Download The First Law of Thermodynamics

Thermodynamics II
The First Law of Thermodynamics
•
Heat and Work. First Law of Thermodynamics
•
Heat and Work on Quasi-Static Processes for a Gas.
The Second Law of Thermodynamics
•
Heat Engines and the Second Law of Thermodynamics
•
Refrigerators and the Second Law of Thermodynamics
•
The Carnot Engine
•
Heat Pumps
•
Irreversibility and disorder. Entropy
References: Tipler; wikipedia,…
The First Law of Thermodynamics
Energy exists in many forms, such as mechanical energy, heat,
light, chemical energy, and electrical energy. Energy is the
ability to bring about change or to do work.
Thermodynamics is the study of energy.
Surroundings
System
The frontier of the system is
arbitrarily chosen
The system can interchange mass and energy
through the frontier with the environment.
An example of “closed system” - no mass flow- is
the gas confined in a cylinder. The frontier –in this
case physical- is made by the cylinder and the
piston walls.
The First Law of Thermodynamics
First Law of Thermodynamics → Conservation of Energy:
Energy can be changed from one form to another, but it cannot be created or
destroyed. The total amount of energy and matter in the Universe remains
constant, merely changing from one form to another.
The First Law of Thermodynamics (Conservation) states that energy is
always conserved, it cannot be created or destroyed. In essence,
energy can be converted from one form into another.
The energy balance of a system –as a consequence of FLT- is a
powerful tool to analyze the interchanges of energy between the system
and its environment.
We need to define the concept of internal energy of the system, Eint as
an energy stored in the system.
Warning: It is no correct to say that a system has a large amount of heat
or a great amount of work
http://www.emc.maricopa.edu/faculty/farabee/BIOBK/BioBookEner1.html
The First Law of Thermodynamics. Heat, Work and Internal Energy
Joule’s Experiment and the First Law of Thermodynamics.
Equivalence between work and heat
1 calorie = 4.184 Joules
Work is done on water. The energy is transferred to
the water – i. e. the system- . The energy transferred
appears as an increment of temperature.
We can replace the insulating walls by conducting
walls. We can transfer heat through the walls to the
system to produce the same increment of temperature.
Schematic diagram for Joule´s
experiment. Insulating walls to
prevent heat transfer enclose water.
As the weights fall at constant speed,
they turn a paddle wheel, which does
work on water.
If friction in mechanism is negligible,
the work done by the paddle wheel
on the water equal the change of
potential energy of the weights.
The increment of temperature of the system reflects the
increase of Internal Energy. Internal energy is a
function of state of the system
The sum of the heat transfer into the
system and the work done on the
system equals the change in the
internal energy of the system
Eint  Qin  Won
The First Law of Thermodynamics
Another method of
doing work.
Electrical work is
done on the
system by the
generator, which
is driven by the
falling weight.
The First Law of Thermodynamics. Application to a particular case:
A gas confined in a cylinder with a movable piston
The state of the gas will be
described by the Ideal Gas-Law.
PV  n R T
How the confined gas
interchange energy (heat and
work) with the surroundings?.
What is the value of the internal
energy for the gas in the cylinder
First Law
Eint  Qin  Won
dEint  Qin  Won
How can we calculate the
energy –heat and/or worktransferred, added of
subtracted, to the system?
“Quasi static processes”: a type of processes where the gas moves through a
series of equilibrium states. Then, we can apply the IGL. In practice, if we move
slowly the piston, will be possible to approximate quasi-static processes fairly well.
First Law of Thermodynamics. Fluxes of energy and mass on the earth
surface. Energy balance.
Rn = Rns + Rnl
λET
ΔE
H
Ph
Ph
CO2
Energy fluxes:
Rn : Net gain of heat energy from
radiation
λET Latent heat, Energy associated
to the flux of water vapor leaving
from the system
H Sensible Heat.
G Heat energy by conduction to the
D
soil
Ph: Net photosynthesis
ΔEint: Change of the internal energy
of the system
D: Advection
G
Net fluxes of mass
Water vapor
Carbon –CO2
Energy balance (applying First Law):
Rn – H – λET – G – D - Ph = ΔEint
The First Law of Thermodynamics. Application to a particular case:
A gas confined in a cylinder with a movable piston. Internal Energy
Internal Energy for an Ideal Gas.
Only depends on the temperature of the
gas, and not of its volume or pressure
Experiment: Free expansion.
For a gas at low density – an ideal gas-, a
free expansion does not change the
temperature of the gas.
What is the value of the internal
energy for the gas in the cylinder?
If heat is added at constant volume, no work
is done, so the heat added equals the
increase of thermal energy
Eint  Qin
Qin  CV T
and
dEint  CV dT  n cV dT
Internal Energy is a state function, i.e. it is not dependent on the
process, only it depends of the initial and final temperature
The First Law of Thermodynamics. Application to a particular case:
A gas confined in a cylinder with a movable piston. Heat
Heat transferred to a system
If heat is added at constant
pressure the heat energy
transferred will be used to
expand the substance and to
increase the internal energy.
QP  CP T
QP  CP dT
If the substance expands, it
does work on its surroundings.
Applying the First Law of Thermodynamics
If heat is added at constant
volume, no work is done, so
the heat added equals the
increase of thermal energy
Qin,V  CV dT  n cV dT
Qin,V  CV T  n cV T
dEint  QP  Won  CP dT  PdV
PdV  (CP  CV ) dT
as d ( PV )  PdV  dP V
and P const  dP 0
CP  CV  n R
The expansion is usually negligible for solids
and liquids, so for them CP ~ CV.
The First Law of Thermodynamics. Application to a particular case:
A gas confined in a cylinder with a movable piston
Heat transferred to a system. A summary
Heat energy can be added (or lost) to the system. The value of the heat
energy transferred depends of the process.
Typical processes are
QV  CV T ; QV  CV dT
- At constant volume
- At constant pressure
Ideal Gas
For the case of ideal gas
QP  CP T ; QP  CP dT
CP  CV  n R Relationship of Mayer
From the Kinetic theory,
for monoatomic gases
for biatomic gases
3
3
J
CV  n R;  cV  R  12.47
2
2
mol K
5
5
J
CV  n R  cV  R  20.79
2
2
mol K
For solids and liquids, as the expansion at constant pressure is usually
negligible CP ~ CV.
Adiabatic: A process in which no heat flows into or out of a system is
called an adiabatic process. Such a process can occur when the system is
extremely well insulated or when the process happens very quickly.
The First Law of Thermodynamics. Application to a particular case:
A gas confined in a cylinder with a movable piston. Work
Work done on the system, Won , is the energy transferred as work to the system.
When this energy is added to the system its value will be positive.
The work done on the gas in an
expansion is
V2
Won gas    P dV
V1
Won gas  Wby gas
P- V diagrams
Constant pressure
V2
Won gas    P dV  P(V1  V2 )
V1
If 5 L of an ideal gas at a pressure of 2 atm is cooled
so that it contracts at constant pressure until its
volume is 3 l, what is the work done on the gas?
[405.2 J]
The First Law of Thermodynamics. P-V diagrams
P- V diagrams
Conecting an initial state and a final state
by three paths
Isothermal
V2
Constant pressure
Constant Volume
Constant Temperature
Won gas    P dV  P(V1  V2 )
V1
V2
Won gas    P dV  0
V1
V2
Won gas   
V1
n RT
V2
dV  n R T ln
V
V1
The First Law of Thermodynamics
A biatomic ideal gas undergoes a cycle starting at
point A (2 atm, 1L). Process from A to B is an
expansion at constant pressure until the volume is 2.5
L, after which is cooled at constant volume until its
pressure is 1 atm. It is then compressed at constant
pressure until the volume is again 1L, after which it is
heated at constant volume until it is back in its original
state. Find (a) the work, heat and change of internal
energy in each process (b) the total work done on the
gas and the total heat added to it during the cycle.
A system consisting of 0.32 mol of a monoatomic ideal gas
occupies a volume of 2.2 L, at a pressure of 2.4 atm.
The system is carried through a cycle consisting:
1. The gas is heated at constant pressure until its volume
is 4.4L.
2. The gas is cooled at constant volume until the pressure
decreased to 1.2 atm
3. The gas undergoes an isothermal compression back to
initial point.
(a) What is the temperature at points A, B and C
(b) Find W, Q and ΔEint for each process and for the entire
cycle
The First Law of Thermodynamics. Processes. P-V Diagrams
Adiabatic Processes. No heat flows into or out of the system
The First Law of Thermodynamics. Processes. P-V Diagrams
Adiabatic Processes. No heat flows into or out of the system
Qin  0
Adiabatic process
then Eint  Won,adiabatic  n cV T
The equation of curve describing the adiabatic
process is
P V   const ;  
T V  1  const
T  P1  const
A quantity of air is compressed adiabatically
and quasi-statically from an initial pressure of
1 atm and a volume of 4 L at temperature of
20ºC to half its original volume. Find (a) the
final pressure, (b) the final temperature and (c)
the work done on the gas.
cP = 29.19 J/(mol•K); cV = 20.85 J/(mol•K).
M=28.84 g
CP
CV
adiabatic coefficient
We can use the ideal gas to rewrite
the work done on the gas in an
adiabatic process in the form
Won gas,adiab 
Pf V f  Pi Vi
 1
The First Law of Thermodynamics. Processes. P-V Diagrams
A polytropic process is a thermodynamic process that obeys the relation:
PVn = C,
where P is pressure, V is volume, n is any real number (the polytropic index), and C is a
constant. This equation can be used to accurately characterize processes of certain systems,
notably the compression or expansion of a gas, but in some cases, possibly liquids and
solids.
For certain indices n, the process will be synonymous with other processes:
if n = 0, then PV0=P=const and it is an isobaric process (constant pressure)
if n = 1, then for an ideal gas PV= const and it is an isothermal process (constant
temperature)
if n = γ = cp/cV, then for an ideal gas it is an adiabatic process (no heat transferred)
if n = ∞ , then it is an isochoric process (constant volume)
The First Law of Thermodynamics.
Cyclic Processes. P-V Diagrams
Two moles of an ideal monoatomic gas have an initial pressure P1 = 2 atm and an initial
volume V1 = 2 L. The gas is taken through the following quasi-static cycle:
A.- It is expanded isothermally until it has a volume V2 = 4 L.
B.- It is then heated at constant volume until it has a pressure P3= 2 atm
C.- It is then cooled at constant pressure until it is back to its initial state.
(a) Show this cycle on a PV diagram. (b) Calculate the head added and the work done by
the gas during each part of the cycle. (c) Find the temperatures T1, T2, T3
Solve the above problem considering the STEP A is an adiabatic
expansion. Determine the efficiency of the both cycles. Determine the
efficiency of a Carnot cycle operating between the temperature extremes
of the both cycles..
The First Law of Thermodynamics.
Cyclic Processes. P-V Diagrams
The First Law of Thermodynamics.
Cyclic Processes. P-V Diagrams
At point D in figure the pressure and temperature of
2 mol of an ideal monoatomic gas are 2 atm and
360 K. The volume of the gas at point B on the PV
diagram is three times that at point D and its
pressure is twice that a point C. Paths AB and DC
represent isothermal processes. The gas is carried
through a complete cycle along the path DABCD.
Determine the total work done by the gas and the
heat supplied to the gas along each portion of the
cycle
The First Law of Thermodynamics.
Cyclic Processes. P-V Diagrams
The First Law of Thermodynamics.
Cyclic Processes. P-V Diagrams
Second Law of Thermodynamics. Heat Engines
• Heat Engines and the Second Law of
Thermodynamics
• Refrigerators and the Second Law of
Thermodynamics
• The Carnot Engine
• Heat Pumps
• Irreversibility and disorder. Entropy
A steamboat or steamship, sometimes
called a steamer, is a ship in which the
primary method of propulsion is steam
power
Second Law of Thermodynamics. Heat Engines
Zeroth Law → Temperature
First Law of Thermodynamics → Energy balance on the system.
(Conservation of Energy)
What are the rules to obtain useful energy (those that drives a machine,…)?
Why the heat flows spontaneously from the hotter body to the colder one?
Second Law of Thermodynamics
No system can take energy as heat from a single source and
convert it completely into work without additional net changes in
the system or in the surroundings.
SECOND LAW, KELVIN STATEMENT
A process whose only net result is to transfer energy as heat from
a cooler object to a hotter one is impossible.
SECOND LAW, CLAUSIUS STATEMENT
Second Law of Thermodynamics.
Heat Engines. Steam Engine
A heat engine is a cyclic device whose purpose is to convert as much heat
input into work as possible. Working substance (water in steam engine, air and
gasoline vapor in internal-combustion engine), that absorbs a quantity of heat,
Qh, does work on its surroundings, and gives an amount of heat, Qc, as it returns
to initial state.
Several hundreds atmospheres and
water vaporizes at about 500 ªC
Schematic drawing of a steam engine.
Heat Engines.
Internal-Combustion Engine
Second Law of Thermodynamics.
Otto cycle representing
the internal-combustion
engine
Second Law of Thermodynamics.
Heat Engines.
No system can take energy as heat from a single source and
convert it completely into work without additional net changes in the
system or in the surroundings.
SECOND LAW, KELVIN STATEMENT
Efficiency of a heat engine
W Qh  Qc
Qc


1
Qh
Qh
Qh
It is impossible to make a heat engine
with a efficiency of 100 per cent
It is impossible for a heat engine
working in a cycle to produce only the
effect of extracting heat from a single
reservoir and performing an equivalent
amount of work
Second Law of Thermodynamics.
Refrigerators. Heat Pumps
Schematic representation of a
refrigerator.
COP. Coefficient
of Performance
of a Refrigerator
Qc
COP 
W
Second Law of Thermodynamics.
Refrigerators.
A process whose only net result is to
transfer energy as heat from a cooler object
to a hotter one is impossible.
SECOND LAW, CLAUSIUS STATEMENT
It is impossible for a refrigerator
working in a cycle to produce only the
effect of extracting heat from a cold
object and reject the same amount of
heat to a hot object
COP. Coefficient
of Performance
of a Refrigerator
Qc
COP 
W
Second Law of Thermodynamics.
Refrigerators. Heat Pumps
The objective of a heat pump is to heat a
region of interest
Useful energy
Heat Pump
Qh
COPHP 
W
COPHP. Coefficient of
Performance of a Heat
pump
Equivalence of the Heat Engine
and Refrigerator Statements
Second Law of Thermodynamics.
Maximum efficiency for a heat engine.
The Carnot Engine
What is the maximum possible
efficiency for a heat engine working
between two heat reservoirs?
Carnot Theorem
No engine working between two given
heat reservoirs can be more efficient
than a reversible engine working
between those two reservoirs
Carnot engine: A reversible engine
working in a cycle between two heat
reservoirs. The cycle is called a Carnot
cycle
Maximum efficiency for a heat engine.
Carnot cycle is a reversible cycle
between only two heat reservoirs
The Carnot Cycle
1.- A quasi-static isothermal absorption of
heat from a heat reservoir
2.- A quasi-static adiabatic expansion to a
lower temperature
3.- A quasi-static isothermal exhaustion of
heat to a cold reservoir
4.- A quasi-static adiabatic compression
back to the original state
W Qh  Qc
Qc


1
Qh
Qh
Qh
Maximum efficiency for a heat engine.
The Carnot Cycle
Carnot cycle is a reversible cycle
between two heat reservoirs

W Qh  Qc
Q

1 c
Qh
Qh
Qh
Isothermal processes
V2
Qh  Wby gas  
V1
V2
P dV  n R Th ln
V1
V4
Qc  Won gas    P dV  n R Tc ln
V3
Adiabatic processes
 1
 1
Th V2  Tc V3
Th V1 1  Tc V4 1
V2
Qc
V1 Tc


Qh T ln V3 Th
h
V4
Tc ln

V3
V4
V2 1 V3 1
V2 V3
  1  
 1
V1
V4
V1 V4
W Qh  Qc
Q
T

1 c 1 c
Qh
Qh
Qh
Th
Second Law of Thermodynamics. Maximum efficiency for a Heat Engine;
Maximum COP for a Refrigerator and for a Heat Pump
W Th  Tc
C 

Qh
Th
Qc
Tc
COPmax 

W Th  Tc
Q
Th
COPHP max  h 
W Th  Tc
A steam engine works between a hot reservoir at 100 ºC and a cold reservoir at 0ºC.
(a) What is the maximum possible efficiency of this engine? If the engine is run
backwards as refrigerator, what is its maximum coefficient of performance? If the
engine is running as heat pump, what is the maximum coefficient of performance?
Second Law of Thermodynamics.
Irreversibility, desorder:
Entropy
The free expansion of an idealgas: No work, no heat, no
change of internal energy,…
But, is it the same state after
and before of the free
expansion?
Entropy, S: a physical magnitude whose net increment (system +
surroundings) indicates the irreversibility of a process:
In a irreversible process, the entropy of the universe increases
For any process, the entropy of the universe never decrease
A spontaneous heat transfer (from hotter body to a colder one) implies
an increment of entropy (It is a irreversible process)
Entropy: a thermodynamic function of disorder
dS 
Qrev
T