# Work in Thermodynamic Processes

Mécanique

27 oct. 2013 (il y a 5 années et 3 mois)

108 vue(s)

Work in Thermodynamic Processes

Energy can be transferred to a
system by heat and/or work

The system will be a volume
of gas always in equilibrium

Consider a cylinder with a
movable piston

As piston is pressed a
distance
Δ
y, work is done on
the system reducing the
volume

W =
-
F
Δ
y =
-

P A
Δ
y

Work in Thermodynamic Processes

Cont.

Work done compressing
a system is defined to be
positive

Since
Δ
V is negative
(smaller final volume)
& A
Δ
y = V

W =
-

P
Δ
V

Gas compressed

W
on
gas
= pos.

Gas expands

W
on gas
=
neg.

Work in Thermodynamic Processes

Cont.

Can only be used if gas is
under constant pressure

An isobaric process (
iso

=
the same) P
1

= P
2

Represented on a pressure
vs. volume graph

a PV
diagram

Area under
any curve
=
work done on the gas

If volume decreases

work
is positive (work is done
on the system)

THERMODYNAMICS

First Law of Thermodynamics

Energy is conserved

Heat added to a system goes
into internal energy, work or
both

ΔU = Q + W

Heat

internal energy

Q is
positive

Work
done to the system

internal energy

W is
positive (again)

First Law

Cont.

A system will have a
certain amount of
internal energy (U)

It will
not have
certain
amounts of heat or work

These change the system

U depends only on state
of system, not what
brought it there

ΔU is independent of
process path (like
U
g
)

Isothermal Process

Temperature remains
constant

Since P = N
k
B

T / V

=
constant / V

An isotherm (line on
graph) is a hyperbola

Isothermal Process

Cont.

Moving from 1 to 2,
temperature is constant,
so P & V change

Work is done = area
under curve

Internal energy is
constant because
temperature is constant

Q =
-
W

Heat is converted into
mechanical work

Isometric (
isovolumetric
) Process

The volume is not
allowed to change

V
1

= V
2

Since no change in
volume, no work is done

Δ
U = Q

internal energy

it

Heat extracted is at the
expense

of internal
energy

it

Isometric Process

Cont.

The PV diagram
representation

No change in volume

Area under curve = 0

That is, no work done

The process moves from
one isotherm to another

Isobaric Process

As heat is added to system,
pressure is required to be
constant

The ratio of V / T = constant

Some of the heat does work
and the rest causes a change
in temperature

Thus moving to another
isotherm

Recall: changes in
temperature = changes in
internal energy

Δ
U = Q + W

No heat is transferred
into or out of system

Q = 0

Δ
U = W

All work done to a system
goes into internal energy
increasing temperature

All work done by the
system comes from
internal energy & system
gets cooler

Cont.

Either system is
insulated to not
allow heat
exchange or the
process happens
so fast there is
no time to
exchange heat

Cont.

Since temperature
changes, we move
isotherms

The Second Law of
Thermodynamics & Heat Engines

Heat will not flow
spontaneously from a
colder body to a warmer

OR: Heat energy cannot
be transferred
completely into
mechanical work

OR: It is impossible to
construct an operational
perpetual motion
machine

Heat Engines

Any device that
converts heat energy
into work

Takes heat from a
high temperature
source (reservoir),
converts some into
work, then transfers
the rest to
surroundings (cold
reservoir) as waste
heat

Heat Engines

Cont.

Consider a cylinder and piston

Surround by water bath & allow
to expand along an isothermal

The heat flowing in (Q) along
AC equals the work done by the
gas as it expands (W) since
Δ
U =
0

isothermal, work is done on the
gas and heat flows out

Work expanding = work
compressing

Heat Engines

Cont.

A cycle naturally can have
positive work done

In going from A to B work is
done by gas, temperature

(
Δ
U

) and heat enters
system

B to C

No work done, T

,
Δ
U

, &
heat leaves system

C to A

Δ
U = 0, heat leaving = work
done

The work out = the net heat
in (
Δ
U = 0)

Heat Engines

Cont.

Thermal Efficiency

Used to rate heat engines

efficiency = work out / heat in

e =
W
out

/ Q
in

Qin = heat into heat engine

Qout

= heat leaving heat engine

For one cycle, energy is
conserved

Q
in

= W +
Q
out

Since system returns to its
original state
Δ
U = 0

The Carnot Engine

Any cyclic heat engine
will always lose some
heat energy

What is the maximum
efficiency?

Solved by

Carnot
(France) (Died at 36)

Must be reversible

The Carnot Engine

Cont.

Carnot Cycle

A four stage reversible
process

2 isotherms & 2

Consider a hypothetical
device

a cylinder & piston

Can alternately be brought
into contact with high or
low temperature
reservior

High temp

heat source

Low temp

heat sink

heat is exhausted

The Carnot Engine

Cont.

Step 1: an
isothermal
expansion, from A
to B

heat from source

expansion, from B
to C

The Carnot Engine

Cont.

Step 3: an isothermal
compression, C to D

Ejection of heat to sink at
low temp

compression, D to A

Represents the most
efficient (ideal) device

Sets the upper limit

Entropy

A measure of disorder

A messy room > neat
room

Pile of bricks > building

A puddle of water > ice
came from

All real processes
increase disorder

increase entropy

of entropy of one
system can be reduced at
the expense of another

Entropy

Cont.

Entropy of the universe
always increases

The universe only moves
in one direction

towards

entropy

This creates a “direction
of time flow”

Nature does not move
systems towards more
order

Entropy

Cont.

As entropy

, energy is
less able to do work

The “quality” of energy
has been reduced