Transcript Chapters 16&17 - personal.tcu.edu

Chapters 16, 17
Temperature, Heat, and the Thermal
Behavior of Matter
Temperature
• Thermodynamics – branch of physics studying
thermal energy of systems
• Temperature (T), a scalar – measure of the thermal
(internal) energy of a system
• SI unit: K (Kelvin)
• Kelvin scale has a lower limit (absolute
zero) and has no upper limit
William Thomson
(Lord Kelvin)
(1824 - 1907)
Kelvin scale
• Kelvin scale is defined by the temperature of the
triple point of pure water
• Triple point – set of pressure and temperature
values at which solid, liquid, and gas phases can
coexist
• International convention:
T of the triple point of water is
T3  273.16 K
The zeroth law of thermodynamics
• If two (or more) bodies in contact don’t change their
internal energy with time, they are in thermal
equilibrium
• 0th law of thermodynamics: if bodies are in thermal
equilibrium, their temperatures are equal
Measuring temperature
• Temperature measurement principle: if bodies A and
B are each in thermal equilibrium with a third body C,
then A and B are in thermal equilibrium with each
other (and their temperatures are equal)
• The standard temperature for the Kelvin scale is
measured by the constant-volume gas thermometer
Constant-volume gas thermometer
P  P0  gh
T  CP
T3  CP3
P
T  T3
P3
P
 273.16K 
P3
Celsius and Fahrenheit scales
• Celsius scale:
TC  T  273.15
• Fahrenheit scale:
9
TF  TC  32
5
Anders Cornelius
Celsius
(1701 - 1744)
Gabriel Daniel
Fahrenheit
(1686 - 1736)
Temperature and heat
• Heat (Q): energy transferred between a system and
its environment because of a temperature difference
that exists between them
• SI Unit: Joule
• Alternative unit: calorie (cal):
1 cal  4.1868 J
Absorption of heat
Q  cmT  cm(Tf  Ti )
• Specific heat (c): heat capacity per unit mass
• Common states (phases) of matter: solid, liquid, gas
Q  Lm
• Latenet heat (L): the amount of energy per unit
mass transferred during a phase change (boiling,
condensation, melting, freezing, etc.)
Q
Q
Absorption of heat
Q
Q
Absorption of heat
Absorption of heat
Chapter 17
Problem 25
How much energy does it take to melt a 65-g ice cube?
Heat transfer mechanisms
• Thermal conduction
• Conduction rate:
Hcond
• Thermal resistance:
Th  Tc
Q
   kA
t
L
L
R
k
Thermal conductivity
• Conduction through a composite rod:
Hcond
ATh  Tc 

L1 / k1  L2 / k2
ATh  Tc 

R1  R2
Absorption of heat
Heat transfer mechanisms
• Thermal radiation
• Radiation rate:
Emissivity
Prad  eAT
• Stefan-Boltzmann constant:
• Absorption rate:
4
  5.67108W / m2  K 4
Pabs  eAT
4
env
Pnet  Pabs  Prad
 eA(T  T )
4
env
Josef Stefan
(1835-1893)
4
Heat transfer mechanisms
• Convection
Heat transfer mechanisms
Chapter 16
Problem 35
An oven loses energy at the rate of 14 W per °C temperature difference between
its interior and the 20°C temperature of the kitchen. What average power must
be supplied to maintain the oven at 180°C?
Avogadro’s number
• Mole – amount of substance containing a number of
atoms (molecules) equal to the number of atoms in a
12 g sample of 12C
• This number is known as Avogadro’s number (NA):
NA = 6.02 x 1023 mol -1
• The number of moles in a sample
N
m
m
n


N A m0 N A M
Amedeo Avogadro
(1776 -1856)
N – total number of atoms (molecules)
m – total mass of a sample, m0 – mass of a single
atom (molecule); M – molar mass
Ideal gases
• Ideal gas – a gas obeying the ideal gas law:
PV  nRT
R – gas constant
R = 8.31 J/mol ∙ K
Ludwig Eduard
Boltzmann
(1844-1906)
PV  nRT  ( N / N A )  RT  N  ( R / N A )  T  Nk BT
kB – Boltzmann constant
kB = 1.38 x 1023 J/K
PV  Nk BT
Ideal gases
• The gas under consideration is a pure substance
• All molecules are identical
• Macroscopic properties of a gas: P, V, T
• The number of molecules in the gas is large, and the
average separation between the molecules is large
compared with their dimensions – the molecules
occupy a negligible volume within the container
• The molecules obey Newton’s laws of motion, but as
a whole they move randomly (any molecule can move
in any direction with any speed)
Ideal gases
• The molecules interact only by short-range forces
during elastic collisions
• The molecules make elastic collisions with the walls
and these collisions lead to the macroscopic
pressure on the walls of the container
• At low pressures the behavior of molecular gases
approximate that of ideal gases quite well
Ideal gases
(m0v) xi  (m0vxi )  (m0vxi )  2m0vxi
Fxi 
(m0 v) xi
t
m0 (v xi )
2m0vxi


d
2d / vxi
N
F
xi
2
N
 m (v
0
2
xi
) /d
Fx
P
 i 1 2  i 1
2
A
d
d
N
2
m0  (v xi )
2
2
m0 N vx m0 nNA v
i 1



3
d N
V
3V
v 
2
x
2
(
v
)
 xi
i 1
N
v 2  v x2  v y2  v z2  3v x2
m0 nN A v
P
3V
2
Ideal gases
m0 N A v 2
 nRT
PV  n
3
m0 N A v 2
 RT
3
• Root-mean-square (RMS) speed:
vrms  v 
2
3RT
m0 N A
Translational kinetic energy
• Average translational kinetic energy:
2
K avg
m0 v
m0 v


2
2
2
2
m0 vrms

2
K avg
3RT
m0
3RT
m0 N A


2N A
2
3
 k BT
2
• At a given temperature, ideal gas molecules have
the same average translational kinetic energy
• Temperature is proportional to the average
translational kinetic energy of a gas
Internal energy
• For the sample of n moles, the internal energy:
Eint  (nNA )Kavg
3
3
 nN A kT  nRT
2
2
3
Eint  nRT
2
• Internal energy of an ideal gas is a function of gas
temperature only
Distribution of molecular speeds
• Not all the molecules have the same speed
• Maxwell’s speed distribution law:
 m0 

N v  4N 
 2k BT 
3/ 2
m0 v 2

2 k BT
2
ve
James Clerk Maxwell
(1831-1879)
Nvdv – fraction of molecules with speeds in the range
from v to v + dv
Distribution of molecular speeds

• Distribution function is normalized to 1:

vavg
• Average speed:

• RMS speed:
vrms
• Most probable
speed:
vmp
v
2
(v) dv  1
0
8 RT
  vN v (v ) dv 
M
0
3RT
  v N v (v)dv 
M
0
dN v
vmp   0
dv
2RT

M
N
Thermal expansion
• Thermal expansion: increase in size with an
increase of a temperature
• Linear expansion:
L
  T
L
• Volume expansion:
V
 T
V
  3
Thermal expansion
Chapter 17
Problem 30
A copper wire is 20 m long on a winter day when the temperature is - 12°C. By
how much does its length increase on a 26°C summer day?
Questions?
Answers to the even-numbered problems
Chapter 16
Problem 22
2500 J/(kg K)
Answers to the even-numbered problems
Chapter 16
Problem 40
2.0 × 102 Pa/K
Answers to the even-numbered problems
Chapter 17
Problem 18
3.2 × 1023
Answers to the even-numbered problems
Chapter 17
Problem 36
11 L