The First Law of Thermodynamics

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27 Οκτ 2013 (πριν από 3 χρόνια και 11 μήνες)

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References: Tipler; wikipedia,…

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


The First Law of Thermodynamics

System

Surroundings

The system can exchange mass and energy
through the boundary with the environment.

An example of “closed system”
-

no mass flow
-

is
the gas confined in a cylinder. The boundary

in
this case real wall
-

is made by the cylinder and the
piston walls.

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.


The boundary of the system
is arbitrarily chosen

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 exchanges of energy between the system
and its environment.



We need to define the concept of internal energy of the system, E
int

as
an energy stored in the system.


Warning: It is not 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

Schematic diagram for Joule
´
s
experiment. Insulating walls are
necessary to prevent heat transfer
from the enclosed water to the
surroundings.

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 equals the change of
potential energy of the weights.

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 increase in temperature.

We can replace the insulating walls by conducting
walls. We can
transfer heat

through the walls to the
system to produce the same increase in temperature.

The increase in temperature of the system is a
consequence of an increase in
Internal Energy
.
Internal energy is a state function of the system

The sum of the heat transferred into
the system and the work done on the
system equals the change in the
internal energy of the system


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

How does the confined gas
exchange energy (heat and
work) with the surroundings?.

How can we calculate the
energy

heat and/or work
-

transferred, added or
subtracted, to the system?

What is the value of the internal
energy for the gas in the cylinder?

The state of the gas will be
described by the Ideal Gas Law.

“Quasi static processes”:
a type of process where the gas moves through a
series of equilibrium states. Then, we can apply the Ideal Gas Law. In practice, if
we move the piston slowly, it will be possible to approximate quasi
-
static processes
fairly well.

First Law

H

λ
ET

CO
2

Rn = Rns + Rnl

D

G

Δ
E

Ph

Ph

Net fluxes of mass

Water vapor
Carbon

CO
2

Energy fluxes
:


Rn

: Net gain of heat energy from
radiation
λ
ET

Latent heat, Energy associated
to the flux of water vapor leaving
from the system


H

Sensible Heat.


G

Heat energy by conduction to the
soil

Ph
: Net photosynthesis
Δ
E
int
: Change of the internal energy
of the system
D:

Advection

First Law of Thermodynamics. Fluxes of energy and mass on the earth
surface. Energy balance.


Energy balance (applying First Law):

Rn


H


λ
ET


G


D
-

Ph =
Δ
E
int


The First Law of Thermodynamics. Application to a particular case:

A gas confined in a cylinder with a movable piston

Internal Energy for an Ideal Gas.
It only depends on the temperature of
the gas, and not on its volume nor its
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 to the
increase in thermal energy

Internal Energy is a state function, i.e. it is not dependent on the
process, it only depends of the initial and final temperature

Heat
transferred to a system


The First Law of Thermodynamics. Application to a particular case:

A gas confined in a cylinder with a movable piston

If heat is added
at constant
volume
, no work is done, so
the heat added equals the
increase in thermal energy

If heat is added
at constant
pressure

the heat energy
transferred will be used to
expand the substance and to
increase the internal energy.



If the substance expands, it
does work on its surroundings.

The expansion is usually negligible for solids
and liquids, so for them C
P

~ C
V.

Applying the First Law of Thermodynamics

Heat
transferred to a system. A summary


The First Law of Thermodynamics. Application to a particular case:

A gas confined in a cylinder with a movable piston

Heat energy can be added to (or lost from) the system. The value of the heat
energy transferred depends on the process.

Typical processes are


-

At constant volume


-

At constant pressure


For the case of ideal gas

For solids and liquids, as the expansion at constant pressure is usually
negligible C
P

~ C
V.

Relationship of Mayer

From the Kinetic theory,

for monoatomic gases



for biatomic gases

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.

Ideal Gas

Work
done on the system,
W
on ,
is the energy transferred as work to the system.
When this energy is added to the system its value will be positive.

The First Law of Thermodynamics. Application to a particular case:

A gas confined in a cylinder with a movable piston

The work done on the gas in an
expansion is

P
-

V diagrams

Constant pressure

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

Constant pressure


Constant Volume


Constant Temperature

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, it 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 to 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
decreases to 1.2 atm

3.
The gas undergoes an isothermal compression back to
its initial point.

(a) What is the temperature at points A, B and C

(b) Find W, Q and
Δ
Eint 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

The equation of curve describing the adiabatic
process is

We can use the ideal gas to rewrite
the work done on the gas in an
adiabatic process in the form

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.
c
P

= 29.19 J/(mol
•K)
; c
V

= 20.85 J/(mol
•K).
M=28.84 g

The First Law of Thermodynamics
. Cyclic Processes.
P
-
V Diagrams

Two moles of an ideal monoatomic gas have an initial pressure P
1

= 2 atm and an initial
volume V
1

= 2 L. The gas is taken through the following quasi
-
static cycle:

A.
-

It is expanded isothermally until it has a volume V
2

= 4 L.

B.
-

It is then heated at constant volume until it has a pressure P
3
= 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 heat added and the work done by
the gas during each part of the cycle. (c) Find the temperatures T
1
, T
2
, T
3

The First Law of Thermodynamics
. Cyclic Processes.
P
-
V Diagrams

The First Law of Thermodynamics
. Cyclic Processes.
P
-
V Diagrams

At point D in the 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 at 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