IB Physics Thermodynamic Processes

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Oct 27, 2013 (3 years and 9 months ago)

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IB











Physics

T
hermodynamic Processes


The study of thermodynamics resulted from the desire during the
industrial revolution to understand and improve the performance of
heat

engines such as the steam engine and later, the internal
combustion engine.

This section contains many references to heat and temperature so it
is important to define these terms. Strictly speaking:


When heat energy is supplied to a gas two t
hings may happen:



the internal energy of the gas may increase



the gas may do external work


Considering this in another way, the internal energy of a gas will increase if either:



heat energy is added to it by heating it or



work is done
on
the gas by compre
ssing it


This leads us to a proposal know as the First Law of thermodynamics.


The First Law of thermodynamics:

The First Law of thermodynamics is basically a statement of the conservation of energy.
Very simply it states that:


Put a little more formally:


This means that there is a finite amount of energy in the Universe and although this
energy can be changed from one form to another the total amount never changes


if we
want to use energy in one form then we have to 'pay for it' by converting it from energy in
another form.

You can't get something
for nothing


The energy content of the Universe is constant

Heat

is the energy that will flow between two bodies that are
not
in thermal equilibrium and that thus have different temperatures.


In any body, the
internal energy

of the bo
dy is equal to the sum
of the kinetic energy and potential energy of all the particles.


If we consider the First Law in equation form as it applies to a gas then:

Increase in internal energy (

U) = Heat energy supplied
to

the gas
(

Q)
-

Work done
by

the gas (

W)





U =

Q
-


W





Note that

U represents both the change in the internal kinetic energy of the gas (an
increase in molecular velocity) and the increase in the internal potential energy (due
to
an
increase in energy overcoming intermolecular forces due to separation of the molecules).


The potential energy increase is zero for ideal gases

(that are assumed to have no
intermolecular forces acting between the particles) and negligible for most real gases
except at temperatures near liquefaction and/or at very high pressures.


Work done
by an ideal gas during expansion

Consider an ideal gas at a pressure P enclosed in a cylinder of cross sectional area A.

The gas is

first

compressed by pushing the piston in a distance

x, the volume of the gas
decreasing by

V. (We assume that the p
ressur
e remains almost constant,
P).









Work done on the gas during this compression =

W

= F

x

Force on piston = P
A





(P = F/A)

So the work done during compression =

W = P
A

x










If the
external force was removed and the
gas
was

allowed to expand back, it would do
an equal amount of work.


The first law of thermodynamics
could thus
be written as:



First law of thermodynamics:

Q =

U +

W



Q



U + P

V



Δ

V

Δ

x

Pressure
P

F

Area A


W = P

V

A
p
V
diagram

(pressure against volume graph)
can be sketched

fo
r

this
change of state:








The volume is increasing. Thus the gas must be doing work on
its surroundings

so

W

must

be

positive.

If the pressure is constant then the temperature must be increasing. Thus the
change in
internal energy

U

must also be
positive
.

Thus (from the f
irst law of thermodynamics
)

there must also be a positive flow of heat into
the gas in the cylinder (

Q =

U

+

W

).

As in any flow of heat, this is as a result of the
gas and its surroundings being at different temperatures.


Thermodynamic Processes

The gas inside the piston in the previous example is sometimes referred to as a ‘
system’
.
The piston and its ex
ternally connected parts are referred to as the ‘
surroundings’

and
may themselves be parts of another, external system. The systems we will consider are
‘closed systems’. This means the mass of gas remains constant.

Any set of values of p,V and T for the

system is called
its ‘
state

.

A process that changes
the state of a system (from one set of values of
p, V and T
to another set of values) is
called a

thermodynamic process
.

Note:

Any particular point on the pV

diagram represents a certain state with a fixed
internal energy
. So in any thermodynamic cycle that starts and ends at the same point on
the pV graph the net change in internal energy s zero.

Also note that
in any cycle the area contained within the line
s on the pV diagram
represents the
difference between
work done by the
gas and
work done on the gas
.




V

V

P

Clearly the area under the graph is equal to the Work
done by the gas during expansion.


V

V

P

If the cycle starts and ends at
this point, the net
change

in
internal energy is zero.

This area represents the net
work done
by the gas during
the cycle.


P

Question












Conclusion
:

This example illustrates how the
heat supplied to the system and work done by the
system have different values depending upon how the change was carried out.

Also, the change in internal energy of a system between any two states (points on the pV
diagram)
is constant and does not depend upon the way in which the change was carried
out.





Q


U


W

i




ii




iii





Description

i


ii


iii

Changing volume at constant pressure followed by changing pressure at constant volume.

A fixed mass of gas has its state changed from A to B as
shown in the PV diagram. Initial internal energy was 300J and
final internal energy is 1350J.

a.

Describe how the pressure and volume changes in
each case (complete the first table below).

b.

Determine the change in internal energy in each case
(show calculations and answers in the second table)

c.

Determine how much work has been
done
by the
gas
in
each case
.

d.

Thus determine the heat supplied to the gas
in each
case. Show you calculations and answers in the table.


Types of Thermodynamic Processes

1.

Isothermal change

-

This is a change where temperature is constant so internal
energy does not change

(ΔU=0)
.

-

Volume changes so

work is done on or by the
gas
.

-

The pV diagram shows a curve.


2.

Isobaric change

-

This is a change where pressure is constant.

-

Volume changes so work is done on or by the gas.

-

Temperature changes so internal energy changes.

-

pV

diagram shows a horizontal straight line.


3.

Isochoric change

-

This is a change where volume is constant so no work is
done (ΔW=0).

-

Temperature changes so internal energy changes.

-

pV diagram shows a vertical straight line.


4.

Adiabatic change

-

This is a change where no heat flows in or out of the system
(ΔQ=0).

-

Volume changes so work is done on or by the gas.

-

Temperature changes so internal energy changes.

-

pV diagram shows a curve.


Note:

It can be hard to tell the difference between an adiabatic curve
and an isothermal curve (an isotherm). If the two cross, the adiabatic curve is the
steepest one at the point of crossing.


V

P

V

P

V

P

V

P