Download Heat Work

Heat
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What is heat?
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Heat (Q) is the “flow” or “transfer” of energy from
one system to another
Often referred to as “heat flow” or “heat transfer”
Requires that one system must be at a higher
temperature than the other
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Heat will only flow from the system with the higher
temperature to the system with the lower temperature
Heat will only flow from the system with the higher average
internal energy to the system with the lower average
internal energy
Total internal energy does not matter.
Work
V
W = ∫V 2 PdV
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First Law of Thermodynamics
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When temperature changes, internal energy has changed –
may happen through heat transfer or through mechanical work
First law is a statement of conservation of energy
Change in internal energy of system equals the difference
between the heat added to the system and the work done by the
system
ΔU = Q − W
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dU = dQ − dW
Differential form
Heat added +, heat lost -, work done by system +, work done on system –
Internal Energy U is a state property
Work W and heat Q are not
But work and heat are involved in thermodynamic processes that change
the state of the system
Molar Specific Heats for Gasses
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Molar specific heats for gasses are different if heat is
added at constant pressure vs. constant volume
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Isobaric, ΔP = 0
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QP = nCPΔT
QV = nCVΔT
W = PΔV
QP = ΔU + PΔV
Isochoric, ΔV = 0
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W = 0 ⇒ QV = ΔU
If the two processes result in the same temperature change, ΔU is the same.
⇒ QV = QP − PΔV
⇒ nC P ΔT − nCV ΔT = nRΔT
⇒ C P − CV = R
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Types of Transformations
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Isothermal, ΔT = 0
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ΔU = 0, ⇒ W = Q
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Work done by the system equals the
heat added to the system
⎛V ⎞
nRT
dV =nRT ln⎜⎜ B ⎟⎟
A
V
⎝ VA ⎠
V
V
W = ∫V B PdV = ∫V B
A
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Adiabatic, Q = 0
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⇒ ΔU = -W
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Work done by the system lowers the
internal energy of the system by an
equal amount
Temperature can change only if work
is done.
PV γ = constant, where γ =
CP
CV
Wadiabatic =
P1V1 − P2V2
γ −1
Types of Transformations
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Isobaric, ΔP = 0
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W = PΔV
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Work = Pressure*Change in Vol
W = ∫V B PdV =P ∫V B dV =P(VB − V A )
V
A
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V
A
ΔU calculated from 1st law
Isochoric, ΔV = 0
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W = 0 ⇒ ΔU = Q
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The change in internal energy of
the system equals the heat added
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Heat Transfer
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Conduction
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Results from molecular
interactions
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Energy is transferred
through interaction
Convection
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Collisions?
ΔQ
T −T
T −T
= kA 1 2 = A 1 2
Δt
l
R
l
R-Value: R =
k
dT
dQ
= − kA
dx
dt
Results from the mass
transfer of material
Think fluid flow
ΔQ
= eσAT 4
Net heat flow
Energy transferred by Δt
between two objects
electromagnetic
0
e
1
≤
≤
radiation (waves)
ΔQ
4
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σ = 5.67 ×10 −8 W / m 2 ⋅ K 4 Δt = eσA T1 − T2
Does not require a
“medium”
Radiation
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(
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Reversible & Irreversible Processes
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Example of a Reversible Process:
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Cylinder must be pulled or pushed slowly
enough (quasistatically) that the system
remains in thermal equilibrium (isothermal).
Change where system is always in
thermal equilibrium: reversible process
Change where system is not always in
thermal equilibrium: irreversible process
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Examples of irreversible processes:
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Free expansion of a gas
Melting of ice in warmer liquid
Frictional heating
Anything that is real All real processes
are irreversible!
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Heat Engine
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An engine is a device that cyclically
transforms thermal energy (heat?)
into mechanical energy (useful work).
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Efficiency: Fraction of heat flow becomes mechanical work:
e=
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W QH − QL
Q
=
=1− L
QH
QH
QH
A minimal version of an engine has two reservoirs
at different temperatures TH and TL, and follows a
idealized reversible cycle known as the Carnot
cycle.
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Efficiency of the Carnot cycle
Realistically, What is TL?
What is a reasonable eC?
eC =
W
Q
T
= 1− L = 1− L
QH
QH
TH
Heat Pumps, Refrigerators, and
Air Conditioners
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Heat pumps, refrigerators, and air conditions
are engines run in reverse:
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Refrigerator and air conditions remove heat from
the cold reservoir and put it into the surroundings
(hot reservoir), keeping the food/room cold.
A heat pump takes energy from the cold reservoir
and puts it into a room or house (hot reservoir),
thereby warming it.
In either case, energy must be added!
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Work must be performed ON the system!
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Heat Pumps and Refrigerators
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Since the (idealized) Carnot engine is the
most efficient heat engine, the Carnot
refrigerator is the most efficient refrigerator.
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Coefficient of Performance:
CP =
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QL
QL
TL
=
=
W QH − QL TH − TL
Heat Pumps work similarly but have a
different objective, namely warm the house.
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Coefficient of Performance:
CP =
QH
QH
TH
=
=
W QH − QL TH − TL
The Second Law of Thermodynamics
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There are many ways of expressing the
second law of thermodynamics; here are two:
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The Clausius form: It is impossible to construct a
cyclic engine whose only effect is to transfer
thermal energy from a colder body to a hotter body.
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Spontaneous heat flow always goes from the highertemperature body to the lower-temperature one.
The Kelvin form: It is impossible to construct a
cyclic engine that converts thermal energy from a
body into an equivalent amount of mechanical work
without a further change in its surroundings.
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Thermal energy cannot be entirely converted to work.
A 100% efficient engine is impossible.
These definitions are incomplete!
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Entropy and the Second Law
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Entropy is a measure of disorder.
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There is some controversy about this!
The process of creating disorder (as well as order)
increases entropy.
Entropy is a measure of the energy
unavailable to do work.
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It is a measure of the dispersal of energy.
Energy is dispersed (used up?) in processes that
create both order and disorder.
Entropy and the Second Law
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The entropy of an isolated system never decreases;
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spontaneous (irreversible) processes always increase
entropy.
All the consequences of the second law of
thermodynamics follow from the treatment of
entropy as a measure of disorder. (?)
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Making engines that would convert mechanical energy
entirely to work would require entropy to decrease in
isolated system – can’t happen.
Many familiar processes increase entropy – shuffling cards,
breaking eggs, and so on.
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We never see these processes spontaneously happening in
reverse – a movie played backwards looks silly. This
directionality is referred to as the arrow of time.
So, to what state is the universe heading?
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Schedule
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Monday, 4/24, Exam 6 in room 108
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Tuesday 4/25 – Thursday 4/27
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Usual drill, 1 pg “cheat sheet,” yada, yada, yada
Cover sheet with constants, etc.
Project Presentations – see website for schedule
Friday 4/28
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Monday 5/1 and Tuesday 5/2
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Office hours/help 1:00 – 4:00
Check the Announcements page for any changes
Wed, 5/3, Final Exam, 12:30 – 2:30, in 108
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You can use all sheets from this semester (6 pgs max)
Cover sheet with constants, etc.
A P-V diagram for a reversible heat engine in which 1.00
mole of argon, a nearly ideal monatomic gas, is initially at
STP (point a). Points b and c are on an isothermal. If the
engine produces positive work, a) is the cycle clockwise or
counter clockwise, b) what is the efficiency of the cycle?
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