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

Before

Lecture 37:

ACT 2 Solution

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 In SI units,

R

=8.315 J / mol·K universal gas constant

PV = N k B T k B

is called the Boltzmann’s constant

k B = R/N A = 1.38

X 10 -23 J/K Physics 151: Lecture 38, Pg 4

Lecture 37:

Problem 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 m 3 . 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/m 3 .) T o B = r To V g V, T r T Vg 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

energy transferred by this method of  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 14.5

o C to 15.5

o C  In the US Customary system, the unit is a BTU Thermal Unit) (British  One BTU is the amount of energy transfer necessary to raise the temperature of 1 lb of water from 63 o F to 64 o F  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 energy in 1843 established the equivalence between mechanical energy and internal  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 14.5

o C to 15.5

o C is 4.186 J

1 cal = 4.186 J

Physics 151: Lecture 38, Pg 9

Heat Capacity

 The

heat capacity

amount of energy needed to raise the temperature of that sample by 1 o C ( C ) of a particular sample is defined as the  If energy

Q

produces a change of temperature of D

T

, then

Q

=

C

D

T



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 10 13 W over a time interval of warming 2.50 ns 0.800 kg . Compare its energy output in one such time interval to the energy required to make a pot of tea by of water from 20.0

o C to 100 o C .

 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 :

Q

cold = -

Q

hot 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 substance of the  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

solid to liquid is used when the phase change is from  The

latent heat of vaporization

from liquid to gas is used when the phase change is 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 ( -10 o C ) and dropped into a glass of water at 0 o 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 evaluated between the initial and final states

PV

diagram,  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

= -

P i

(

V f

–

V i

)

W

= -

P f

(

V f

–

V i

) 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 Conservation of Energy is a special case of the Law of  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

independent of the path +

W

is  The First Law of Thermodynamics states that D

E

int =

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 Since » Having the process proceed so quickly that no heat can be exchanged

Q

= 0, D

E

int =

W

If the gas is compressed adiabatically,

W

positive so D

E

int is positive and the temperature of the gas increases is  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, D

E

int = 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

pressure =

P

(

V f

–

V i

) where

P

is the constant 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 D

E

int = 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 p 1 , p 2 , V 1 , V 2 ?

W

net  

P

1 

V

2 

V

1  ln

P

2

P

1 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