TEMPERATURE AND HEAT

Thermodynamics part 1

Temperature and Thermal Equilibrium

What is Temperature?

The degree of hotness or coldness of a body or environment

A measure of the ability of a substance, or more generally of any physical system, to transfer heat energy to another physical system.

A measure of the average kinetic energy of the particles in a sample of matter, expressed in terms of units or degrees designated on a standard scale.

How to measure hotness and coldness?

We can use materials that has measurable properties that varies with hotness and coldness

Example:mercury or ethanol (expands when

hot, contracts when cold)

This material can be used as thermometer.

How to use thermometers?

For example:Measuring the temperature of a hot coffee:

The thermometer interacts with the coffee. The thermometer becomes hotter while the coffee becomes a little colderThe reading will stabilized. The interaction does not further cause the system to change.Thermal Equilibrium has been reach!

What is Thermal Equilibrium?

Two system is said to be in thermal equilibrium if and only if they have the same temperature.

Temperature Scales

Celsius and Fahrenheit Scale

They are based on the boiling point and freezing point of water

TF = (9/5) TC + 32

TC = (5/9)(TF- 32)

Kelvin Scale

Base on the relationship of temperature and pressure at constant volume with ideal gases.

The absolute zero temperature is the temperature when the absolute zero pressure is attained.-273.15 oC = 0 K

TK = TC + 273.15

Seat Work 3

Convert the following to desired temperature scale:

1. 500 oC to oF2. 212 oF to oC3. 500 K to oF4. 100 oF to oC5. 1000 K to oC6. 150 oC to K7. 50 oF to K

Thermal Expansion

Thermal Expansion

Most materials expand when its temperature increases and contract when its temperature decreases.

Railways bend because of thermal expansion

Example:- Opening a jar.

Linear Expansion

∆L = Lf – Li

∆T = Tf – Ti

∆L = Li∆T

= coefficient of linear expansionMaterial ( K-1)

Aluminum 2.4 x 10-5

Brass 2.0 x 10-5

Copper 1.7 x 10-5

Glass 0.4-0.9 x 10-5

Invar (Nickel-Iron alloy

0.09 x 10-5

Quartz 0.04 x 10-5

Steel 1.2 x 10-5

Coefficients of linear expansion

Example:

1. A surveyor uses a steel measuring tape that is exactly 50,000 m long at a temperature of 20oC. What is its length on a hot summer day when the temperature is 35oC?

2. In example 1, the surveyor uses the measuring tape to measure a distance when the temperature is 35oC; the value that she reads off the tape is 35.794 m. What is the actual distance? Assume that the tape measure is calibrated for use at 20oC.

Volume Expansion

∆V = Vf – Vi

∆V = Vi∆T

= 3 = coefficient of volume expansion

Solids ( K-1)

Aluminum 7.2 x 10-5

Brass 6.0 x 10-5

Copper 5.1 x 10-5

Glass 1.2-1.7x 10-5

Invar (Nickel-Iron alloy

0.27 x 10-5

Quartz 0.12 x 10-5

Steel 3.6 x 10-5

Liquids ( K-1)

Ethanol 75 x 10-5

Carbon disulfide

115 x 10-5

Glycerin 49 x 10-5

Mercury 18 x 10-5

Coefficients of Volume expansion

Example

1. A glass flask with volume 200 cm3 is filled to the brim with mercury at 20oC. How much mercury overflows when the temperature of the system is raised to 100oC? The coefficient of linear expansion of glass is 0.40 x 10 -5.

2. A metal rod is 40.125 cm long at 20.0oC and 40.148 cm long at 45oC. Calculate for the average coefficient of linear expansion of the rod on this temperature range.

Heat

What is Heat?

Energy transfer that takes place solely because of temperature difference is called heat flow or heat transfer. This is usually called heat.

Since heat is a transfer of energy, the standard unit for heat is joules.

Heat and temperature is not the same!

Heat vs Temperature

Heat is in Joules while temperature is in Kelvin

Temperature is a quantitative description of hotness and coldness while heat is the energy transferred due to difference in temperature.

Temperature can change by adding or taking away heat or energy through mechanical work.

Units of Heat

Standard unit Joule.Other units of Heat

1calorie (cal) = 4.186 J1 kilocalorie (kcal) = 4186 J

How much heat is needed?

Specific Heat

Specific Heat

Q = mcTQ – heat required to raise or to lower the

temperature of an objectm – massT – change in temperaturec – specific heat – the amount of heat

required to raise 1 kg of a substance by 1K or 1oC.

Specific Heat

- The greater the specific heat of a material, the more heat must be transferred to it or taken from it to change the temperature of a given mass of it.

Example Sand and water in beach (water has high

specific heat) At day water is cold, sand is hot At night water is hot, sand is cold

Specific Heat

Substance Specific Heat (J/kg*oC or K)

Air 1050

Alcohol, ethyl 2430

Aluminum 920

Copper 390

Iron or Steel 460

Lead 130

Mercury 140

Water 4186

Wood 1680

Example

1. During a bout with the flu an 80-kg man ran a fever of 39.0oC instead of the normal body temperature of 37.0oC. Assuming that the human body is mostly water, how much heat is required to raise his temperature by that amount? Specific heat of water is 4186 J/kgK.

Example

2. A half-liter of water at 350 K is cooled by removing 63 kJ of heat. What is its final temperature?

3. A 0.250-kg cup at 20oC is filled with 0.250 kg of boiling coffee. The cup and the coffee come to thermal equilibrium at 80oC. If no heat is lost, what is the specific heat of the cup material? Consider coffee as water.

Phase Change and Latent Heat

Phase Change

Matter usually comes in three phases, solid, liquid and gas.

Matter changes phase due to temperature change

Example: Water- solid, below 0oC- liquid, 0oC to 100oC - gas, above100oC

Additional heat is required when changing phase

Phase Change

More heat is taken away when water is converted to ice at 0oC compared to bringing water in liquid form to 0oC.

More heat is put in when water is converted into water vapor at 100oC compared to bringing water in liquid form to 100oC

Additional energy is needed to break or make intermolecular bonds between molecules.

The additional energy is accounted for by Latent Heat

Latent Heat

Latent Heat of Fusion (Lf)

- heat required to change the phase of 1 kg of material from liquid to solid.

Latent Heat of Vaporization (Lv)

- heat required to change the phase of 1 kg of material from liquid to gas.

Q = +/- mLf

Q = +/- mLv

Latent Heat

Some Latent heats of materials:

Substance Normal Melting Point(K)

Lf

(J/kg)Normal Boiling

Point(K)

Lv

(J/kg)

Hydrogen 13.84 58.6 x 103 20.26 452 x 103

Nitrogen 63.18 25.5 x 103 77.34 201 x 103

Oxygen 54.36 13.3 x 103 90.18 213 x 103

Mercury 234 11.8 x 103 630 854 x 103

Water 273.15 334 x 103 373.15 2256 x 103

Sulfur 392 38.1 x 103 717.75 326 x 103

Gold 1336.15 64.5 x 103 2933 1578 x 103

Example

1. A physics student wants to cool 0.25 kg of Diet Omni-Cola (mostly water), initially at 25oC, by adding ice at -20oC. How much ice should she add so that the final temperature will be 0oC with all the ice melted if the specific heat of the container may be neglected?

2. A heavy copper pot of mass 2.0 kg (including the copper lid) is at a temperature of 150oC. You pour 0.10 kg of water at 25oC into the pot, then quickly close the lid of the pot so that no steam can escape. Find the final temperature of the pot and its contents, and determine the phase (liquid or gas) of the water. Assume that no heat is lost to the surroundings.

Example

3. A 0.10-kg of piece of ice at 0oC is placed in a liter of water at room temperature (20oC) in an insulated container. Assuming that no heat is lost to the container, what is the final temperature of water?

4. A 20kg block of ice at -10oC, is put inside a cylinder containing water at 50oC. All the ice is melted and their final temperature is 10oC. How much water is present initially inside the cylinder?

SW

1. A cube of aluminum 10cm on each side is cooled from 100oC to 20oC. If the heat removed from the aluminum cube were added to a copper cube of the same size at 20oC, what would be the final temperature of the copper cube?((Al) = 2.7g/cm3 , (Cu) = 8.9g/cm3)

2. How much ice (0oC) must be added to 1.0 kg of water(liquid) at 100oC so as to end up with all liquid at 20oC?

Conduction, Convection and Radiation

Methods of Heat Transfer

Methods of Heat Transfer

Conduction- use of thermal conductor (ex.

Metals) Convection

- use of fluids (liquids or gas) Radiation

- no medium, uses EM wave to transfer heat

Conduction

Modern theory views that thermal conductions are due to electrons that are free to move.

Metals have many free electrons. They are good heat conductors.

Non-metals such as wood or cloth have few free electrons. They are poor heat conductors or thermal insulator

Conduction

In general, ability to conduct heat depends on phase.

Gases are poor conductors, molecules are relatively far apart.

Solids are better conductors, molecules are closer.

Heat conduction can be quantitatively described as the time rate of heat flow in a material for a given ∆T.

H = ∆Q/ ∆t, change of heat/change in time.

H= heat current

Conduction

A = total surface aread = distance, thickness of slabk = thermal conductivity constant∆T/d = heat gradient

Good conductors have high thermal conductivity constant while poor conductors have low thermal conductivity constants.

Conduction

Substance Thermal Conductivity (k) (J/(m*s*oC)

Aluminum 205

Copper 385

Iron and Steel 50.2

Silver 406

Transformer Oil 0.18

Water 0.57

Air 0.024

Brick 0.71

Concrete 0.8

Styrofoam 0.01

Wood, oak 0.15

Vacuum 0

Examples 1

A Styrofoam box used to keep drinks cold at a picnic has a total area of 0.80 m2 and wall thickness of 2.0 cm. it is filled with ice, water, and cans of Omni-Cola at 0oC. What is the rate of heat flow into the box if the temperature of the outside wall is 30oC?

Example 2

A silver bar with length of 200 cm with a cross sectional area of 4 cm2 is put in contact with steam at 100oC at one end and with water at 20oC on the other end. Compute for the heat current if the silver bar is perfectly insulated.

Example 3

A steel bar 10.0 cm long is welded end to end to a copper bar 20.0 cm long. Both bars are insulated perfectly on their sides. Each bar has a square cross-section, 2.00 cm on a side. The free end of the steel bar is maintained at 100oC by placing it in contact with steam, and the free end of the copper bar is maintained at 0oC by placing it in contact with ice. Find the temperature at the junction of the two bars and the total rate of heat flow.

Convection

Transfer of heat by mass motion of a fluid from one region of space to another.

Example- house cooling and heating system - cooling system of automobile

Convection

Forced convection – if the fluid moves by using a pump.

Example:- blood circulation (heart-

pump) Natural convection or free convection – if

the flow is caused by difference in density.

Example:- daily weather

Radiation

Transfer of heat by electromagnetic waves such as visible light, infrared and ultraviolet radiation.

Most heat are transferred through radiation

Example:- heat from the sun- heat from charcoal grill

Radiation

Heat current due radiation is;

Stefan-Boltzmann Law

H- heat currentT – Temperature of the body, must be in KelvinA- surface areae – emissivity, between 0 to 1 - Stefan – Boltzmann constant

= 5.670400 x 10-8 W/m2 K4

Example 1

A thin square steel plate, 10 cm on a side, is heated in a blacksmith’s forge to a temperature of 800oC. The emissivity is 0.60, what is the total rate of radiation energy (heat current)?

Radiation

Net rate of radiation from a body to the surrounding.

Ts – temperature of the surrounding

Example 2

If the total surface area of the human body is 1.20 m2 and the surface temperature is 303 K, find the total rate of radiation of energy from the body if the surroundings are at a temperature of 293.15 K. assume that the emissivity is 0.6.