Physics 151: Lecture 37, Pg 1 Physics 151: Lecture 37 Today’s Agenda l Topics çTemperature and...

Physics 151: Lecture 37, Pg 1

Physics 151: Lecture 37 Physics 151: Lecture 37 Today’s AgendaToday’s Agenda

TopicsTemperature and Zeroth Law of Thermodynamics Temperature scalesThermal expansionIdeal gas


TemperatureTemperature Temperature: measure of the motion of the individual atoms and

molecules in a gas, liquid, or solid. related to average kinetic energy of constituents

High temperature: constituents are moving around energetically In a gas at high temperature the individual gas molecules are

moving about independently at high speeds. In a solid at high temperature the individual atoms of the solid

are vibrating energetically in place. The converse is true for a "cold" object.

In a gas at low temperature the individual gas molecules are moving about sluggishly.

There is an absolute zero temperature at which the motions of atoms and molecules practically stop.

There is an absolute zero temperature at which the classical motions of atoms and molecules practically stop

Animation


HeatHeat

Solids, liquids or gases have internal energyKinetic energy from random motion of molecules

translation, rotation, vibration

At equilibrium, it is related to temperature Heat: transfer of energy from one object to another as a

result of their different temperatures Thermal contact: energy can flow between objects

T1T2

U1U2

>


Zeroth Law of ThermodynamicsZeroth Law of Thermodynamics

Thermal equilibrium: when objects in thermal contact cease heat transfersame temperature

T1T2

U1 U2

=

If objects A and B are separately in thermal equilibrium with a third object C, then objects A and B are in

thermal equilibrium with each other.

AC

B

Animation


ThermometersThermometers

A thermometer is a device that is used to measure the temperature of a system

Thermometers are based on the principle that some physical property of a system changes as the system’s temperature changes

These properties include: The volume of a liquid The dimensions of a solid The pressure of a gas at a constant volume The volume of a gas at a constant pressure The electric resistance of a conductor The color of an object

A temperature scale can be established on the basis of any of these physical properties


Thermometer, Liquid in GlassThermometer, Liquid in Glass

A common type of thermometer is a liquid-in-glass

The material in the capillary tube expands as it is heated

The liquid is usually mercury or alcohol

A thermometer can be calibrated by placing it in contact with some natural systems that remain at constant temperature


Thermometer, Celsius ScaleThermometer, Celsius Scale

A thermometer can be calibrated by placing it in contact with some natural systems that remain at constant temperature

Common systems involve water A mixture of ice and water at atmospheric pressure

» Called the ice point of water A mixture of water and steam in equilibrium

» Called the steam point of water

Celsius Scale : The ice point of water is defined to be 0o C The steam point of water is defined to be 100o C


Constant Volume Gas ThermometerConstant Volume Gas Thermometer

The physical change exploited is the variation of pressure of a fixed volume gas as its temperature changes

The volume of the gas is kept constant by raising or lowering the reservoir B to keep the mercury level at A constant


Absolute ZeroAbsolute Zero The thermometer readings are virtually independent of the gas used If the lines for various gases are extended, the pressure is always zero when

the temperature is –273.15o C This temperature is called

absolute zero

Absolute zero is used as the basis of the absolute temperature scale The size of the degree on the absolute scale is the same as the size

of the degree on the Celsius scale To convert: TC = T – 273.15


Temperature scalesTemperature scales

Three main scales

212

Farenheit

100

Celcius

32 0 273.15

373.15

Kelvin

Water boils

Water freezes

0-273.15-459.67Absolute Zero


Some interesting factsSome interesting facts In 1724, Gabriel Fahrenheit made thermometers

using mercury. The zero point of his scale is attained by mixing equal parts of water, ice, and salt. A second point was obtained when pure water froze (originally set at 30oF), and a third (set at 96oF) “when placing the thermometer in the mouth of a healthy man”.

On that scale, water boiled at 212. Later, Fahrenheit moved the freesing point of

water to 32 (so that the scale had 180 increments).

In 1745, Carolus Linnaeus of Upsula, Sweden, described a scale in which the freezing point of water was zero, and the boiling point 100, making it a centigrade (one hundred steps) scale. Anders Celsius (1701-1744) used the reverse scale in which 100 represented the freezing point and zero the boiling point of water, still, of course, with 100 degrees between the two defining points.

T (K)

108

107

106

105

104

103

100

10

1

0.1

Hydrogen bomb

Sun’s interior

Solar corona

Sun’s surface

Copper melts

Water freezes

Liquid nitrogen

Liquid hydrogen

Liquid helium

Lowest T~ 10-9K


Thermal expansionThermal expansion

In most liquids or solids, when temperature risesmolecules have more kinetic energy

» they are moving faster, on the averageconsequently, things tend to expand

amount of expansion depends on…change in temperature Toriginal length L coefficient of thermal expansion

» L0 + L = L0 + L0 T

L = L0 T (linear expansion)

V = L0 T (volume expansion)

L0 L

V

V + V


Thermal expansionThermal expansion


Bimetallic stripBimetallic strip A bimetallic strip is made of two

ribbons of dissimilar metals bonded together.

Assume that the strip is originally straight. As they are heated, the metal with the greater average coefficient of expansion (2) expands more than the other, forcing the strip into an arc, with the outer radius having a greater circumference (as in the Fig). A compact spiral bimetallic strip is used in a home thermostat. Find the angle () through which the free end of the strip turns when the temperature changes by 1°C for such bimetalic strip with the initial length L= 21.0 cm and the separation of the centers of the strips (r = r2 - r1 = 0.410 mm). The two metals are bronze and invar.

(2 - 1 )L (dT/dr)

1.06o

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.




Lecture 37Lecture 37,, ACT 1ACT 1Thermal expansionThermal expansion

As you heat a block of aluminum from 0 oC to 100 oC, its density

(a) increases (b) decreases (c) stays the same

• SolutionHere is positive

Volume increases

Density decreases

T = 0 C

M, V0

0 = M / V0

T = 100 C

M, V100

100 = M / V100

< 0

Answer: (b)


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

Both objects have positive thermal coefficients all dimensions increase plate and ball both get larger

Before

(b) fits more easily

After


Special system: WaterSpecial system: Water

Most liquids increase in volume with increasing T

water is specialdensity increases from

0 to 4 oC !ice is less dense than

liquid water at 4 oC: hence it floats

water at the bottom of a pond is the denser, i.e. at 4 oC

Water has its maximum density at 4 degrees.

999.55

999.60

999.65

999.70

999.75

999.80

999.85

999.90

999.95

1000.00

0 2 4 6 8 10

Density

(kg/m3)

T (oC)

Reason: chemical bonds of H20 (see your chemistry courses !)


Lecture 37: Lecture 37: ACT 3ACT 3

Not being a great athlete, and having lots of money to spend, Gill Bates decides to keep the lake in his back yard at the exact temperature which will maximize the buoyant force on him when he swims. Which of the following would be the best choice?

(a) 0 oC (b) 4 oC (c) 32 oC (d) 100 oC (e) 212 oC


Lecture 37: Lecture 37: ACT 3ACT 3SOLUTIONSOLUTION

The buoyancy force is

since his volume and g are constant, only is changing

Water has its maximum density at 4 degrees.

999.55

999.60

999.65

999.70

999.75

999.80

999.85

999.90

999.95

1000.00

0 2 4 6 8 10

Density

FB = lVg

(a) 0 oC


Lecture 37: Lecture 37: Problem 1Problem 1

For a typical system, such as a mercury thermometer, why is it a good approximation to neglect the expansion of the shell ?



h =(Vi /A) ( - 3) T

(for glass) << (for mercury), so ( -3 within 5%.

A liquid with a coefficient of volume expansionjust fills a spherical shell of volume Vi at a temperature of Ti (see Fig. to the right). The shell is made of a material that has an average coefficient of linear expansion . The liquid is free to expand into an open capillary of area A projecting from the top of the sphere.

When the temperature increases by T how high does the liquid rises in the capillary ( h ) ?


Ideal gasIdeal gas

Consider a gas in a container of volume V, at pressure P, and at temperature T

Equation of stateLinks these quantitiesGenerally very complicated: but not for ideal gas

n = m/M : number of moles m=mass M=mass of one mole

One mole contains NA=6.022 X 1023 particles : Avogadro’s number

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


Boltzmann’s constantBoltzmann’s constant

In terms of the total number of particles N

P, V, and T are the thermodynamics variables

PV = nRT = (N/NA ) RT

kB is called the Boltzmann’s constant

In SI units, with R =8.315 J / mol·K, we get

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

PV = N kB T

Animation (p,T)

Animation (p,V)

Animation (p,N)


Lecture 37: Lecture 37: Problem 2Problem 2 A vertical cylinder of cross-

sectional area A=0.001 m2 is fitted with a tight-fitting, frictionless piston of mass m = 20.0 kg (see the Fig. To the right)

If n = 0.200 moles of an ideal gas are in the cylinder at a temperature of T = 350 K, what is the height h at which the piston is in equilibrium under its own weight ?

h = n R T/(mg + PA)



h = 1.94 m


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


Lecture 37: Lecture 37: Problem 2bProblem 2b

A cylinder is closed by a piston connected to a spring of constant 2.0 x 103 N/m (as on the Fig.). With the spring relaxed, the cylinder is filled with 5.00 L of gas at a pressure of 1.00 atm and a temperature of 20.0°C.

If the piston has a cross-sectional area of 0.010 m2 and a negligible mass, how high will it rise when the temperature is raised to 250°C ?

V=Vo +A h

h = 0.169 m



p=po +kh / A

poVo / To = pV / T


Recap of today’s lectureRecap of today’s lecture

Chap. 19: temperature Temperature and Zeroth Law of Thermodynamics Temperature scalesThermal expansionIdeal gas

Physics 151: Lecture 37, Pg 1 Physics 151: Lecture 37 Today’s Agenda l Topics çTemperature and...

Documents

Transcript of Physics 151: Lecture 37, Pg 1 Physics 151: Lecture 37 Today’s Agenda l Topics çTemperature and...