Thermodynamics (Chapter 15)

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27 Οκτ 2013 (πριν από 3 χρόνια και 9 μήνες)

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Lecture 13:

Thermodynamics (Chapter 15)

Thermodynamic Systems

Thermodynamics: Fundamental laws that heat and work obey


System: Collection of objects on which the attention is being paid


Surrounding


Everything else around


System can be separated from surrounding by:


Diathermal Walls


Allows heat to flow through


Adiabatic Walls
-

Perfectly insulating walls that do not allow flow of




heat


State of a system


the physical condition


can be defined using various
parameters such as volume, pressure, temperature etc.






Zeroth Law of Thermodynamics



Deals with Thermal equilibrium




Two systems are said to be in
thermal
equilibrium

if there is no net flow of heat between
them when they are brought into thermal contact.




Temperature is the indicator of thermal
equilibrium




Two systems individually in thermal equilibrium
with a third system are in thermal equilibrium with
each other.

First Law of Thermodynamics



When a substance involves in a process involving energy in the form
of work and heat, the internal energy of the substance can change.




First Law: Relationship between work, heat and change in the internal
energy




Internal energy changes when heat is imparted:

U = Q




Internal energy changes when work is done on the system or by the
system:

U =
-

W


Work is +ve when it is done by the system and


Work is

ve when it is done on the system.



Thus system can lose or gain energy through heat


or work:





U = U
f
-
U
i

= Q
-

W


Thermal Processes

A System can interact with the surrounding in several ways


but has to
obey the first law of thermodynamics.


Isobaric process



Constant pressure




Work done is +ve when it expands (V
f

> V
i
)


Isobaric compression: work done is
-
ve

Thermal Processes

Isochoric Process
: Constant volume process


Area under the P V graph = 0 => No work is done


So the heat given is only used to change the
internal energy.


U = Q


W = Q


Isothermal Process
: Constant temperature
process.


Adiabatic Process: Occurs without the transfer of
heat => Q = 0 =>

U =


W

When work is done by a system adiabatically, W
is +ve and when work is done on the system
adiabatically, W is

ve

Thermal Processes

Area under a P
-
V graph is the work for any
kind of thermal process

Thermal Processes using an Ideal Gas

Ideal Gas
: A gas for which the potential energy of
interaction between the molecules is independent of their
separation and hence is independent of the gas volume.
The internal energy of such a gas depends on the
temperature.


Isothermal Compression or Expansion

When a system performs work isothermally, the
temperature stays constant.



Thermal Processes using an Ideal Gas

What is the origin of energy for this work?


-

Internal energy of an ideal gas is proportional to its Kelvin
temperature, U = 3/2 (n RT)


-
Internal energy remains constant throughout an isothermal
process and so the change in internal energy = 0

(ie)

U = Q
-
W = 0 => Q = W

Energy for the work originates from the heat provided.


Expansion: heat flows from the hot water to the gas

Compression: heat flows from the gas into the water






Thermal Processes using an Ideal Gas

Adiabatic Compression or Expansion

When a system performs work adiabatically, NO heat flows
into or out of the system.



Expands adiabatically => +ve work => T
i

> T
f

Compress adiabatically =>
-
ve work => T
i
<T
f


Ti

=
P
i
V
i/(
nR
) and
Tf

=
P
f
V
f/(
nR
)


P
i
V
i


=
P
f
V
f





Is the ratio of specific heat capacities at constant pressure and constant vol

Specific Heat Capacities

Q = c m

T (last chapter)


Q =
C

n

T:
molar specific heat capacity

in units of J/(mol∙K)


n = number of moles


T = T
f



T
i



The molar specific heat capacities can now be determined







(
1
5
.
8
)






The ratio


of the specific heats is






Specific Heat Capacities

Second Law of Thermodynamic

THE SECOND LAW OF THERMODYNAMICS: THE HEAT FLOW
STATEMENT:

Heat flows spontaneously from a substance at a higher temperature to a
substance at a lower temperature and does not flow spontaneously in the
reverse direction.



Heat Engines

Uses heat to perform work


-

Hot reservoir provides heat

-

Part of the heat is used to do work

-

remaining heat is rejected to a cold reservoir

Efficiency = Work done / input heat = W / Q
H


Should obey the principle of conservation of energy:


Q
H

= W +Q
C


E = (Q
H


Q
C
) / Q
H

Carnot’s Principle and Carnot’s Engine

Sadi Carnot (1796
-
1832)


A reversible process is one in which both the system and its environment can
be returned to exactly the states they were in before the process occurred.


No irreversible engine operating between two reservoirs at
constant temperatures can have a greater efficiency than a
reversible engine operating between the same temperatures.
Furthermore, all reversible engines operating between the same
temperatures have the same efficiency.

Refrigerators, Air conditioners and

Heat Pumps

Entropy

In general, irreversible processes cause us to lose some,
but not necessarily all, of the ability to perform work. This
partial loss can be expressed in terms of a concept called
entropy.

To introduce the idea of entropy we recall the relation
Q
C
/
Q
H

=
T
C
/
T
H

that applies to a Carnot engine. This
equation can be rearranged as
Q
C
/
T
C

=
Q
H
/
T
H
, which
focuses attention on the heat
Q

divided by the Kelvin
temperature
T
. The quantity
Q
/
T

is called the change in
the entropy

S
:



Change in entropy of Carnot’s engine

Reversible process does not alter the total entropy of the universe (2
nd

Law in
terms of entropy).


S
universe

= 0


Entropy : Degree of disorder

Entropy and Arrow of time

Third Law of Thermodynamics

THE SECOND LAW OF THERMODYNAMICS STATED IN TERMS OF ENTROPY

The total entropy of the universe does not change when a reversible process occurs

THE THIRD LAW OF THERMODYNAMICSIt is not possible to lower the
temperature of any system to absolute zero (
T

= 0 K) in a finite number of
steps.