Transcript Physics 131: Lecture 14 Notes

Physics 151: Lecture 38
Today’s Agenda

Today’s Topics (Chapter 20)
Internal Energy and Heat
Heat Capacity
First Law of Thermodynamics
Special Processes
Physics 151: Lecture 38, Pg 1
Lecture 37: ACT 2
Thermal expansion

An aluminum plate has a circular hole cut in it. A copper ball (solid
sphere) has exactly the same diameter as the hole when both are
at room temperature, and hence can just barely be pushed
through it. If both the plate and the ball are now heated up to a
few hundred degrees Celsius, how will the ball and the hole fit ?
(a) ball won’t fit
(b) fits more easily
(c) same as before
Physics 151: Lecture 38, Pg 2
Lecture 37: ACT 2
Solution
Before
After (higher T)
(b) fits more easily
Physics 151: Lecture 38, Pg 3
Ideal gas / Review
•
Equation of state for an ideal gas
PV = nRT
R is called the universal gas constant
In SI units, R =8.315 J / mol·K
PV = N kB T
kB is called the Boltzmann’s constant
kB = R/NA = 1.38 X 10-23 J/K
Physics 151: Lecture 38, Pg 4
Lecture 37: Problem 3
To

The mass of a hot-air balloon and its
cargo (not including the air inside) is
200 kg. The air outside is at 10.0°C
and 101 kPa. The volume of the
balloon is 400 m3. To what
temperature must the air in the
balloon be heated before the balloon
will lift off ?
(Air density at 10.0°C is 1.25 kg/m3.)
B = rTo V g
V, T
rTVg
m
mg
T = 472 K !
Physics 151: Lecture 38, Pg 5
Internal Energy

Internal energy is all the energy of a system that is
associated with its microscopic components
These components are its atoms and molecules
The system is viewed from a reference frame at rest
with respect to the center of mass of the system

Internal energy does include kinetic energies due to:
Random translational motion (not motion through space)
Rotational motion
Vibrational motion
Potential energy between molecules
Animation
Physics 151: Lecture 38, Pg 6
Heat

Heat is defined as the transfer of energy across the
boundary of a system due to a temperature difference
between the system and its surroundings

The term heat will also be used to represent the amount of
energy transferred by this method

Units of Heat : historically-> the calorie
One calorie is the amount of energy transfer necessary to
raise the temperature of 1 g of water from 14.5oC to 15.5oC

In the US Customary system, the unit is a BTU (British
Thermal Unit)
One BTU is the amount of energy transfer necessary to
raise the temperature of 1 lb of water from 63oF to 64oF

The SI uinits are Joules, as we used before !
Physics 151: Lecture 38, Pg 7
Changing Internal Energy

Both heat and work can change the internal energy of a system

The internal energy can be changed even when no energy is
transferred by heat, but just by work
Example, compressing gas with a piston
Energy is transferred by work
Physics 151: Lecture 38, Pg 8
Mechanical Equivalent of Heat

James Joule in 1843 established
the equivalence between
mechanical energy and internal
energy

His experimental setup is shown
at right

The loss in potential energy
associated with the blocks
equals the work done by the
paddle wheel on the water
• The amount of mechanical energy
needed to raise the temperature of
water from 14.5oC to 15.5oC is 4.186 J
1 cal = 4.186 J
Physics 151: Lecture 38, Pg 9
Heat Capacity

The heat capacity (C) of a particular sample is defined as the
amount of energy needed to raise the temperature of that
sample by 1oC

If energy Q produces a change of temperature of DT, then
Q = C DT

Specific heat (c) is the heat capacity per unit mass
Physics 151: Lecture 38, Pg 10
Some Specific Heat Values
Physics 151: Lecture 38, Pg 11
ACT-1

The Nova laser at Lawrence Livermore National Laboratory
in California is used in studies of initiating controlled nuclear
fusion. It can deliver a power of 1.60 x 1013 W over a time
interval of 2.50 ns. Compare its energy output in one such
time interval to the energy required to make a pot of tea by
warming 0.800 kg of water from 20.0oC to 100oC.

Which one is larger ?
Physics 151: Lecture 38, Pg 12
Calorimetry

One technique for measuring specific heat involves heating
a material, adding it to a sample of water, and recording the
final temperature

This technique is known as calorimetry
A calorimeter is a device in which this energy transfer
takes place

The system of the sample and the water is isolated

Conservation of energy requires that the amount of energy
that leaves the sample equals the amount of energy that
enters the water
Cons. of Energy : Qcold= -Qhot
Physics 151: Lecture 38, Pg 13
Phase Changes

A phase change is when a substance changes from one form to
another. Two common phase changes are
» Solid to liquid (melting)
» Liquid to gas (boiling)

During a phase change, there is no change in temperature of the
substance

If an amount of energy Q is required to change the phase of a
sample of mass m, we can specify the Latent Heat associated
with this transition is: L = Q /m

The latent heat of fusion is used when the phase change is from
solid to liquid

The latent heat of vaporization is used when the phase change is
from liquid to gas
Physics 151: Lecture 38, Pg 14
Graph of Ice to Steam
Physics 151: Lecture 38, Pg 15
Problem

An ice cube (m=0.070 kg) is taken from a freezer
( -10o C) and dropped into a glass of water at 0o C.
How much of water will freeze ? (C(ice) = 2,000
J/kg K; L(water) =334 kJ/kg)
m =4.19 g
Physics 151: Lecture 38, Pg 16
State Variables

State variables describe the state of a system

In the macroscopic approach to thermodynamics, variables
are used to describe the state of the system
Pressure, temperature, volume, internal energy
These are examples of state variables

The macroscopic state of an isolated system can be
specified only if the system is in thermal equilibrium
internally
Physics 151: Lecture 38, Pg 17
Transfer Variables

Transfer variables are zero unless a process occurs in which
energy is transferred across the boundary of a system

Transfer variables are not associated with any given state of
the system, only with changes in the state

Heat and work are transfer variables
Example of heat: we can only assign a value of the heat if
energy crosses the boundary by heat
Physics 151: Lecture 38, Pg 18
Work in Thermodynamics

Work can be done on a deformable system,
such as a gas

Consider a cylinder with a moveable piston

A force is applied to slowly compress the gas
The compression is slow enough for all
the system to remain essentially in thermal
equilibrium
This is said to occur quasi-statically
Therefore, the work done on the gas is dW = -P dV
Physics 151: Lecture 38, Pg 19
PV Diagrams

The state of the gas at each step
can be plotted on a graph called a
PV diagram
This allows us to visualize the
process through which the gas
is progressing

The work done on a gas in a
quasi-static process that takes the
gas from an initial state to a final
state is the the area under the
curve on the PV diagram,
evaluated between the initial and
final states
This is true whether or not the pressure stays constant
The work done does depend on the path taken
Physics 151: Lecture 38, Pg 20
Work Done By Various Paths
W = -Pi (Vf – Vi)



W = -Pf (Vf – Vi)
W= …
Each of these processes has the same initial and final states
The work done differs in each process
The work done depends on the path
Physics 151: Lecture 38, Pg 21
The First Law of Thermodynamics

The First Law of Thermodynamics is a special case of the Law of
Conservation of Energy
It takes into account changes in internal energy and energy
transfers by heat and work

Although Q and W each are dependent on the path, Q + W is
independent of the path

The First Law of Thermodynamics states that DEint= Q + W
All quantities must have the same units of measure of energy

One consequence =>> there must exist some quantity known as
internal energy which is determined by the state of the system
Animation
Physics 151: Lecture 38, Pg 22
ACT
Which statement below regarding the First Law of
Thermodynamics is most correct ?
a. A system can do work externally only if its internal energy
decreases.
b. The internal energy of a system that interacts with its environment
must change.
c. No matter what other interactions take place, the internal energy
must change if a system undergoes a heat transfer.
d. The only changes that can occur in the internal energy of a system
are those produced by non-mechanical forces.
e. The internal energy of a system cannot change if the heat
transferred to the system is equal to the work done by the system.
Physics 151: Lecture 38, Pg 23
Adiabatic Process




An adiabatic process is one during which
no energy enters or leaves the system by
heat
Q = 0
This is achieved by:
» Thermally insulating the walls of the
system
» Having the process proceed so
quickly that no heat can be
exchanged
Since Q = 0, DEint = W
If the gas is compressed adiabatically, W is
positive so DEint is positive and the
temperature of the gas increases
If the gas expands adiabatically, the
temperature of the gas decreases
Physics 151: Lecture 38, Pg 24
Isothermal Process

An isothermal process is one that
occurs at a constant temperature

Since there is no change in
temperature, DEint = 0

Therefore, Q = - W

Any energy that enters the system by
heat must leave the system by work
Isothermal Expansion
for an ideal gas :
PV = nRT and
Physics 151: Lecture 38, Pg 25
Isobaric Processes

An isobaric process is one that occurs at a constant
pressure

The values of the heat and the work are generally both
nonzero

The work done is W = P (Vf – Vi) where P is the constant
pressure
Physics 151: Lecture 38, Pg 26
Problem

Identify processes A-D in the pV diagram below:
Physics 151: Lecture 38, Pg 27
ACT
In an adiabatic free expansion :
a. no heat is transferred between a system and its surroundings.
b. the pressure remains constant.
c. the temperature remains constant.
d. the volume remains constant.
e. the process is reversible.
Physics 151: Lecture 38, Pg 28
Cyclic Processes

A cyclic process is one that starts and ends in the same
state
On a PV diagram, a cyclic process appears as
a closed curve

The change in the internal energy must be zero since it is
a state variable

If DEint = 0, Q = -W

In a cyclic process, the net work done on the system per
cycle equals the area enclosed by the path representing
the process on a PV diagram
Physics 151: Lecture 38, Pg 29
ACT-2

An ideal gas is carried through a
thermodynamic cycle consisting
of two isobaric and two
isothermal processes as shown
in Figure .

What is the work done in this
cycle, in terms of p1, p2, V1, V2 ?
W net
P2
 P1 V2  V1 ln
P1
Animation
Physics 151: Lecture 38, Pg 30
Recap of today’s lecture

Chap. 20:
Internal Energy and Heat
Heat Capacity
First Law of Thermodynamics
Special Processes
Physics 151: Lecture 38, Pg 31