普通物理－熱力學I

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普通物理

Lecture 15

Thermodynamics I

熱力學 I

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A Macroscopic Description of Matter

p

Macroscopic systems are

characterized as being either

solid liquid

or

gas

These

solid, liquid

, or

gas

. These

are called the phases of

matter and in this chapter

matter, and in this chapter

we’ll be interested in when

and how a system changes

from one phase to another.

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Work, Heat, and the First Law of

Thermodynamics

This false-color thermal image

(an infrared photo) shows

h

h t

i

where heat energy is escaping

from a house. In this chapter

we investigate the connection

between work and heat.

Chapter Goal: To expand our

understanding of energy

and to develop the first law of

thermodynamics as a general

statement of energy

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A Macroscopic Description of Matter

p

Topics:

••

Solids Liquids and Gases

••

Solids, Liquids, and Gases

••

Atoms and Moles

••

Temperature

Phase Changes

••

Phase Changes

••

Ideal Gases

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General Principles

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Density

Densityyy

Th ti f t ’ t it l i ll d th

The ratio of a system’s mass to its volume is called the

mass density, or sometimes simply “the density.”

The SI units of mass density are kg/m3 _{In this chapter}

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Density

Densityyy

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Density

Densityyy

1 Example 1

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Atoms and Moles

• The mass of an atom is determined primarily by its • The mass of an atom is determined primarily by its

most massive constituents, the protons and neutrons in its nucleus

nucleus.

• The sum of the number of protons and neutrons is called the atomic mass number A.

• The atomic mass scale is established by defining the

mass of 12_{C to be exactly 12 u, where u is the symbol for}

the atomic mass unit.

• The conversion factor between atomic mass units and kilograms is

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Atoms and Moles

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Atoms and Moles

• By definition one mole of matter be it solid liquid or gas • By definition, one mole of matter, be it solid, liquid, or gas,

is the amount of substance containing as many basic particles as there are atoms in 12 g of 12_C

basic particles as there are atoms in 12 g of C.

• The number of basic particles per mole of substance is called Avogadro’s number, _g _, N_A = 6.02 × 1023 _mol−1_.

A

• The number of moles in a substance containing N basic particles is

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Atoms and Moles

• If the atomic mass is specified in kilograms, the number of p g , atoms in a system of mass M can be found from

• The molar mass of a substance is the mass in grams of 1 mol of substance. The molar mass, which we’ll designate M, g _mol_mol, has , units g/mol.

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Atoms and Moles

Example 2 Example 2

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Temperature

The Celsius temperature scale is defined by setting Tp y g _C_C=0 for

the freezing point of pure water, and T_C=100 for the boiling point.

The Kelvin temperature scale has the same unit size as Celsius,

with the zero point at absolute zero. The conversion between

h C l i l d h K l i l i

the Celsius scale and the Kelvin scale is

The Fahrenheit scale, still widely used in the United States,

i d fi d b it l ti t th C l i l f ll

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Temperature

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Applications

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Phase Changes

gg

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Phase Changes

• The temperature at which a solid becomes a liquid or, ifThe temperature at which a solid becomes a liquid or, if the thermal energy is reduced, a liquid becomes a solid is called the melting pointg p or the freezing pointg p . Melting g and freezing are phase changes.

• The temperature at which a gas becomes a liquid or, if the thermal energy is increased, a liquid becomes a gas is

called the condensation point or the boiling point.

C d i d b ili h h

Condensing and boiling are phase changes.

• The phase change in which a solid becomes a gas is ll d bli ti

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Ideal Gases

Th id l d l i i hi h d l t i

• The ideal-gas model is one in which we model atoms in a gas as being hard spheres. Such hard spheres fly

through space and occasionally interact by bouncing off through space and occasionally interact by bouncing off each other in perfectly elastic collisions.

• Experiments show that the ideal-gas model is quite goodExperiments show that the ideal gas model is quite good for gases if two conditions are met:

1. The density is low (i.e., the atoms occupy a volume y ( , py much smaller than that of the container), and

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The Ideal

The Ideal--Gas Law

Gas Law

The pressure p, the volume V, the number of moles n and the temperature T of an ideal gas are related by the ideal the temperature T of an ideal gas are related by the ideal-gas law as follows:

where R is the universal gas constant, R = 8.31 J/mol K. The ideal gas law may also be written ase dea gas aw ay a so be w e as

where N is the number of molecules in the gas rather than the number of moles n The Boltzmann’s constant is k = 1 38 ×

number of moles n. The Boltzmann s constant is k_B = 1.38 × 10−23 _J/K_.

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Important Concepts

p

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Important Concepts

p

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Important Concepts

p

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The Ideal

The Ideal--Gas Law

Gas Law

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Ideal

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Ideal

Ideal--Gas Processes

Gas Processes

Many important gas processes take place in a container of y p g p p constant, unchanging volume. A constant-volume process is called an isochoric process.

Consider the gas in a closed, rigid container. Warming the gas with a flame will raise its pressure without changing its

l

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Ideal

Ideal--Gas Processes

Gas Processes

Other gas processes take place at a constant unchanging Other gas processes take place at a constant, unchanging pressure. A constant-pressure process is called an isobaric process

process.

Consider a cylinder of gas with a tight-fitting piston of mass M that can slide up and down but seals the container so that no p atoms enter or escape.

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Isobaric Process

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Isobaric Process

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Work, Heat, and the First Law of

Thermodynamics

ii

Thermodynamics

Topics:

••

It

It’’s All About Energy

s All About Energy

••

Work in Ideal

Work in Ideal--Gas Processes

Gas Processes

••

Heat

••

Heat

••

The First Law of Thermodynamics

Th

l P

i

f M

Th

l P

i

f M

••

Thermal Properties of Matter

••

Calorimetry

••

The Specific Heats of Gases

••

Heat

Heat--Transfer Mechanisms

Transfer Mechanisms

••

Heat

Heat Transfer Mechanisms

Transfer Mechanisms

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Work in Ideal

Work in Ideal--Gas Processes

Gas Processes

Consider a gas li d l d cylinder sealed at one end by a moveable piston moveable piston.

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Work in Ideal

Work in Ideal--Gas Processes

Gas Processes

If we let the piston move in a slow quasi-static process

p

q

p

from initial volume V

_i

to final volume V

_f

, the total work

done by the environment on the gas is

y

g

hi ll

or, graphically

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Problem

Problem--Solving Strategy: Work in

Solving Strategy: Work in

Ideal

Ideal Gas Processes

Gas Processes

Ideal

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Work in Ideal

Work in Ideal--Gas Processes

Gas Processes

In an isochoric process, when the volume does not change, no work is done.

In an isobaric process, when pressure is a constant and the volume changes by ΔV = Vg y _f_f − V_i_i, the work done during the , g process is

In an isothermal process, when temperature is a constant, the work done during the process is

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The work of an isothermal compression

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The work of an isothermal compression

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Heat, Temperature, and Thermal

Energy

• Thermal energy EThermal energy E_th_h is an energy of the system due to theis an energy of the system due to the motion of its atoms and molecules. Any system has a

thermal energy even if it is isolated and not interacting with its environment. The units of E_th are Joules.

• Heat Q is energy transferred between the system and • Heat Q is energy transferred between the system and

the environment as they interact. The units of Q are Joules. • Temperature T is a state variable that quantifies

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The First Law of Thermodynamics

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Work and heat are two ways of transferring energy

between a system and the environment, causing the

system’s energy to change If the system as a whole is

system s energy to change. If the system as a whole is

at rest, so that the bulk mechanical energy due to

translational or rotational motion is zero, then the

,

conservation of energy equation is

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Temperature Change and Specific Heat

The amount of energy that raises the temperature of 1 kg of a substance by 1 K is called the specific heat of that

b Th b l f ifi h i

substance. The symbol for specific heat is c.

If W = 0, so no work is done by or on the system, then the heat needed to bring about a temperature change ΔT is

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Temperature Change and Specific Heat

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Quenching hot aluminum in ethyl alcohol

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Phase Change and Heat of Transformation

A

h

i h

i d b

h

i

A

phase change

is characterized by a change in

thermal energy without a change in temperature.

The amount of heat energy that causes 1 kg of

substance to undergo a phase change is called the

heat

substance to undergo a phase change is called the

heat

of transformation

of that substance.

The symbol for heat of transformation is

L

.

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Phase Change and Heat of Transformation

Two specific heats of transformation are the

heat of

Two specific heats of transformation are the

heat of

fusion L

_f

, the heat of transformation between a solid

and a liquid, and the

heat of vaporization L

_v

, the heat

of transformation between a liquid and a gas. The heat

needed for these phase changes is

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Turning ice into steam

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Calorimetry

y

Suppose to systems

start at different

t

T

d

temperatures T

₁

and

T

₂

. Heat energy will

naturally be

transferred from the

hotter to the colder

system until they

reach a common

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Problem

Problem--Solving Strategy: Calorimetry

Solving Strategy: Calorimetry

Problems

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Problem

Problem--Solving Strategy: Calorimetry

Solving Strategy: Calorimetry

Problems

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The Specific Heats of Gases

It is useful to define two different versions of the specific

h f f l (i h i )

heat of gases, one for constant-volume (isochoric) processes and one for constant-pressure (isobaric)

processes We will define these as molar specific heats processes. We will define these as molar specific heats

because we usually do gas calculations using moles instead of mass. The quantity of heat needed to change the q y g

temperature of n moles of gas by ΔT is

where C_V is the molar specific heat at constant volume and C is the molar specific heat at constant pressure and C_P is the molar specific heat at constant pressure.

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The Specific Heats of Gases

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Conduction

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Conduction

For a material of cross-section area A and length L,

spanning a temperature difference

ΔT = T

_H

– T

_C

, the

t

f h t t

f i

rate of heat transfer is

where k is the

thermal conductivity

, which

characterizes whether the material is a good conductor

of heat or a poor conductor.

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Conduction

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Keeping a freezer cold

p g

Example 9

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Convection

Ai i d f h b

Air is a poor conductor of heat, but thermal energy is easily transferred through air water and other fluids through air, water, and other fluids because the air and water can flow. A

pan of water on the stove is heated at the bottom. This heated water expands,

becomes less dense than the water above it and thus rises to the surface while

it, and thus rises to the surface, while cooler, denser water sinks to take its place. The same thing happens to air.

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Radiation

All objects emit energy in the form of radiation,

electromagnetic waves generated by oscillating electric charges in the atoms that form the object. If heat energy Q is radiated in a time interval Δt by an object with surface is radiated in a time interval Δt by an object with surface area A and absolute temperature T, the rate of heat transfer is found to be

The parameter e is the emissivity of the surface, a measure of how effectively it radiates. The value of e ranges from 0 to 1 σ is a constant known as the Stefan Boltzmann

to 1. σ is a constant, known as the Stefan-Boltzmann constant, with the value σ = 5.67 × 10–8 _W/m2_K4_.

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Important Concepts

p

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Summary of Basic Gas Processes

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Assignment 11

Due Date: 12/30/2009

1.

How many atoms are in a 2.0 cm  2.0 cm  2.0 cm cube of aluminum? 2.

A rigid container holds 2.0 mol of gas at a pressure of 1.0 arm and a temperature of 30°C

temperature of 30 C.

a. What is the container’s volume?

b. What is the pressure if the temperature is raised to 130C? 3.

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Assignment 11 Assignment 11

4.

A 750 g aluminum pan is removed from the stove and plunged into a sink filled with 10.0 L of water at 20.0°C. The water temperature quickly rises to 24.0°C. What was the initial temperature of the pan in °C and in F?

24.0 C. What was the initial temperature of the pan in C and in F?

5.

Radiation from the head is a major source of heal loss from the human body Radiation from the head is a major source of heal loss from the human body. Model a head as a 20-cm-diameter, 20-cm-tall cylinder with a flat top. If the body’s surface temperature is 35C, what is the net rate of heat loss on a

hill 5C d ? All ki dl f l i ff ti l bl k i th i f d chilly 5C day? All skin, regardless of color, is effectively black in the infrared where the radiation occurs, so use an emissivity of 0.95.

6.

How much energy must be removed from a 6.0 cm  6.0 cm  6.0 cm block of ice to cool it from 0C to 30C?