Transcript Chapters 19&20

Chapters 19, 20
Temperature, Heat, and the First Law of
Thermodynamics
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
 273.16 K 
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)
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 19
Problem 5
A copper telephone wire has essentially no sag between poles 35.0 m apart on
a winter day when the temperature is – 20.0°C. How much longer is the wire on
a summer day when T = 35.0°C?
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(T f  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 20
Problem 17
A 1.00-kg block of copper at 20.0°C is dropped into a large vessel of liquid
nitrogen at 77.3 K. How many kilograms of nitrogen boil away by the time the
copper reaches 77.3 K? (The specific heat of copper is 0.0920 cal/g °C. The
latent heat of vaporization of nitrogen is 48.0 cal/g.)
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  NkBT
kB – Boltzmann constant
kB = 1.38 x 1023 J/K
PV  NkBT
Heat and work
 
dW  F  ds  ( PA)  ds  P( Ads)  PdV
Vf
W   PdV
Vi
Thermodynamic cycle
Heat and work
• Work is done by the system:
Vf
W   PdV
Vi
• Work is done on the system :
Vf
W    PdV
Vi
The first law of thermodynamics
• Work and heat are path-dependent quantities
• Quantity Q + W = ΔEint (change of internal energy)
is path-independent
• 1st law of thermodynamics: the internal energy of a
system increases if heat is added to the system or
work is done on the system
Eint  Eint, f  Eint,i  Q  W
The first law of thermodynamics
• Adiabatic process: no heat transfer between the
system and the environment
Eint  0  W  W
• Isochoric (constant volume) process
Eint  Q  0  Q
• Free expansion:
Eint  0  0  0
• Cyclical process:
Eint  Q  W  0
Q  W
Chapter 20
Problem 29
Consider the cyclic process depicted in the figure. If Q is negative for the
process BC and ΔEint is negative for the process CA, what are the signs of Q,
W, and that are associated with each process?
Heat transfer mechanisms
• Thermal conduction
• Conduction rate:
Pcond
• Thermal resistance:
Th  Tc
Q
  kA
t
L
L
R
k
Thermal conductivity
• Conduction through a composite rod:
Pcond
ATh  Tc 

L1 / k1  L2 / k 2
ATh  Tc 

R1  R2
Heat transfer mechanisms
• Thermal radiation
• Radiation rate:
Emissivity
Prad  eAT
• Stefan-Boltzmann constant:
• Absorption rate:
4
  5.67 10 8W / m 2  K 4
Pabs  eAT
4
env
Pnet  Pabs  Prad
 eA(T
4
env
Josef Stefan
(1835-1893)
T )
4
Chapter 20
Problem 46
At high noon, the Sun delivers 1000 W to each square meter of a blacktop road.
If the hot asphalt loses energy only by radiation, what is its steady-state
temperature?
Heat transfer mechanisms
• Convection
Heat transfer mechanisms
Questions?
Answers to the even-numbered problems
Chapter 19
Problem 2
(a) 810°F
(b) 450 K
Answers to the even-numbered problems
Chapter 19
Problem 6
1.20 cm
Answers to the even-numbered problems
Chapter 19
Problem 18
(a) 2.99 mol
(b) 1.80 × 1024 molecules
Answers to the even-numbered problems
Chapter 20
Problem 26
(a) 12.0 kJ
(b) –12.0 kJ