Transcript Example

Thermodynamics
Introduction: what is thermodynamics about?
• Study heat, temperature, internal energy, gas, liquid,
solid, melting, boiling, exploding, P-V-T.
• Explain bulk properties of matter and the correlation
with the mechanics of atoms and molecules.
• Understand why/ how the refrigerator cools stuff
• Understand why/ how automobile engines power cars
• Understand why/ how power plants work
• Understand where the work due to friction goes
Note: presentation main figures are that of Halliday and
Resnick 6th edition unless otherwise specified.
Chapter 18
Temperature, Heat and the First Law of
Thermodynamics
18.2 Thermodynamics
18.3 Zeroth law of thermodynamics
18.4 Measuring temperature and the constant volume gas
thermometer
18.5 The Celsius and the Fahrenheit scales
18.6 Thermal expansion
18.7 Temperature and Heat
18.8 The Absorption of Heat by Solids and Liquids
18.9 Heat and Work
18.10 The FLTD
18.11 Special cases of FLTD
18.12 Heat Transfer
18.2 Thermodynamics:
is the study of thermal (internal) energy of systems.
The zero kelvin (or absolute
zero) temperature is the
limiting low temperature.
Room temperature ~ 300 K
Frozen water: 273.15 K
Boiling water: 373.15 K
Outer space ~ 3 K
Big Bang ~ 1039
Liquid helium ~ 4 K
(limiting) lowest: 0 K
18.3 The Zeroth Law of thermodynamics (ZLTD):
“If bodies A and B are each in thermal
equilibrium with a third body C, then they are
in thermal equilibrium with each other.”
What do we mean by thermal equilibrium?
If two systems (confined within an insulating box) are put in
contact, and there is no net transfer of thermal energy
between them, we say that the two systems are in “thermal
equilibrium”.
ZLTD:
Every body has a property which we call temperature. When
two bodies are in thermal equilibrium they have the same
temperature; when two bodies have the same temperature
they are in thermal equilibrium!
Why did we call it the “zeroth” law?
It is a logical afterthought; came to light only in the 1930s’!!
18.4 Measuring Temperature:
Triple Point of Water:
Water may exist at different temperatures; however, there is only
one temperature at which liquid water, water vapor and solid water
(ice) can coexist.
We call this temperature the “triple point of water” and is denoted
T3. We define this temperature to be 273.16 K.
T3 = 273.16 K
Hence, a degree kelvin is 1/273.16 of the difference in temperature
between triple point of water and absolute zero!
The constant-volume gas thermometer:
pV=nRT
Therefore,
T=Cp
(1)
T3 = C p3
(2)
also,
dividing (1) by (2):
T = T3 (p/ p3) (3)
As usual, for real gases, the Universal gas law works better for
high T, low p and low n (low density of gas). Therefore,
T = (273.16 K) limgas -> 0 (p/ p3)
T and p are absolute temperature and pressure
Gases behave according to the Universal gas law:
18.5 The Celsius and Fahrenheit Scales:
If TC is the temperature on the Celsius scale, and TF is
the temperature on the Fahrenheit scale, then:
TC = T - 273.15
and
TF = (9/5) TC + 32
Note that:
DTC = DT
and
DTF = (9/5) DTC
It will help to remember that:
0 oC = 32 oF = 273.15 K
and,
100 oC = 212 oF = 373.15 K
Example:
What is 104 degrees Fahrenheit on the Celsius and Kelvin scales?
18.6 Thermal Expansion:
Linear expansion:
When a metal rod of length L heats up by a difference in
temperature DT, it will increase in length by DL according to:
DL = L a DT
a is called the coefficient of linear expansion.
a is usually positive.
When the rod cools down, is DT positive or negative?
Is DL positive or negative?
Does the rod expand or shrink/ contract?
Is linear expansion good or bad?
It is normally bad (teeth fillings, railroad tracks/ expansion slots,
…etc. ), but can be good (thermostat bimetal strip, aircraft
manufacturing !!)
What would it mean for a to be negative? Does this make sense?
Are there material with negative a ?
Assuming a is positive (as is the case in almost all materials),
what happens to a hole when a punctured metal bar heats up?
Note: In general,
agas > aliquid > asolid
Does this make sense to you?
What effect does this have on the ‘familiar’ liquid-in-glass
thermometers?
Example: H&R (19-E10)
An aluminum flagpole is 33 m high. By how much does its
length increase as the temperature increases by 15 Co?
Hint: aAl = 23 x 10(-6) /Co
18.7 Temperature, Heat and Thermal Energy:
Internal energy: all of the energy belonging to a system (while
stationary) including nuclear energy, chemical energy, elastic
energy as well as thermal energy.
Thermal energy: is that portion of internal energy that consists of
kinetic and potential energies associated with random motion of
atoms and molecules. It changes when temperature changes.
Thermal energy transfer (heat): is the transfer of thermal
energy caused by temperature difference between the system
and its surroundings.
Heat is usually denoted Q.
Sign convention:
Q > 0 when heat is absorbed by the system.
Q < 0 when heat is released/ lost / expelled
from the system.
Q = 0 when there is no thermal energy transfer.
Can energy be transferred between two systems even
when there is no heat (i.e. no thermal energy transfer)?
Must heat change the amount of thermal energy in the system!
Heat and work are not intrinsic properties of a system. They
describe a process not a state.
Units of heat:
The amount of heat necessary to raise the temperature of 1 g of
water from 14.5 to 15.5 degrees Celsius is called a calorie,
abbreviated cal
1 calorie = 1 cal = 4.186 J
1 Calorie = 1 kilocalorie = 4.186 kJ
The amount of heat necessary to raise the temperature of 1 lb of
water from 63 to 64 degrees Fahrenheit is called a Btu.
1 cal = 3.969 10-3 Btu = 4.186 J
Interaction: How many joules is a Btu?
18.8 The Absorption of Heat by Solids and Liquids:
Heat Capacity (C):
If an object absorbs energy Q when heating from temperature Ti
to temperature Tf, then the heat capacity (C) is such that:
Q = C (Tf - Ti) = C DT
What are the units for C?
J/K or cal/K or J/oC or kJ/K, …etc.
Example: 1440 joules of heat is
supplied to an aluminum nugget. It is
found that its temperature increases
by 8 degrees Celsius. What is the
heat capacity of this nugget?
Specific Heat (c):
Is the heat capacity per unit mass:
c = C/m
Q = m c DT
What are the units of c?
Example: What is the mass of the aluminum nugget in
previous example?
Hint: cAl = 900 J/(kg K)
Can the heat capacity of different objects made from the same
material be different?
Can the specific heat of different objects made from the same
material be different?
What is the specific heat of water?
1 cal/(g oC) = 1 Btu/(lb oF) = 4190 J/(kg K)
What is great about cH2O ?
Molar Specific Heat (cm):
Is the heat capacity per mole of substance:
cm = C/n
Q = n cm DT
What are the units of cm?
Example: What is the molar specific heat of aluminum nugget
of the previous example?
Hint: MAl = 27 gram/mole
Can C, c or cm be negative?
We said that heat and work are processes; so, does the specific
heat depend on the process or is it a ‘property’ of the substance?
For solid and liquids, there is little dependence on the process.
For gases, the specific heat depends considerably on the process.
Must the temperature of an object increase when we add heat?
It can “transform” from one state (solid, liquid or gas) to
another while staying at the same temperature!!
The amount of heat per unit mass needed for the
transformation is called the latent heat of transformation (L).
Q=mL
What are the units for L?
For vaporization or condensation use Lv.
For melting or freezing use Lf.
Which is larger for a specific material: Lv or Lf ?
Braintweezer: why does your hand feel cold
when perfume evaporates of it?
Interaction: What happens to 1/5 kg of water, in a 340 liter closed
container, originally at -2oC when supplied with:
i- 12000 cal?
ii- 19600 cal?
iii- 100000 cal?
iv- 150000 cal?
cp = 35.4 J/(mol K)
cv = 27 J/(mol K)
Lv = 2256 kJ/kg
Lf = 333 kJ/kg
cice = 0.5 cal/ (g K)
18.9 A Closer look at Heat and Work:
A “thermodynamic process” can proceed
from an initial “state” to a final state.
Let’s calculate the infinitesimal the work
done by the system:
dW = F · ds = p dV
The work done by the system during a process is:
W = dW = p dV
Sign convention for W:
work done by the system: W is positive
work done on the system: W is negative
Work (W) and heat (Q) depend on the process, not only on
the initial and final states.
W = p dV
The ‘amount’ of work is
the area under the curve
of a p-V diagram!!
In (e), the work
is negative!
In which process (a, b, c, du, dd) is the
work done by the system greatest?
The net work in a
thermodynamic cycle is the
area inside the closed curve.
Clockwise: positive
W & Q are path dependent!!
Counterclockwise: negative
18.10 The First Law of Thermodynamics:
Experimentally, Q-W is independent of the process!!
It makes sense to think that Q-W represents a change in some
intrinsic property of the system. We call this property internal
energy (Eint).
FLTD:
DEint = Eint,f - Eint,i = Q - W
This does make sense!!
The internal energy increases when heat is added or when there is
negative work (when work is done on the system).
Check point (19-5): in which of the four processes is: (see figure)
A- the change in internal energy of the system greatest?
B- the work done by the system greatest?
C- the heat absorbed by the system greatest?
18.11 Some Special Cases of the First Law of
Thermodynamics:
Adiabatic process:
No thermal energy transfer; when the system is
very well insulated, or when the process is very
rapid (e.g. internal combustion engine).
Q=0
DEint = -W
What does this mean/ does this make sense?
Constant volume (Isovolumetric) process:
constant volume, no work!
W=0
DEint = Q
Q (i.e.heat goes into increasing the internal energy; e.g. during
the explosion in an engine cylinder).
Cyclical process:
No change in system properties including internal energy!
DEint = 0
Q =W
Free expansion:
Q=W=0
DEint = 0
Adiabatic Free Expansion in
an ideal gas:
T does not change
(why?)
18.12 Heat transfer Mechanisms:
1- Conduction:
Heat transfers by the exchange of kinetic energy between molecules;
cooler (less energetic) molecules increase in temperature through
collisions with more energetic (hotter) molecules / atoms/ electrons.
(e.g., holding a rod over a flame).
Good conductors:
Poor conductors:
Law of heat conduction:
For an insulated rod of length L and cross section A with ends in
thermal contact with heat reservoirs at TH and TC. The average power
conducted (Pcond) is:
Pcond = Q/t = (-) k A DT/Dx
k: thermal conductivity. Large k means
good conductors
Pcond: thermal energy transfer rate
Dx = x-end – x-start
DT = Tx-end – Tx-start`
Negative sign indicates that heat flows from
higher temperature to lower temperature.
No temperature gradient no transfer!
L = |Dx|
Thermal resistance to conduction (R):
R = L/k
High R means good resistor (poor conductor).
Conduction through a composite slab:
Pcond = A DT/SRi
Example: H&R (19-E54)
The average rate at which energy is conducted outward through
the ground surface in North America is 54.0mW/m2, and the
average conductivity of the near surface rocks is 2.5 W/(m K).
Assuming a surface temperature of 10.0 oC, find the temperature
at a depth of 35.0 km.
2- Convection:
Transfer of heat through motion of fluid (e.g. candle, wind,
oceans, inside the sun)
3- Radiation:
Have you ever thought why a car
radiator is painted black?
Prad = s e A T4
s = 5.6703 10-8 W/(m2 K4)
e is the “emissivity”.
Good absorbers are good radiators and have e ~ 1.
Bad absorbers are good reflectors and have e ~ 0.
Pabs = s e A Tenv4
Pnet, abs = s e A (Tenv4 - T4)
Example: H&R (19-P62)
A sphere of radius 0.500 m, temperature 27.0 oC, and emissivity
0.850 is located in an environment of temperature 77.0 oC. At
what rate does the sphere: (a) emit and (b) absorb thermal
radiation. (c) what is the sphere’s net rate of energy exchange?