Thermodynamics is the study of processes where energy is ...

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27 Οκτ 2013 (πριν από 3 χρόνια και 7 μήνες)

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Chapter 15

LECTURE NOTES


Thermodynamics is the study of processes where energy is transferred as heat and work. We
have already studied the Zeroth Law: If two systems are in thermal equilibrium witha third
system, they are in thermal equilibrium (no heat flow) with each other.


First Law:


U is the change in internal energy of a closed system (no mass enters or leaves).

Q is the net heat added to the system; Q
added

is positive, Q
lost

is negative.

W is the net work done by the system;

W
done

by the system is positive, W
done

on the
system is negative.




Note: All quantities
, U, Q, W are measured in joules (J). This law is a precursor to the
more general conservation of energy law. This law can apply to open syste
ms if we account
for
U due to mass transfer. For an isolated system (closed system in which no energy
passes to or from the environment), W = Q =
U = 0,



Note: In the language of thermodynamics internal energy

U is a property of the system, a so
-
called state variable. Other state variables are P, V, T, and n. Heat (Q) and Work (W) are
processes
--

they can change the state of a system, but are not a property of the system itself.


Applications of the First L
aw




Isothermal processes
occur at constant temperature (so
T = 0)

o

For an ideal gas, this gives

U = 0 and Q = W meaning the work done by the gas
equals the heat added to the gas. Work can be pictured as the are
a under the curve of
a pressure verses volume plot (a PV diagram).



Adiabatic processes
are those where no heat enters or leaves

(
Q = 0). Thus
U =
-
W; if
the system does work, its internal energy decreases. If

work is done on the system, its
temperature rises.



Isobaric processes
occur at constant pressure; the work done is W = P
V.



Isochoric processes

occur at constant volume; the work done is W = 0.


Second Law

S
≥ 0


Actually we present three equivalent formulations of the second law.



The Clausius form states: heat flows naturally from hot to cold objects; heat will not flow
spontaneously from a hot to a cold object.



The Kelvin
-
Planck form states: no device is pos
sible whose sole effect is to transform a
given amount of heat completely into work. A heat engine is any device that changes
thermal energy into mechanical energy. It is found that a quantity of heat Q
H

input at a
high temperature T
H

can be partly trans
formed into mechanical work W and partly
exhausted as waste heat Q
L

at a lower temperature. We write Q
H

= W + Q
L
. The
efficiency of a heat engine is defined to be e =

or e = 1
-
; in an ideal
(Carnot) heat en
gine we find Q
H



T
H

and Q
L


T
L

so e = 1
-

T
L
/T
H
. Real engines
achieve only 60
-
80% of this ideal.

Chapter 15

LECTURE NOTES

The Kelvin
-
Planck form of the second law states e < 1. No heat engine can be 100% or
more efficient


perpetual motion machines a
re not possible.


Question:

Explain the operation of a refrigerator.




The general statement of the second law states: The total entropy of a system and its
environment increases as a result of any natural process or
S
≥ 0. Let’s elaborate. We
define
S = Q/T; when heat is added to a system by a reversible process at constant
absolute temperature T there is a change in entropy (in units of cal/K or J/K) of the
system. When 10g of water boils at 37
3K we have
.

But what is entropy? Entropy can be viewed as a measure of the disorder of a system.
Natural processes tend to move to a state of greater disorder. In natural processes, some
energy becomes “unusable” (unable to do us
eful work)


this is the waste or exhaust heat
which the second law states can never be zero.


Since natural processes are those in which entropy increases, entropy is called time’s
arrow, pointing out in which direction time flows. We never see a broken
egg
spontaneously reassemble as a movie run backwards. The disorder of the system would
have to decrease for this to occur. Statistically, the second law can be thought of as
saying processes occur which are most probable. Statistical Mechanics may allo
w some
slight possibility of the egg spontaneously reassembling, but that would be
very

improbable.


Third Law




This states: The absolute zero of temperature can never be attained. We can approach T
= 0 K as closely as we like, but we will never be able
to reach this temperature. Thus the
lower temperature environment to which waste heat is exhausted by a heat engine cannot
have T
L

= 0 and no heat engines can have efficiency e = 1.


Application


Thermodynamics was a useful guide during the industrial rev
olution. Today, we need to
consider methods of energy production and the pollution they inevitably entail. The waste or
exhaust heat guaranteed by the second law is unavoidable thermal pollution from all forms of
energy generation. Other forms of pollut
ion (such as greenhouse gasses from fossil fuels) may
contribute to climate change within your lifetime.