Physics 151: Lecture 38, Pg 1 Physics 151: Lecture 38 Today’s Agenda l Today’s Topics (Chapter...

Physics 151: Lecture 38, Pg 1

Physics 151: Lecture 38 Physics 151: Lecture 38 Today’s AgendaToday’s Agenda

Today’s Topics (Chapter 20)Internal Energy and Heat Heat CapacityFirst Law of ThermodynamicsSpecial Processes


Lecture 37: Lecture 37: ACT 2ACT 2Thermal expansionThermal 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


Lecture 37: Lecture 37: ACT 2ACT 2SolutionSolution

(b) fits more easily

Before After (higher T)


Ideal gas / ReviewIdeal gas / Review

PV = nRT

• Equation of state for an ideal gas

R is called the universal gas constant

In SI units, R =8.315 J / mol·K

kB is called the Boltzmann’s constant

kB = R/NA = 1.38 X 10-23 J/K PV = N kB T


Lecture 37: Lecture 37: Problem 3Problem 3

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.)

T = 472 K !

m

V, T

mg

B = To V g

TVg

To


Internal EnergyInternal Energy

Internal energy is all the energy of a system that is associated with its microscopic components

These components are its atoms and moleculesThe 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 motionVibrational motionPotential energy between molecules

Animation


HeatHeat 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 calorieOne 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 !


Changing Internal EnergyChanging 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 pistonEnergy is transferred by work


Mechanical Equivalent of HeatMechanical 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


Heat CapacityHeat 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 T, then

Q = C T

Specific heat (c) is the heat capacity per unit mass


Some Specific Heat ValuesSome Specific Heat Values


ACT-1ACT-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 ?


CalorimetryCalorimetry 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 calorimetryA 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


Phase ChangesPhase 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


Graph of Ice to SteamGraph of Ice to Steam


ProblemProblem

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


State VariablesState 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 energyThese are examples of state variables

The macroscopic state of an isolated system can be specified only if the system is in thermal equilibrium internally


Transfer VariablesTransfer 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 variablesExample of heat: we can only assign a value of the heat if

energy crosses the boundary by heat


Work in ThermodynamicsWork 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 gasThe 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


PVPV Diagrams 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 constantThe work done does depend on the path taken


Work Done By Various PathsWork Done By Various Paths

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

W = -Pi (Vf – Vi) W = -Pf (Vf – Vi) W= …


The First Law of ThermodynamicsThe 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 Eint= Q + WAll 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


ACTACTWhich 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.


Adiabatic ProcessAdiabatic Process

An adiabatic process is one during which no energy enters or leaves the system by heat

Q = 0This 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, Eint = W If the gas is compressed adiabatically, W is

positive so Eint is positive and the temperature of the gas increases

If the gas expands adiabatically, the temperature of the gas decreases


Isothermal ProcessIsothermal Process

An isothermal process is one that occurs at a constant temperature

Since there is no change in temperature, Eint = 0

Therefore, Q = - W

Any energy that enters the system by heat must leave the system by work

Isothermal Expansionfor an ideal gas :

PV = nRT and


Isobaric ProcessesIsobaric 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


ProblemProblem

Identify processes A-D in the pV diagram below:


ACTACT

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.


Cyclic ProcessesCyclic Processes A cyclic process is one that starts and ends in the same

stateOn 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 Eint = 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


ACT-2ACT-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 ?

Wnet P1 V2 V1 lnP2

P1

Animation


Recap of today’s lectureRecap of today’s lecture

Chap. 20:Internal Energy and Heat Heat CapacityFirst Law of ThermodynamicsSpecial Processes

Physics 151: Lecture 38, Pg 1 Physics 151: Lecture 38 Today’s Agenda l Today’s Topics (Chapter...

Documents

Transcript of Physics 151: Lecture 38, Pg 1 Physics 151: Lecture 38 Today’s Agenda l Today’s Topics (Chapter...