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Chapter 10 Thermal Physics. William Thomson (Lord Kelvin) (1824 - 1907). 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) - PowerPoint PPT Presentation
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Chapter 10
Thermal Physics
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
KT 16.2733
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
ghPP 0
CPT
33 CPT
33 P
PTT
3
16.273P
PK
Celsius and Fahrenheit scales
• Celsius scale:
• Fahrenheit scale:
Anders Cornelius Celsius
(1701 - 1744)
Gabriel DanielFahrenheit
(1686 - 1736)
15.273TTC
325
9CF TT
Chapter 10Problem 3
Convert the following temperatures to their values on the Fahrenheit and Kelvin scales: (a) the boiling point of liquid hydrogen, –252.87°C; (b) the temperature of a room at 20°C.
Thermal expansion
• Thermal expansion: increase in size with an increase of a temperature
• Linear expansion:
• Volume expansion:
TL
L
3
TV
V
Thermal expansion
Chapter 10Problem 14
A cube of solid aluminum has a volume of 1.00 m3 at 20°C. What temperature change is required to produce a 100-cm3 increase in the volume of the cube?
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): Jcal 1868.4 1
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 – total number of atoms (molecules)m – total mass of a sample, m0 – mass of a single atom (molecule); M – molar mass
Amedeo Avogadro(1776 -1856)
M
m
Nm
m
N
Nn
AA
0
Ideal gases
• Ideal gas – a gas obeying the ideal gas law:
R – gas constant
R = 8.31 J/mol ∙ K
kB – Boltzmann constant
kB = 1.38 x 1023 J/K
nRTPV
nRTPV RTNN A )/( TNRN A )/( TNkB
TNkPV B
Ludwig EduardBoltzmann
(1844-1906)
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
xixixixi vmvmvmvm 0000 2)()()(
t
vm xi
)( 0
xi
xi
vd
vm
/2
2 0d
vm xi2
0 )(xiF
A
FP x
21
d
FN
ixi
2
1
20 /)(
d
dvmN
ixi
31
20 )(
d
vmN
ixi
N
vv
N
ixi
x
1
2
2
)(V
vNm x2
0V
vnNm A
3
20
22222 3 xzyx vvvvv
Ideal gases
• Root-mean-square (RMS) speed:
V
vnNmP A
3
20
3
20 vNm
nPV A nRT
RTvNm A
3
20
Arms Nm
RTvv
0
2 3
Translational kinetic energy
• Average translational kinetic energy:
• 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
2
20vm
Kavg 2
20 vm
2
20 rmsvm
2
3
00
ANmRT
m
AN
RT
2
3
TkK Bavg 2
3
Internal energy
• For the sample of n moles, the internal energy:
• Internal energy of an ideal gas is a function of gas temperature only
avgA KnNE )(int kTnN A 2
3 nRT
2
3
nRTE2
3int
Chapter 10Problem 30
A tank having a volume of 0.100 m3 contains helium gas at 150 atm. How many balloons can the tank blow up if each filled balloon is a sphere 0.300 m in diameter at an absolute pressure of 1.20 atm?
James Clerk Maxwell(1831-1879)
Distribution of molecular speeds
• Not all the molecules have the same speed
• Maxwell’s speed distribution law:
NvΔv – fraction of molecules with speeds in the range
from v to v + Δv
Tk
vm
Bv
BevTk
mNN 22
2/3
0
20
24
Distribution of molecular speeds
• Average speed:
• RMS speed:
• Most probable speed:
M
RTvavg
8
M
RTvrms
3
M
RTvmp
2
Questions?
Answers to the even-numbered problems
Chapter 10
Problem 28
(a) 3.0 mol(b) 1.80 × 1024 molecules
Answers to the even-numbered problems
Chapter 10
Problem 42
3.34 × 105 Pa