Physics

Temperature and Heat

Teacher: Luiz Izola

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1. Zeroth Law of Thermodynamics

2. Temperature Scales

3. Thermal Expansion

4. Heat and Mechanical Work

5. Specific Heats

6. Conduction, Convection, and Radiation

Introduction

Up to now, we studied mass, length, and time. Now, we will:

Introduce a fourth physical quantity: temperature

Learn about Heat: A particular type of energy transfer

Discuss the connection between changes in temperature and changes in other physical quantities such as length, pressure, and volume.

Consider mechanisms by which thermal energy is exchanged.

Temperature and Heat Flow

Heat is the energy transferred between objects because of a difference in temperature.

When heat flows from object A to object B, A loses energy and B gains it.

When heat flows between the objetcs, they are in thermal contact.

When the transfer of heat stops, the objects reached thermal equilibrium.

Thermodynamics studies the physical processes involving the transfer of heat.

Zeroth Law of Thermodynamics

Basic idea of Thermodynamics: Thermal Equilibrium is determined by a single physical quantity, Temperature.

“If object A is in thermal equilibrium with B, and C is in equilibrium with B, then, A is in equilibrium with C.”

Celsius Temperature Scale

There are three main temperature scales: Celsius, Kelvin, and Fahrenheit.

Celsius defines 00C as freezing water and 1000C as boiling water temperature.

In Celsius scale, there is no limit for how high a temperature can go. There is a lower limit: -2730C

Celsius Notation:

Temperature: 1000CTemperature Change: 100C0

Fahrenheit Temperature Scale

Fahrenheit defines 320F as freezing water and 2120F as boiling water temperature.

Fahrenheit Notation:

Temperature: 1000FTemperature Change: 100F0

Conversion of Celsius to Fahrenheit

Tf = 9/5Tc + 32

Conversion of Celsius to Fahrenheit

Tc = 5/9(Tf - 32)

Example - 1

Find the corresponding temperatures for the following:

200C to 0F 950F to 0C 600C to 0F 2120F to 0C 1000C to 0F 320F to 0C

Absolute Zero

Lowest possible at which is impossible to cool an object.

A precise determination of the absolute zero can be made with constant-volume gas thermometer.

Absolute Zero

Different gases have different pressures but all gases extend to zero pressure precisely at the same temperature: -273.150C.

Example - 2

The gas in a constant-volume thermometer has a pressure of 80kPa at 0.000C. Assuming the ideal behavior of the picture below, what is the pressure at 1050C? Find the temperature of the gas at 70.0kPa of pressure.

Kelvin Scale

It is based on existence of the absolute zero.

The zero on the Kelvin scale (0K) is the absolute zero.

Kelvin scale has the same degree size as the Celsius scale. Therefore the -273.150C is equal to 0K.

Conversion between 0C and K

Tk = Tc + 273.15

Change F to K in example – 2 and calculate the new temperatures.

Temperature Scales

Thermal Expansion

Most substances expand when heated. For example, fever is measured by the expansion of mercury in a tube.

We will discuss three types of thermal expansion: linear, area, and volume.

Linear Expansion (ΔL)

Length changes are proportional to the temperature change.

ΔL = (constant)ΔT

Thermal Expansion

Most substances expand when heated. For example, fever is measured by the expansion of mercury in a tube.

We will discuss three types of thermal expansion: linear, area, and volume.

Linear Expansion (ΔL)

Length changes are proportional to the temperature change.

ΔL = (constant)ΔT

Thermal Expansion When rod 1 is heated by an amount ΔT, its length increases by ΔL. If rod2, which is twice as long as rod1 and made of the same material, is heated by the same amount, does its length increase by (a) ΔL, (b) 2ΔL, or (c) ΔL/2?

The constant that determines the proportionality of expansion, called coefficient of linear expansion (α) is defined as follows: ΔL = αL0 ΔT

Ex: An iron tower is 301 meters high at 220C. How much does its height decrease when the temperature goes to 00C?

Thermal Expansion

Two different metals have different coefficients of linear expansions.

Area Expansion (ΔA)

Using the square as the area to generate the final formula we have:

A’ = (L + ΔL)2 = L2 + 2αL2ΔT + α2L2ΔT2

If αΔT is much less than one, then α2ΔT2 is even

smaller. Then, A’ = L2 + 2αL2ΔT = A + 2αL2ΔT.

ΔA = A’ – A = 2αAΔT

Thermal Expansion A washer has a hole in the middle. As the washer is heated, does the hole (a) expand, (b) shrink, or (c) stay the same?

Volume Expansion (ΔV)

Using the cube as the area with side L, prove that ΔV is equals:

ΔV = V’ – V = 3αVΔT

Coefficient of Volume Expansion (β) are given for different liquids: ΔV = βVΔT

Coefficients of Thermal Expansion

Substance Coefficient of linear Expansion, (K–1)

Lead 29 x 10–6

Aluminum 24 x 10–6

Brass 19 x 10–6

Copper 17 x 10–6

Iron (Steel) 12 x 10–6

Concrete 12 x 10–6

Window glass 11 x 10–6

Pyrex glass 3.3 x 10–6

Quartz 0.50 x 10–6

Substance Coefficient of volume expansion, (K–1)

Ether 1.51 x 10–3

Carbon tetrachloride

1.18 x 10–3

Alcohol 1.01 x 10–3

Gasoline 0.95 x 10–3

Olive oil 0.68 x 10–3

Water 0.21 x 10–3

Mercury 0.18 x 10–3

Heat and Mechanical Work

Heat is the energy transferred from one object to another.

Joule was the scientist that explored the eqivalence between work and heat.

Heat and Mechanical Work

In the previous picture, a total mass 2m falls through a certain distance h. This generates loss of work equals to 2mgh. The masses falling generated paddles´ movement on which created a ΔT increase of water temperature.

Joule´s experiments established the precise amount of mechanical work that has the same effect as a given transfer of heat.

Before Joule, heat was measure in calorie (cal). One kilocalorie (kcal) was the amount of heat needed to raise the temperature of 1kg of water from 14.50C to 15.50C.

Heat and Mechanical Work

Joule was able to show that 1 kcal = 4186J.

Mechanical equivalent of Heat

1 cal = 4.186J

Other units are

C (Calorie nutrition) = 1 kcalBtu (British Thermal Unit) = 0.252 kcal = 1055 J

Finally, Q denotes heat (energy transferred due to 2 different temperatures)

Heat and Mechanical Work

A 74-kg person drinks a thick 305-C shake. How many stairs must this person climb to work off the shake? Let the height of the stair be 20.0cm.

Specific Heats – Heat Capacity

It takes 4186J of heat to raise the temperature of 1kg of water by 10C.

The heat required for an increase in temperature is given by the heat capacity of the substance.

Heat Capacity (C)

C = Q / ΔT

The unit for heat capacity is J/K = J/C0

An object can gain/release heat when in thermal contact with other objects. Objects cannot be taught of as holding a certain amount of heat.

Specific Heats – Heat Capacity

Heat capacity is always positive.

Q is positive if ΔT is positive

Q is negative if ΔT is negative

Ex: The heat capacity of 1.00kg of water is 4186J/K. What is the temperature change in the water if (a) 505J of heat is added to the system, or (b) 1010J of heat is removed?

Ex: Suppose 63J of heat is added to a 128-g piece of aluminum at 250C. What is the final temperature of the aluminum piece?

Specific Heats – Heat Capacity

Heat capacity varies not only with the type of material but also with the amount of substance.

Specific Heat (c) – It is a type of heat that depends only on the type of substance, not the amount.

Specific Heat (c)

c = Q / m ΔT (J / (kg.C0)

Water specific heat is the largest of any common material.

Water can give off or take in large quantities of heat with little change in temperature

Table 16-2Specific Heats at Atmospheric Pressures

Water 4186

Ice 2090

Steam 2010

Beryllium 1820

Air 1004

Aluminum 900

Glass 837

Silicon 703

Iron (steel) 448

Copper 387

Sliver 234

Gold 129

Lead 128

Substance Specific Heat, c [J/(kg•K)]

Calorimetry

Suppose a block of mass mb, specific heat cb, and initial temperature Tb is dropped into a calorimeter containing water with mass mw, specific heat cw, and initial temperature Tw. Assume (a) Final temperature of block and water are the same and (b) the total energy of the system is conserved.

Qb + Qw = 0

Applying the specific heat formula, we have:

mb cb(T - Tb) + mw cw(T - Tw) = 0

Solving for T, we have:

T = (mb cbTb + mw cwTw) / (mb cb + mw cw)

Calorimetry

Ex: Suppose 550-g of water at 320C are poured into a 210-g aluminum can with an initial temperature of 150C. Find the final temperature of the system, assuming no heat is exchanged with the surroundings.

Ex: A 0.50-kg block of metal with an initial temperature of 300C is dropped into a container holding 1.12-kg of water at 200C. If the final temperature of the system is 20.40C, what is the specific heat of the metal? Assume the container can be ignored, and that no heat is exchanged with the surroundings.

Conduction, Convection, and Radiation

Conduction

The flow of heat directly through a physical material.

Conduction depends on the material being used. Poor conductors are considered Insulators.

Experiments show that the amount of heat Q that flows through a rod:

Increases in proportion to the rod´s area (A).Increases in proportion to ΔT = T2 – T1Increases with time t.Decreases with the length of the rod, L.

Conduction, Convection, and Radiation

Conduction

The flow of heat directly through a physical material.

Conduction depends on the material being used. Poor conductors are considered Insulators.

Experiments show that the amount of heat Q that flows through a rod:

Increases in proportion to the rod´s area (A).Increases in proportion to ΔT = T2 – T1

Increases with time t.Decreases with the length of the rod, L.

Conduction, Convection, and Radiation

Heat (Q) flow by Conduction

Q = kA(ΔT / L)t

Thermal Conductivities

Substance Thermal Conductivity, k [W/(m•K)] Silver 417 Copper 395 Gold 291 Aluminum 217 Steel, low carbon 66.9 Lead 34.3 Stainless steel 16.3 Ice 1.6 Concrete 1.3 Glass 0.84 Water 0.60 Asbestos 0.25 Wood 0.10 Wool 0.040 Air 0.0234

Conduction, Convection, and Radiation

Ex: One of the windows in a house has a squared shape with 1.00-m side. The glass of the windows is 0.50-cm thick. How much heat is lost through the window in one one day if the temperature in the house is 21.00C and outside 0.00C?

Ex: Two meta rods are used to conduct heat from a region 1000C to a 00C region. The rods can be arranged as below. Is the heat conducted in the parallel arrangement greater, same, or less that the one in series?

Conduction, Convection, and Radiation

Convection

Convection occurs when a fluid is unevenly heated. As with room heater, the warm portions of the fluid because of their lower density and the cool portions sink because of their higher density.