Transcript Slide 1

Today (Chapters 14 and 15)
Temperature and thermal expansion
Specific Heat Capacity
Phase changes and Heat
Molecular picture of a gas
Ideal gas law
Kinetic theory of the ideal gas
Tomorrow (Chapters 15 and 16)
Heat
Internal Energy, Kinetic Energy of Ideal
Gas
Temperature
Heat: The energy that flows between two objects or systems
due to temperature difference between them is called heat.
Thermal contact: If heat can flow between two objects or
systems, the objects or systems are said to be in thermal
contact.
Zeroth law of thermodynamics: If two objects are each in
thermal equilibrium with a third object, then the two are in
thermal equilibrium with each other.
Continued………..
Temperature scales
Three most commonly used temperature scales:
1. Celsius scale
2. Fahrenheit scale
3. Kelvin scale
All these temperatures are at 1 atm pressure
Celsius:
Fahrenheit:
Kelvin:
Water freezes at:
0 ºC
32 º F
273.15 K
Water boils at:
100 º C
212 º F
373.15 K
Most commonly used temperature scale in the world is Celsius scale.
Temperature conversion
Following conversion
Celsius

Fahrenheit
Fahrenheit 
Celsius
Celsius

Kelvin
TF
TC
9
 TC  32 
5

5

TF  32 
9
TK  TC  273.15

Why 273.15 ?
It is believed that 0 K (-273.15 ºC) is the
absolute coldest that anything can get. 0 K
represents absolute zero.
The temperature at which liquid nitrogen
boils (at atmospheric pressure) is 71 K.
Express this temperature in:
(a)°C
(b)°F
How would you dress if the temperature
outside
was:
(a) 70 degrees Fahrenheit?
(b) 70 degrees Celsius?
(c) 70 degrees Kelvin?
Thermal expansion (Linear)
When a substance is heated, it tends to expand.
If we have a long thin cylindrical wire we can find out
the amount of linear expansion!
L  L0T
Where
L  L  L0 and
T  T  T0
Thus the length at temperature T is:
L  L0  L  (1  T ) L0

Coefficient of linear thermal expansion: unit 1 / C
L0
L0  L
A concrete roadbed is divided into sections that are 2 meters
long. How much will each section expand when the
temperature changes from 0 ºC to 37 ºC (100 ºF)?
Linear thermal expansion coefficient for concrete is 12x10-6
/oC.
A bridge is 400 m (1/4 mile) long. How much will the steel
support structure expand under the same temperature
change? Linear thermal expansion coefficient for steel is
12x10-6 /oC.
Thermal expansion (area, volume and differential)
Area expansion
A  A0 T
  Area thermal expansion
coefficient
A  A  A0 and
T  T  T0
Volume expansion
V  V0T
V  V  V0 and
T  T  T0
  Volume thermal expansion
coefficient
Differential expansion
When two strips made of different metals are joined together and
heated, one expands more than the other (unless they have the
same coefficient of thermal expansion)
Relationship among
  2
and
 ,  and 
  3
The coefficient of linear expansion of brass is
1.9 × 10-5 °C-1. At 20 °C, a hole in a sheet of
brass has an area of 1.00 mm2. How much
larger is the area of the hole at 34°C?
You place 1 cup of water (0.000237 m3) in a Pyrex
measuring cup and place it in the microwave on high
for 3 minutes. As the temperature of the water (and
cup) changes from 21 ºC to 100 ºC, how does the
measured amount of water change?
Heat capacity
A measure of how much heat
you need to change the temperature
of a system.
Q  CT
Definitions:
Q: heat added or removed [J]
C: heat capacity [J / (C°)] or [J / K]
∆T: change in temperature [C°] or [K]
Specific heat capacity
A measure of how much heat
you need to change the temperature
of a substance.
Q  cmT
Definitions:
Q: heat added or removed [J]
c: specific heat capacity [J / (kg C°)] or [J / (kg K)]
m: mass [kg]
∆T: change in temperature [C°] or [K]
calories or Calories?
calorie:(cal) the amount of heat needed to raise the
temperature of 1 gram of water by 1 C°.
kilocalorie:
(kcal) the amount of heat needed to raise the
temperature of 1 kilogram of water by 1 C°.
Calorie:
(Cal) the same as 1 kcal. Used as a measure
of the amount of energy in foods.
1 kcal = 4180 Joules
The specific heat capacity for a human body is about
3500 J/kg C°. A half-hour run will burn about
800,000 J of heat.
(a) If the runner does not sweat, how much will his
temperature increase? (The runner has a mass of
about 60 kg.)
(b) How many Calories does the runner burn?
How much heat is required to raise the temperature of a 3
kg block of steel by 50 K?
On page 441 of our book, there is a table that tells us the
specific heat of steel is 450 J/(kg*K).
Phase transitions
T (C )
Q(kJ )
Latent heat is the heat required per unit mass of substance
Q  mL
to produce a phase change.
Latent heat
Latent Heat of Fusion, Lf: heat that must be added or
removed when a substance changes phase between solid and
liquid.
Latent Heat of Vaporization, Lv: heat that must be added or
removed when a substance changes phase between liquid
and gas.
Q f  m Lf
Qv  m Lv
5,000,000 J of heat are added to a 10 kg of
water. If the water’s initial temperature is -4
°C, what will the water’s final temperature
be?
Phase diagram for water
Phase diagram for carbon dioxide
A quantity of pure substance is enclosed in a container
and its temperature is monitored. Describe the conditions
under which each of the following behaviors can occur as
heat is added to the substance.
(a) As heat is added the temperature does not change.
(b) The temperature rises in proportion to the amount of
heat added.
(c) As heat is added, there is no temperature change at
first, but as more heat is added the temperature begins to
rise.
A certain gas is enclosed in a container and the temperature is monitored
as a function of time. Heat is extracted from the container at a constant
rate. The temperature versus time graph is shown.
T
t
(a) For each of the 5 straight line portions of the graph, explain what is
happening to the material in the container.
(b) Which is greater, the latent heat of vaporization or the latent heat of
fusion? Explain your response.
(c) Compare the specific heats of the gas, liquid, and solid phase. (Hint:
the specific heat controls the rate of temperature change.)
Specific heat of ideal gas
Average kinetic energy of an ideal gas containing N
molecule (n moles)
3
3
3
Q  K tr  nRT
K tr  NkT  nRT
2
2
2
Q
3
CV 
 Q  nRT  nCV T
nT
2
Q: heat added or removed [J]
CV: molar specific heat at constant volume [J / (kg C°)] or [J / (kg K)]
n: no of moles
∆T: change in temperature [C°] or [K]
3
CV  R
2
(monoatomic ideal gas)
5
CV  R
2
(diatomic ideal gas)
Vocabulary: Molecular picture of a gas
Number density: The no. of molecules per unit volume is
called number density
Atomic mass: how massive one atom of a substance is.
Units: u (chemists call this the atomic weight)
atomic mass unit, u: the mass of one “normal” carbon atom
(carbon-12) is 12 u.
molecular mass: the mass of one molecule of a substance.
Just add together the masses of the atoms that make up the
molecule to get the molecular mass!
Vocabulary: Molecular picture of a gas
Number density: The no. of molecules per unit volume is
called number density N / V Units: m-3
Two gases can have the same mass per unit volume but different number
densities. If a gas has total mass M, volume V and each molecule has a mass
m, then the no of gas molecules is:
M
Thus number density
N
m
mole, mol: one mole is the number of atoms in 12 grams of
1 mol  6.0221023 atoms
carbon-12:
Avogadro’s number, NA:
NA = 6.022 x 1023 things
One mole of a substance has a mass equal to the atomic mass (in grams)
N 

V m
Vocabulary: Molecular picture of a gas
Number of moles =
number of molecules
----------------------------------no. of molecules per mole
N
n
NA
Atomic mass unit: Mass of atom is expressed in atomic mass unit
atomic mass: how massive one atom of a substance is.Units: u
(chemists call this the atomic weight)
atomic mass unit, u: the mass of one “normal” carbon atom
(carbon-12) is 12 u. 1u=1.66x10-27kg
molecular mass: the mass of one molecule of a substance. Just
add together the masses of the atoms that make up the molecule
to get the molecular mass!
How many molecules of water are there in 10
grams?
Gas laws
Boyle’s law state that pressure of the gas is inversely proportional to its
volume at constant temperature
1
P
(for constant T)
V
If T and n are constant, then
PiVi  Pf V f
Charles's law state that if pressure of the gas held constant, the change
in temperature is indeed proportional to the change in its
VT
(for constant P)
If P and n are constant, then
Vi V f

Ti T f
Gas laws
Gay-Lussac’s law state that pressure of the gas is proportional to its
temperature at constant volume
P T
(for constant V)
If V and n are constant, then
Pf
Pi

Ti T f
Ideal gas law
PV  nRT
(Macroscopic form)
P [Pa] V [m3] n [mol] T [K]
R = 8.31 J / (mol K)
PV  NkT
(Microscopic form)
P [Pa] V [m3] N [particles]
k = 1.38 x 10-23 J / K
T [K]
A small bubble of air is released on the bottom of a
column of beer. Assume that none of the air is
absorbed by the water, and that the temperature is
the same everywhere in the beer.
(a) As the bubble rises, does its volume increase,
decrease, or not change?
(b) As the bubble rises, does the buoyant force on it
increase, decrease, or not change?
An ideal gas that occupies 1.2 m3 at a pressure 1.0x105 Pa
and a temperature of 27oC is compressed to a volume of
0.6 m3 and heated to a temperature of 227 oC. What is the
new pressure?
Kinetic theory of the ideal gas
Ideal gas – point-like molecules moving
independently
Molecule colliding with the wall
Change in momentum:
Time to travel across the container:
Average force due to 1 molecule:
px  2mvx
L
t2
vx
px 2mvx2
F

t
2L
Kinetic theory of the ideal gas
Average force due to 1 molecule:
Average force:
Average pressure:
px 2mvx2
F

t
2L
FN
2L
2m vx2
F
p N

A
2LA
No preferred direction of motion :
Pressure :
2m vx2
v
2
x
2 N Ktr
p
3V
Nm vx2
V
1 2
 v
3
Kinetic theory of the ideal gas
2 N Ktr
p
Pressure :
3V
NkT
p
Ideal gas law :
V
3
Translational kinetic energy of 1 molecule : K tr  kT
2
3kT
2
Root mean square speed :
vrms  v 
m