temperature thermal expansion ideal gas law heat transfer

•Temperature

•Thermal Expansion

•Ideal Gas Law

•Kinetic Theory

•Heat

•Heat Transfer

•Phase Changes

•Specific Heat

•Calorimetry

•Heat Engines

Zeroeth Law

• Two systems individually in thermal

equilibrium with a third system (such as a

thermometer) are in thermal equilibrium

with each other.

• That is, there is no flow of heat within a

system in thermal equilibrium

1st Law of Thermo

• The change of internal energy of a system

due to a temperature or phase change is

given by:

Temperature Change: Q = mcT

Phase Change: Q = mL

• Q is positive when the system GAINS heat

and negative when it LOSES heat.

intE Q W

Specific Heat: Thermal Inertia

The Specific Heat of a substance is the amount of Energy it

requires to raise the temperature of 1 kg, 1 degree Celsius.

Q mc T 0

Q Jc

m T kg C

•The higher the specific heat, the more energy it takes and

the longer it takes to heat up and to cool off.

•The lower the specific heat, the less energy it takes and the

quicker it takes to heat up and cool off.

•Substances with HIGH specific heat STORE heat energy

and make good thermal moderators. (Ex: Water, Oceans)

Phase Change Q mL

•A change from one phase to another

•A phase change always occurs with an exchange of energy!

•A phase change always occurs at constant temperature!

•Heat flows from HOT to COLD

•Conduction (solids)

•Convection (liquids & gases)

•Radiation (solids, gases, plasma)

Thermo Processes• Adiabatic

– No heat exchanged

– Q = 0 and Eint = W

• Isobaric

– Constant pressure

– W = P (Vf – Vi) and Eint = Q + W

• Isochoric

– Constant Volume

– W = 0 and Eint = Q

• Isothermal

– Constant temperature

Eint = 0 and Q = -W

intE Q W

ln i

f

VW nRT

V

n = # moles

R = 8.31 J/(mol-K) Universal Gas Constant

PV = NktN= # particles

k =1.38 x 10-23 J/K Boltzmann’s Constant

Note: PV is units of Energy!

P V = nRT

2nd Law of Thermo

• Heat flows spontaneously from a substance

at a higher temperature to a substance at a

lower temperature and does not flow

spontaneously in the reverse direction.

• Heat flows from hot to cold.

• Alternative: Irreversible processes must

have an increase in Entropy; Reversible

processes have no change in Entropy.

• Entropy is a measure of disorder in a system

3rd Law of Thermo

It is not possible to

lower the

temperature of any

system to absolute

zero.

TC = T – 273.15

• Temperature ~ Average KE of each particle

• Particles have different speeds

• Gas Particles are in constant RANDOM motion

• Average KE of each particle is: 3/2 kT

• Pressure is due to momentum transfer

Speed ‘Distribution’ at

CONSTANT Temperature

is given by the

Maxwell Boltzmann

Speed Distribution

Internal Energy of

Monatomic and Diatomic GasesThe thermal energy of a monatomic gas of N atoms is

A diatomic gas has more thermal energy than a monatomic

gas at the same temperature because the molecules have

rotational as well as translational kinetic energy.




• Isobaric



• Isochoric

– Constant Volume


• Isothermal


Eint = 0 and Q = -W

intE Q W

ln i

f

VW nRT

V

Cyclic Processes

• A cyclic process is one that starts and ends in the same state

– On a PV diagram, a cyclic process appears as a closed curve

• If Eint = 0, Q = -W

• In a cyclic process, the net work done on the system per cycle equals the area enclosed by the path representing the process on a PVdiagram

Eint = 0

Heat EnginesThe Otto cycle approximates the

processes occurring in an internal combustion engine

If the air-fuel mixture is assumed to be an ideal gas, then the efficiency of the Otto cycle is

is the ratio of the molar specific heats V1 / V2 is called the compression ratio

Typical values:Compression ratio of 8 = 1.4e = 56%

Efficiencies of real engines are 15% to 20%Mainly due to friction, energy transfer by conduction, incomplete combustion of the air-fuel mixture

1

1 2

11e

V V

Carnot Engine – Carnot CycleA heat engine operating in an ideal, reversible cycle (now called a Carnot cycle) between two reservoirs is the most efficient engine possible. This sets an upper limit on the efficiencies of all other engines

and 1c c c

c

h h h

Q T Te

Q T T

Temperatures must be in Kelvins

© 2013 Pearson Education, Inc.

Chapter 16 A Macroscopic Description of Matter

Chapter Goal: To learn the characteristics of macroscopic systems.

Slide 16-2

States of MatterSolid Liquid Gas

What is the most common state of matter in the Universe?

Fluids: Liquids & Gases

•Fluids are substances that are free to flow.

•Atoms and molecules are free to move.

•They take the shape of their containers.

•Cannot withstand or exert shearing forces.

Liquids: Incompressible (density constant)

Gases: Compressible (density depends on pressure)

Parameters to describe Fluids:

Density: = mass/volume

Pressure: P = Force/Area

[P] = N/m2 = 1 Pascal (Pa)

Liquid Units

There are 1000 liters in 1 cubic meter!

1 liter = 10-3 m3 = 103 cm3

1 liter of water has a mass of 1 kg and a weight of 9.8N.

2 0 3

1 1000H

kg kg

liter m

Density• Density of water @4°C:

water = 1g/cm3 = 1000 kg/m3 = 1kg/liter

• Density of air @ 0°C:

Air = 1.29x10-3 g/cm3 = 1.29 kg/m3

Density depends on temperature!Most substances EXPAND upon heating.

m

V

How does that change their densities?

REDUCES DENSITY!m

V

m V

© 2013 Pearson Education, Inc. Slide 16-24

Densities of Various Materials

Water: The Exception

• Water @4°C: water =1000 kg/m3

• Ice @ 0°C: ice = 917 kg/m3

Pressure in a fluid is due to the weight

of a fluid.Force

PArea

mg

A

Pressure depends on Depth!

( )V g

A

( )Ah g

A

P gh

Pressure IN a Fluid

•Is due to the weight of the fluid above you

•Depends on Depth and Density Only

•Does NOT depend on how much water is present

•Acts perpendicular to surfaces (no shearing)

•Pressure’s add

•At a particular depth, pressure is exerted equally in ALL directions

including sideways (empirical fact)

Pressure Problem

What is the water pressure 15 m

below the surface of the lake?

Assume it is pure water.

P gh

3 21000 / (9.8 / )15kg m m s m

5 21.47 10 /x N m

147kPa 21 Pascal 1 /N m

Pressure ON a Fluid

Liquids cannot be compressed to a smaller volume.

Liquids are incompressible.

Gases can be compressed to a smaller volume.

Gases are compressible.

The Atmosphere

At sea level,

the atmosphere

has a density of

about 1.29 kg/m3.

The average

density up to

120 km is about

8.59 x10-2 kg/m3.

The Atmosphere

A square meter

extending up through

the atmosphere has a

mass of about

10,000 kg and a weight

of about 100,000 N.

1 N/m2 is a Pascal.

51 1.013 10 14.7atm x Pa psi

Measuring Pressure 51 1.013 10atm x Pa

760h mm

13.6mercury water

mercuryP gh

mercury

Ph

g

2

3 2

101,300 /

13,600 / 9.8 /

N mh

kg m x m s

P gh

Why is the pressure at X equal to atmospheric pressure?

Because if it didn’t, the mercury would

be pushed out of the dish!

31000 /water kg m

Measuring Pressure

Can a barometer be made with Water instead of Mercury?

waterP gh

water

Ph

g

2

3 2

101,300 /

1000 / 9.8 /

N mh

kg m x m s

10.3h m

(Notice: 10.3m is just 13.6 x 760mm!)

13.6mercury water

31000 /water kg m

10.3m

Mercury Barometer Water Barometer

Not to Scale!!!

51 1.013 10atm x Pa 760mm

Barometers

Measuring Air PressureFluid in the tube adjusts until the weight of the fluid column

balances the atmospheric force exerted on the reservoir.

Absolute vs. Gauge Pressure

• Guage pressure is

what you measure in

your tires

• Absoulte pressure is

the pressure at B and

is what is used in

PV = nRT

0Guage Pressure: P gh

0Absolute Pressure: P P gh

Zero Pressure: Making A VacuumMechanical Vacuum Pump

Minimum pressure produced by mechanical pump:~1Pa

Minimum pressure produced by hi tech: 10-12 Pa

Zero pressure not allowed by Quantum Uncertainty!

Absolute pressure cannot be negative: Pressure pushes not pulls!

Gauge pressure can be negative because it is a relative pressure.

Nature abhors a Vacuum.

-Aristotle

•Atomic Number: # protons

•Atomic Mass: # atomic mass units (u)

•Atomic Mass Unit: 1/12 mass of C-12 atom

• amu = u = 1.66 x 10-27 kg

•Atomic Mass of C = 12.011u (1% is C-13)

•Mass of 1 C = (12.011u) (1.66 x 10-27 kg/u)

Atomic Units

The Basics

•Mole (mol) = # atoms or molecules (particles) as

are in 12 grams of Carbon-12:

1 mole = 6.022 x 1023 particles

• Avogadro’s Number: the number of particles in

one mole: NA= 6.022 x 1023 mol-1

•# moles n contained in a sample of N particles:

n = N/ NA

• # particles in a sample is: N = n NA

Moles and Avogadro’s NumberNA= 6.022 x 1023 mol-1

The mass / mol for any substance

has the same numerical value

as its atomic mass:

mass/mol C-12 = 12 g / mol

mass/mol Li = 6.941 g / mol

More on Moles

n = mass / atomic mass

n = mass / (mass/mole) = mass / atomic mass

Q: How many moles are in 1 kg of Sodium?

mass/mole = atomic mass

Na: 22.9898 g / mol

n = mass / (mass/mole)

= 1000 g / (22.9898g/mol)

= 43.5 moles

Q: How many atoms in 1 kg of Sodium?

# particles in a sample is: N = n NA

N = (43.5mol) 6.022 x 1023 mol-1

= 2.62 x 1025 atoms


Number Density

It is often useful to know the

number of atoms or molecules

per cubic meter in a system.

We call this quantity the number

density.

In an N-atom system that fills

volume V, the number density is:

The SI units of number density are m3.

Slide 16-26


The volume of this cube is

A. 8 102 m3.

B. 8 m3.

C. 8 10–2 m3.

D. 8 10–4 m3.

E. 8 10–6 m3.

QuickCheck 16.1

Slide 16-27


The volume of this cube is

A. 8 102 m3.

B. 8 m3.

C. 8 10–2 m3.

D. 8 10–4 m3.

E. 8 10–6 m3.

QuickCheck 16.1

Slide 16-28


Which contains more molecules, a mole of

hydrogen gas (H2) or a mole of oxygen gas (O2)?

A. The hydrogen.

B. The oxygen.

C. They each contain the same number of

molecules.

D. Can’t tell without knowing their temperatures.

QuickCheck 16.2

Slide 16-32


Which contains more molecules, a mole of

hydrogen gas (H2) or a mole of oxygen gas (O2)?

A. The hydrogen.

B. The oxygen.

C. They each contain the same number of

molecules.

D. Can’t tell without knowing their temperatures.

QuickCheck 16.2

Slide 16-33


Temperature

What is temperature?

Temperature is related to how much thermal energy is in a system (more on this in Chapter 18).

For now, in a very practical sense, temperature is what we measure with a thermometer!

In a glass-tube thermometer, such as the ones shown, a small volume of liquid expands or contracts when placed in contact with a “hot” or “cold” object.

The object’s temperature is determined by the length of the column of liquid.

Slide 16-35


Temperature

The Celsius temperature scale is defined by setting TC 0 for the freezing point of pure water, and TC 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 from the Celsius scale to the Kelvin scale is:

The Fahrenheit scale, still widely used in the United States, is defined by its relation to the Celsius scale, as follows:

Slide 16-36


Temperature

Slide 16-37

• The absolute temperature scale is based on two fixed points

– Adopted by in 1954 by the International Committee on Weights and Measures

– One point is absolute zero

– The other point is the triple point of water

• This is the combination of temperature and pressure where ice, water, and steam can all coexist

Absolute Temperature Scale, K


Absolute Zero and Absolute Temperature

Figure (a) shows a constant-volume gas thermometer.

Figure (b) shows the pressure-temperature relationship for three different gases.

There is a linear relationship between temperature and pressure.

All gases extrapolate to zero pressure at the same temperature:

T0 273 C.

This is called absolute zero, and forms the basis for the absolute temperature scale (Kelvin).

Slide 16-40

n = # moles

R = 8.31 J/(mol-K) Universal Gas Constant

PV = NktN= # particles

k =1.38 x 10-23 J/K Boltzmann’s Constant

Note: PV is units of Energy!

P V = nRT

• The only interaction between particles are

elastic collisions (no sticky - no loss of KE)

• This requires LOW DENSITY

• Excellent Approximation for O, N, Ar, CO2

@ room temperature and pressures

• “State” is described by the Ideal Gas Law

• Non “Ideal” are Van der Waals gases

Ideal Gas ProblemAn ideal gas with a fixed number of molecules

is maintained at a constant pressure. At 30.0

°C, the volume of the gas is 1.50 m3. What is

the volume of the gas when the temperature is

increased to 75.0 °C?

1 1PV nRT

2 2PV nRT

1 1

2 2

V T

V T

22 1

1

TV V

T 3 3348

1.5 1.72303

Km m

K


Two identical cylinders, A and B, contain the same type

of gas at the same pressure. Cylinder A has twice as

much gas as cylinder B. Which is true?

A. TA TB

B. TA TB

C. TA TB

D. Not enough information

to make a comparison.

QuickCheck 16.6

Slide 16-50


Two identical cylinders, A and B, contain the same type

of gas at the same pressure. Cylinder A has twice as

much gas as cylinder B. Which is true?

A. TA TB

B. TA TB

C. TA TB

D. Not enough information

to make a comparison.

QuickCheck 16.6

Slide 16-51


Two cylinders, A and B, contain the same type of gas at the

same temperature. Cylinder A has twice the volume as

cylinder B and contains half as many molecules as cylinder

B. Which is true?

A. pA 4pB

B. pA 2pB

C. pA pB

D. pA pB

E. pA pB

QuickCheck 16.7

14

12

Slide 16-52


Two cylinders, A and B, contain the same type of gas at the

same temperature. Cylinder A has twice the volume as

cylinder B and contains half as many molecules as cylinder

B. Which is true?

A. pA 4pB

B. pA 2pB

C. pA pB

D. pA pB

E. pA pB

QuickCheck 16.7

14

12

Slide 16-53

1st Law of Thermo

• The change of internal energy of a system

due to a temperature or phase change is

given by:

Temperature Change: Q = mcT

Phase Change: Q = mL

• Q is positive when the system GAINS heat

and negative when it LOSES heat.

intE Q W

The First Law of Thermodynamics

• The First Law of Thermodynamics is a special case of the Law of Conservation of Energy

– It takes into account changes in internal energy and energy transfers by heat and work

• Although Q and W each are dependent on the path, Q + W is independent of the path

intE Q W


The amount of energy that raises the temperature of

1 kg of a substance by 1 K is called the specific heat

c of that substance.

If W = 0, so no work is done by or on the system, then

the heat needed to bring about a temperature change

T is:

The molar specific heat C is the amount of energy that

raises the temperature of 1 mol of a substance by 1 K.

Temperature Change and Specific Heat

Slide 17-60

Specific Heat: Thermal Inertia

The Specific Heat of a substance is the amount of Energy it

requires to raise the temperature of 1 kg, 1 degree Celsius.

Q mc T 0

Q Jc

m T kg C

•The higher the specific heat, the more energy it takes and

the longer it takes to heat up and to cool off.

•The lower the specific heat, the less energy it takes and the

quicker it takes to heat up and cool off.

•Substances with HIGH specific heat STORE heat energy

and make good thermal moderators. (Ex: Water, Oceans)

PRELAB!!

A combination of 0.250 kg of water at 20.0°C, 0.400 kg

of aluminum at 26.0°C, and 0.100 kg of copper at

100°C is mixed in an insulated container and allowed to

come to thermal equilibrium. Ignore any energy transfer

to or from the container and determine the final

temperature of the mixture.

Work in Thermodynamics• Work can be done on a deformable

system, such as a gas

• Consider a cylinder with a moveable

piston

• A force is applied to slowly compress the

gas

– The compression is slow enough for

all the system to remain essentially in

thermal equilibrium

– This is said to occur quasi-statically

ˆ ˆ dW d F dy Fdy PA dy PdV F r j j

dW PdV


On a pV diagram, the

work done on a gas W

has a nice geometric

interpretation.

W = the negative of the

area under the pV curve

between Vi and Vf.

Work in Ideal-Gas Processes

Slide 17-28

f

i

V

VW P dV

f

i

V

VW P dV

Work

Work Done By Various Paths

( )f f iW P V V

f

i

V

VW P dV

( )i f iW P V V ( )W P V dV

The work done depends on the path taken!

Not necessarily

an isotherm!

For an isochoric process, insert the locking pin so the volume cannot change.

For an isothermal process, keep the thin bottom in thermal contact with the flame or the ice.

For an adiabatic process, add insulation beneath the cylinder, so no heat is transferred in or out.

Three Special Ideal-Gas Processes

Slide 17-52


Constant-Volume Process

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 volume.

Slide 16-62


Constant-Pressure Process

A constant-pressure process

is called an isobaric process.

Consider a cylinder of gas

with a tight-fitting piston of

mass M that can slide up and

down but seals the container.

In equilibrium, the gas pressure

inside the cylinder is:

Slide 16-65


Constant-Temperature Process

A constant-temperature process

is called an isothermal process.

Consider a piston being pushed

down to compress a gas.

Heat is transferred through the

walls of the cylinder to keep T

fixed, so that:

The graph of p versus V for an

isotherm is a hyperbola.

Slide 16-73


Isochoric

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

Slide 17-37


In an isobaric process, when pressure is a constant and the volume changes by V = Vf − Vi, the work done during the process is:

Isobaric

Slide 17-38


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

Isothermal

Slide 17-39


The work done on the

gas in this process is

QuickCheck 17.2

A. 8000 J.

B. 4000 J.

C. 0 J.

D. –4000 J.

E. –8000 J.

Slide 17-29


The work done on the

gas in this process is

QuickCheck 17.2

A. 8000 J.

B. 4000 J.

C. 0 J.

D. –4000 J.

E. –8000 J.

Slide 17-30

W = –(area under pV curve)

If the work done is NEGATIVE then how did

the Temperature go up?

Cyclic Processes

• A cyclic process is one that starts and ends in the same state

– On a PV diagram, a cyclic process appears as a closed curve

• If Eint = 0, Q = -W

• In a cyclic process, the net work done on the system per cycle equals the area enclosed by the path representing the process on a PVdiagram

Eint = 0

A gas is taken through the cyclic process as shown.

Find the work done from AB, BC and CA. What is the net work done?

Work

In a cyclic process, the net work done on the system per cycle equals the area enclosed by the path representing the process on a PV diagram

A gas is taken through the cyclic process as shown.

(a) Find the net energy transferred to the system by heat during one complete cycle. (b) What If? If the cycle is reversed—that is, the process follows the path ACBA—what is the net energy input per cycle by heat? Find the net work done.

int 0E Q W

Cyclic Processes

An adiabatic process is one for which:

where:

Adiabats are steeper than

hyperbolic isotherms because

only work is being done to

change the Temperature. The

temperature falls during an

adiabatic expansion, and rises

during an adiabatic

compression.

Adiabatic Processes

Slide 17-88

Adiabatic Processes: Q=0

It is useful to define two different versions of the specific heat of gases, one for constant-volume processes and one for constant-pressure processes.

The quantity of heat needed to change the temperature of n moles of gas by T is:

where CV is the molar specific heat at constant volume and CP is the molar specific heat at constant pressure.

The Specific Heats of Gases

Slide 17-79

Molar Specific Heats

Processes A and B have

the same T and the

same Eth, but they

require different

amounts of heat.

The reason is that work

is done in process B but

not in process A.

The total change in

thermal energy for any

process, due to work

and heat, is:

The Specific Heats of Gases

Slide 17-78

Specific Heat Depends on Process

CP and CV Note that for all ideal gases:

whereR = 8.31 J/mol K is the universal gas constant.

Slide 17-80

Molar Specific Heats

Molar Specific HeatsIsobaric requires MORE HEAT than Isochoric for the

same change in Temperature!!!!




• Isobaric



• Isochoric

– Constant Volume


• Isothermal


Eint = 0 and Q = -W

intE Q W

ln i

f

VW nRT

V


Three possible processes A, B,

and C take a gas from state i to

state f. For which process is the

heat transfer the largest?

A. Process A.

B. Process B.

C. Process C.

D. The heat is the same for all three.

QuickCheck 17.7

Slide 17-58


Three possible processes A, B,

and C take a gas from state i to

state f. For which process is the

heat transfer the largest?

A. Process A.

B. Process B.

C. Process C.

D. The heat is the same for all three.

QuickCheck 17.7

Slide 17-59

Eth = W + Q

Same for all three

Most negative for A ... ... so Q must be most positive.

A Heat-Engine Example: Slide 1 of 3

Slide 19-38

Draw the Process on a PV

Diagram


Ideal-Gas Processes: PV DIAGRAMS

intE Q W

A 4.00-L sample of a nitrogen gas confined to a

cylinder, is carried through a closed cycle. The

gas is initially at 1.00 atm and at 300 K. First, its

pressure is tripled under constant volume. Then,

it expands adiabatically to its original pressure.

Finally, the gas is compressed isobarically to its

original volume. (a) Draw a PV diagram of this

cycle. (b) Find the number of moles of the gas. (c)

Find the volumes and temperatures at the end of

each process (d) Find the Work and heat for each

process. (e) What was the net work done on the

gas for this cycle?

temperature thermal expansion ideal gas law heat transfer

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