressure in the tire (b) Calculate the gauge pressure if the volume of the tire expands by 10%.

Thermodynamics. The Kinetic Theory of Gases. Molecular Interpretation of Pressure and Temperature

Referenceshttp://en.wikipedia.org/wiki/Image:Translational_motion.gif

Goal : To relate macroscopic point of view aboutt pressure and temperature with the microscopic motion.

For a solid, these microscopic motions are principally the vibrations of its atoms about their sites in the solid. For an ideal monatomic gas, the microscopic motions are the translational motions of the constituent gas particles. For a multiatomic gas, vibrational and rotational motion should be included too.

The kinetic theory of gases is able us to establish quantitatively the relationship between pressure and temperature with molecular motion for gases

The pressure that a gas exerts on its container is due to collisions between gas molecules and the container walls. This pressure is a force per unit of area and, by Newton´s second law, this force is the rate of change of momentum of the gas molecules colliding with the walls.

Crystalline Solids

The absolute temperature is a measure of the average kinetic energy of the molecules.

http://en.wikipedia.org/wiki/Ideal_gas

http://en.wikipedia.org/wiki/Vibration

Thermodynamics I

Temperature


• Absolute Temperature Scale. The Ideal-Gas Law

• The Kinetic Theory of Gases. Pressure and Temperature

Heat

• Heat. Heat capacity and Specific Heat

• Change of Phase and Latent Heat

• Thermal expansion and Phase Diagrams

• Heat Transfer

• Transport Laws

References: Tipler; wikipedia, Britannica

* The exceptions occurs during a change of phase

Thermodynamics. Heat. Heat capacity and Specific Heat

Heat is the energy that is being transferred from one system to another as a result of difference in temperature.

If two bodies at different temperature are brought together, energy is transferred –i.e. heat flows- from the hotter body to the colder. The effect of this transfer of energy usually, but non always*, is an increase in the temperature of the colder body and an decrease of the hotter body; the amount of heat that leaves one equals the amount that enters the other.

Heat Capacity and Specific Heat

mCc

heatspecificccapacityheatC

TcmTCQ

;

The amount of heat energy Q needed to raise the temperature of a substance is proportional to the temperature change and to the mass of substance.

Units of heat: Calorie [cal] : the amount of energy to be transferred to raise the temperature of one gram of water one centigrade degree. 1cal = 4.184 J

cwater: 1 cal/(g•ºC)= 1kcal/(kg•ºC)= 4.184 kJ/(kg•ºC) = 4.184 kJ/(kg•K)

The heat capacity per mole is called the molar specific heatThe specific heat of a substance depends of the way as

the heat is transferred. The most commonly determined specific heats are the specific heat at constant pressure and the specific heat at constant volume


Heat capacity: The amount of heat energy Q necessary to raise the temperature of a substance by one degree.

The Heat capacity per unit mass is called specific heat

The Heat capacity per amount of substance (mol) is called the molar specific heat

Specific Heat kJ/(kg•K)

Molar Specific Heat kJ/(mol•K)

Water 4.184 75.3

Air

cP = 29.19 J/(mol•K); cV = 20.85 J/(mol•K). M=28.84 g

cP= 1.012 kJ/(kg•K); cV = 0.723 kJ/(kg•K);


Heat Capacity and Specific Heat

mCc

heatspecificccapacityheatC

TcmTCQ

;

The amount of heat energy Q needed to raise the temperature of a substance is proportional to the temperature change and to the mass of substance.

cwater: 1 cal/(g•ºC)= 1kcal/(kg•ºC)= 4.184 kJ/(kg•ºC) = 4.184 kJ/(kg•K)

Typical volumetric heat capacity of a soil is 2.1 MJ/(m3 K). Estimate the absorbed heat energy by a layer of 1 m of depth when its temperature is increased by10ºC. Calculate the specific heat of the soil if the bulk density of the solid is 1.7 Mg/m3.

A great part of the soil are pores that can be filled by water. Then the volumetric heat capacity of a soil will vary with its content of water. Explain the behavior when the content of water increase.

How much heat is required to change 1.5 kg of ice at -20ºC and 1 atm into steam.

Thermodynamics. Change of Phase and Latent Heat

Common types of phase change include fusion (liquid to solid), melting (solid to liquid), vaporization (liquid to vapor or gas); condensation (gas or vapor to liquid), and sublimation (solid directly to vapor).

When a phase change appears there is no temperature change when the thermal energy is being transferred to the body in which the phase change is occurring. In the case of a phase change the specific heat (or capacity) is infinitum.

Latent Heat

ff LmQ Latent heat of fusion [or melting], Lf. At a pressure of 1 atm, the latent heat of fusion for water is Lf =333.5 KJ/kg

VV LmQ Latent heat of vaporization, LV . For water at a pressure of 1 atm, the latent heat of vaporization is Lf = 2.25 MJ/kg (at boiling point).

Latent heat of vaporization of water depends on the temperature.

Latent heat of water at 20ºC is 2.45 MJ/kg. A common

relationship is: ][º

]1

[

3)10361.2(501.2

Cetemperatur

MJkgonvaporizatiofheatlatent

xwater

t

t

Thermodynamics. Change of Phase and Latent Heat

Common types of phase change include fusion, freezing, (liquid to solid), melting (solid to liquid), vaporization (liquid to vapor or gas); condensation (gas or vapor to liquid), and sublimation (solid directly to vapor and vapor to solid –in some places the last process is called deposition-).

When a phase change appears there is no temperature change when the thermal energy is being transferred to the body in which the phase change is occurring. In the case of a phase change, the specific heat (or capacity) is infinitum.

http://www.usatoday.com/weather/wwatphse.htm

Thermodynamics. Change of Phase and Latent Heat. Water

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/phase.html

Thermodynamics. Evaporation


Evaporation Ordinary evaporation is a surface phenomenon - some molecules have enough kinetic energy to escape. If the container is closed, an equilibrium is reached where an equal number of molecules return to the surface. The pressure of this equilibrium is called the saturation vapor pressure.

In order to evaporate, a mass of water must collect the large heat of vaporization, so evaporation is a potent cooling mechanism. Evaporation heat loss is a major climatic factor and is crucial in the cooling of the human body.

Thermodynamics. Evaporation vs. Boiling

Evaporation vs Boiling Ordinary evaporation is a surface phenomenon - since the vapor pressure is low and since the pressure inside the liquid is equal to atmospheric pressure plus the liquid pressure, bubbles of water vapor cannot form. But at the boiling point, the saturated vapor pressure is equal to atmospheric pressure, bubbles form, and the vaporization becomes a volume phenomena.


Thermodynamics. Thermal expansion

Thermal expansion. When the temperature of an object increase, the object usually increase

ansionvolumeoftcoefficien

ansionlinearoftcoefficien

TV

dV

TL

L

exp:

exp:

Do holes expand?

Thermodynamics. Thermal Expansion. Case of Water

Discuss the expansion of water in the case of freezing (or fusion) -liquid to solid (ice)-. See the density of ice and the density of liquid water

Volume of 1 g of water at atmospheric pressure versus temperature. The minimum volume, which corresponds to the maximum density, occurs at 4ºC. [ Supercooled water is water that is cooled below the normal freezing point without solidifying. It is showed in the figure]

Thermodynamics. Phase Diagramas. Case of Water

The diagram P-T for water at a constant volume. The pressure and temperature scales are not linear.

Thermodynamics. Heat Transfer

Heat Transfer The spontaneous transfer of heat energy is from a high temperature object to a lower temperature object. Heat Transfer focus on the energy rate that is being transferred and on the mechanism of transport.

Thermal energy is transferred from one place to another by three types of processes. The driving force of heat transfer flow is always the difference of temperature:

• Conduction, In this case, the mechanism of heat energy transport is the interactions among atoms or molecules (collisions), although there is no mass motion. It is the case of heat transfer in opaque solids

• Convection, heat energy is transported by direct mass transport. Convective currents are in charge of the transport

• Radiation; heat energy is transferred through space in the form of electromagnetic waves [ or photons] that move at light speed. Sun´s energy

In all cases we can write: rate of net heat transfer = difference of temperatures/ resistance

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Thermodynamics I