Heat and Temperature

A thermal infrared image of a ball before (left) and after (right) being bounced.

DEFINITION OF HEAT

Heat is thermal energy that flows from a higher-temperature object to a lower-temperature object because of a difference in temperatures.

SI Unit of Heat: joule (J) or calories (cal)

4.184 J = 1 cal

4184 J = 1 Cal = 1 kcal

What is the difference between a hot cup of coffee and a cold cup of water?

Which has more internal energy, a cup of hot water or an iceberg?

The iceberg because it has more molecules jiggling

In a hot cup of coffee there is more activity – the atoms are jiggling around more. We say that they have more kineticenergy. We might even say that they have more thermal energy(energy of random motion) or more internal energy because more energy is internal to the system.

The heat that flows from hot to cold originates in the internal energy ofthe hot substance.

It is not correct to say that a substancecontains heat.

Internal energy is the total energy thatthe molecules possess (kinetic pluspotential).

Kinetic energy can be translational and rotational. Molecules have potential energy because of intermolecular forces.

When we heat a substance, we increaseIts internal energy.

Temperature is related to the internal energyper molecule or the average kinetic energyof translational motion of molecules.

Why do we give sparklers that burn at 12000C to kids ?

There are not many combustible molecules in the sparkler so not much total energy – certainly below the kids threshold of feeling…so

Although the temperature is high, (the amount of internal energy per molecule), the total internal energy is low!

Measuring Temperature

Thermometers use liquids that expand or contract easily with temperature. The liquid absorbs or transfers thermal energy.

We say that a thermometer “measures its own temperature”…because any two things put together will come to the sametemperature.

When this happens, the thermometer and its environment are said to be in thermal equilibrium.

A poorly constructed thermometer thus has the ability to change the temperature of its surroundings by absorbing too much heat.

Temperatures are reported in degreesCelsius, degrees Fahrenheit or degrees Kelvin.

0 K is the temperature at which an idealgas can theoretically be compressed tozero volume (called absolute zero)

Scales of Temperature

Kelvin temperatures are always positive so can be related proportionally to the average kinetic energy per molecule

KEAv = 3/2 kT

There are 180 divisions on the 0F scalecompared with 100 divisions on the oCscale so the scale factor is…..

180 / 100 = 9 / 5

Scale Conversions

because the 0F scale begins at 32 ratherthan 0 we must add this on, so…..

TF = (9/5 TC) + 32.0

For the Kelvin scale, the freezing point of water is 273.15 K above absolute zero so..

TK = TC + 273.15

1. Normal body temperature is 98.6 0F. What is this on the Centigrade scale?

TC = 5/9 (TF – 32)

Temperature Practice

= 5/9 (98.6 – 32) = 370C

2. Room temperature is often taken to be 680F. What is this on the Centigrade and Kelvin scales?

TC = 5/9 (TF – 32) = 5/9 (68 – 32) = 200C

TK = TC + 273.15 = 20 + 273.15 = 293.15 K

3. The temperature of a filament in a light bulb is about 18000C. What is this on the Fahrenheit and Kelvin scales?

TC = (9/5 TC ) + 32 = (9/5 1800) + 32) = 32720F

TK = TC + 273.15 = 1800 + 273.15 = 2073 K

Processes of Thermal Energy Transfer

Conduction

Conduction is the process by which kinetic energy is passed from molecule to molecule

Metals have a lot of loose (free) electrons which can transmit vibrations (KE) quickly when high speed particles collide with slower moving ones. We say they are good heat conductors.

All gasses (and most liquids) tend to be poor conductors. We say that they are good thermal insulators.

Conduction Examples

• Wooden or rubber handles on frying pans

• Clothing worn in layers to trap air – a poor conductor

• Wood or tiled floor feels cooler than carpet even though they are at the same temperature

• Wood or tiled floor feels cooler than carpet even though they are at the same temperature

• Snowflakes trap air in their crystals so are good insulators. Snow slows the escape of heat from the earth’s surface, so good for Eskimo dwellings and protection for animals from the cold.

Processes of Thermal Energy Transfer

Convection

In convection, thermal energy moves between two points because of a bulk movement of matterWhen part of a fluid is heated, it tends to expand and thus its density is reduced. The colder fluid sinks and the hotter fluid rises up.

This thermal infrared image shows hot oil boiling in a pan. The oil is transferring heat out of the pan by convection. Notice the hot (yellow) centers of rising hot oil and the cooler outlines of the sinking oil.

Convection Examples

• Sea breezes (winds) are often due to convection. During the day the land is hotter than the sea. Hot air rises from the land and there is a breeze onto the shore. During the night the situation is reversed.

• Pilots of gliders (and many birds) use naturally occurring convection currents to stay above the ground

• A refrigerator cooling coil is placed at the top of the unit so that colder air sinks downwards and the warmer air is displaced upwards and cooled by the coil thus establishing a convection current.

• Central heating causes a room to warm up because a convection current is set up. The heat source should be near the ground.

Processes of Thermal Energy Transfer

Radiation

Radiation is the process in which energy is transferred by means of electromagnetic waves.

For most everyday objects, this radiation is in the infra-red part of the electromagnetic spectrum.

A thermal infrared image of the center of our galaxy. This heat from numerous stars and interstellar clouds traveled about 24,000 light years (about 150,000,000,000,000,000 miles!) through space by radiation to reach the infrared telescope

The source of EM waves is vibrating electrons in matter

Points to note:

• An object at constant temperature will both absorb and radiate energy at the same rate.

• A surface that is a good radiator is also a good absorber.

• Surfaces that are light in color and smooth (shiny) are poor radiators (and poor absorbers). The reverse is true for dark and rough surfaces.

• If the temperature of an object is increased then the frequency of the radiation increases. The total rate at which the energy is radiated will also increase.

• Radiation can travel through a vacuum (space)

Radiation Examples

• The sun warms the Earth’s surface by radiation (principally short wavelength/high frequency IR)

• People wear light colored clothing in summer as it tends to not absorb the radiation from the sun.

• Thermos flask has silvered inside surface to reduce radiation.

• The earth re-radiates energy back as low frequency radiation because the earth’s temperature is so low. The atmosphere is transparent to visible (high f) light but longer wavelengths are absorbed and reradiated back to earth especially by excess carbon dioxide and water vapor leading to increased global warming.

• A Halogen cook top uses several quartz-iodine lamps underneath a ceramic top (low conductivity). The EM radiation passes through the ceramic top and is absorbed by the bottom of the pot.

Heat and Specific Heat

A person puts a pan on a stove heating ring and returns a few seconds later to find that the pan is hot. The same person puts a pan of water on the stove ring and returns minutes later to find that the pan is warm but far from hot. What does this tell you?

Some substances will absorb a lot of heat for only a small change in temperature.

Iron with a little heat will shoot up in temperature while water takes a lot of heat energy to make the temperature higher.

Why is this?

Heat and Specific Heat

Temperature has a lot to do with the translational back and forth motion of atoms or molecules

Iron’s electrons move rapidly back and forth and the temperature goes up quickly

But…water doesn’t just shake back and forth, the molecules pucker in and out storing the energy in internal rotational states (potential energy) and the hydrogen bonding sticks them together so they don’t shake as much, so the temperature is not driven up as much.

We say that water stores an enormous capacity of heat for small temperature changes – This is called specific heat

Heat and Specific Heat

We can define the heat capacity, C, of an object as the energy required to raise its temperature by 1 K. This is different for different substances.

Specific heat capacity, c, is the energy required to raise a unit mass of a substance by 1 K.

C = Q / T units: J / K or J / 0C

We say that water stores an enormous capacity of heat for small temperature changes – This is called specific heat

c = Q / (m T) units: J / kg K or J / kg 0C

Heat and Temperature Change: Specific Heat Capacity

Heat and Specific Heat

It turns out that water will absorb a whole calorie of heat energy per gram and only change temperature by 1 degree Celcius (centigrade)

We can think of specific heat as “thermal inertia” because it signifies the resistance of a substance to a change in temperature.

Q = m c t

m = mass of object c = specific heat capacity (cal/g0C) t = change in temperature

cwater = 1 cal/g0C or 4.184 J/g0C or 4184 J/kg0C

Heat and Specific Heat

How much energy does it take to raise the temperature of 1.5 liters of water by 200C?

mwater = 1.5 L ( 1kg / 1L) = 1.5 kg cwater = 1000 cal/kg0C or 4184 J/kg0C T = 20oC

Q = m c t

Q = (1.5 kg) (1000 cal/kg0C) (200C)

Q = (1.5 kg) (4184 J/kg0C) (200C)

= 30 000 cal

= 125 520 J = 130 000 J

Heat and Specific Heat

Some high temperature foods, you can eat comfortably when you take them out of the oven as they have a low specific heat capacity and therefore don’t hold much thermal energy but water filled foods like pie filling you can burn your mouth on as the high temperature food will hold a lot of energy.

A hot water bottle contains boiling water that cools gradually during the night releasing a large amount of thermal energy.

Countries surrounded by water (which has a high specific heat) are heated by the warm winds that have absorbed thermal energy from the ocean (cons of energy). The ocean cools gradually during the winter so maintains a constant source of heat energy. The water acts as a temperature moderator, absorbing energy from the air above in the summer and releasing it in the winter.

Heat and Temperature Change: Specific Heat Capacity

A Hot Jogger

In a half-hour, a 65-kg jogger can generate 8.0x105J of heat. This heatis removed from the body by a variety of means, including the body’s owntemperature-regulating mechanisms. If the heat were not removed, how much would the body temperature increase?

TmcQ

58.0 10 J

65 kg 3500J kg C

QT

mc 3.5 C

Heat and Temperature Change: Specific Heat Capacity

CALORIMETRY

If there is no heat loss to the surroundings,the heat lost by the hotter object equals theheat gained by the cooler ones.

Heat and Temperature Change: Specific Heat Capacity

Measuring the Specific Heat Capacity

The calorimeter is made of 0.15 kg of aluminumand contains 0.20 kg of water. Initially, thewater and cup have the same temperatureof 18.0oC. A 0.040 kg mass of unknown material is heated to a temperature of 97.0oC and then added to the water.

After thermal equilibrium is reached, thetemperature of the water, the cup, and the material is 22.0oC. Ignoring the small amountof heat gained by the thermometer, find the specific heat capacity of theunknown material.

Heat and Temperature Change: Specific Heat Capacity

29.00 10 J kg C 0.15 kg 4.0 C 4186J kg C 0.20 kg 4.0 C

0.040 kg 75.0 C

unknownwaterAl TmcTmcTmc

Al waterunknown

unknown

mc T mc Tc

m T

1300J kg C

Phase Changes

Why do you feel cold when you get out of a pool and a breeze is blowing?

Why is evaporation a cooling process?Molecules in a liquid have a distribution of speeds and the average relates to what we call Temperature. When faster moving molecules leave a liquid’s surface they leave behind the slower moving molecules, which lowers the average speed and therefore the temperature of the liquid.

Water evaporates off your body and cools you down. How come?

Normal distribution curves of molecular speeds for ideal gas at 100 K and 900 K respectively

Phase Changes

In hot climates, sacking is put over clay pots and kept wet. Why?

Evaporation of water from the sack cools the sack and thus draws thermal energy outwards from the water inside the pot. This keeps the drinking water nice and cool.

How do we keep cool?

We perspire (sweat), so evaporation takes place from our skin’s surface.

Why do dogs pant? (or other animals without sweat glands)

They can’t sweat so they create a large surface area (tongue and bronchial tract) from which liquid can evaporate and therefore cool them down.

Similarly rubbing your hands under a hand dryer creates a larger surface for water to evaporate.

Phase Changes

Evaporation depends upon the temperature of the liquid and air surrounding the liquid, the surface area of the liquid and the moisture content in the air (humidity). Evaporating molecules form a vapor above the liquid. Equilibrium is reached when the vapor pressure exerted on the fluids surface returns liquid molecules to the liquid at the same rate they leave.

How do fans keep people cool?

Lower vapor pressure so more evaporation so….more cooling

Why are their warning signs on hot tubs about staying in too long?

In a hot tub you sweat like mad but the water can’t evaporate off the skin so your body heats up and can be dangerous if you stay in too long.

Name at least two ways to cool a hot cup of coffee?

Increase evaporation by blowing on it, pouring it into a saucer Cool by conduction by pouring in cool saucer, adding ice cubes, stirring with cool silverware

Phase Changes

Is condensation a heating or a cooling process?

It is a heating process. The slower moving water vapor molecules stick together (forming droplets) while the higher speed molecules remain in the gaseous state thus increasing the average KE of the air molecules and thus the temperature.

Why do people dry off in a steamy bathroom?

The cooling effect of water evaporating off their body is balanced by the heating effect of steam condensing on it. That is why my 4-year old daughter asks for the warm water to be left in the tub while she is drying off.

Phase Changes

If evaporation is a cooling process is boiling a heating process?

Heating the water in a pan is a heating process but the act of boiling is actually a cooling process. Like evaporation, when boiling, molecules leave the surface of the liquid taking thermal energy with them.

What influences the ability of a liquid to boil other than temperature?

The air pressure acting on the liquid

Heat pan of water, bubbles form but 30km of air pushing down (atmospheric pressure) squashes these bubbles. With more heating the temp keeps increasing and the molecules become more energetic until bubbles are able to withstand the pressure. This temps for water is 1000C at sea level.

What happens to this process if you are up a mountain?

Closer to top of air therefore less pressure so bubbles stay formed at a lower temperature.

Phase Changes

You normally cook eggs for 3 minutes at sea level. Do you cook them for a longer or shorter time when living at higher altitude?

Longer as water boils at a lower temp

If you heat water at atmospheric pressure it boils at 1000C but if you turn up the heat it doesn’t get any hotter, how come?

The more you heat, the more vigorous the boiling but you also have more liquid escaping therefore more cooling so they offset each other. (you can also think of it as the heat input going towards breaking intermolecular bonds and not towards changing the average kinetic energy of the molecules).

If you put a cover on a pan of spaghetti will it cook faster?

Yes, the lid increases the pressure so temp goes up more before bubbles stay formed.

Phase Changes

Why are sensitive fruit crops in the South sprayed with water before a forecasted frost?

Like condensation (gas to liquid), changing state from liquid to solid is also a heating process. The heat liberated in freezing the layer of water around the outside of the strawberry, actually protects the strawberry inside.

Phase Changes

In the past, farmers used to put a tub of water in the cellar where they stored their canned food. Why?

If the temperature in the cellar dropped the water in the tub would freeze before the liquid in the cans (which had added salt or sugars) thus releasing heat and warming the room.

Phase Changes

Which will hurt more, a steam burn at 1000C or a water burn at 1000C ?

The steam burn is much more serious because each gram of steam liberates 540 calories when it condenses, whereas water only liberates 1cal for every gram for every degree (or only 100 cal to go from 1000C to 0 0C).

Note: When 540 cal is used to turn a gram of water into steam it does not go into increasing the molecules KE, so it must go into increasing their PE. Intermolecular bonds have to be broken and this takes a lot of energy. When steam condenses, bonds form and this energy is released.

Phase Changes

Why is an ice rink flooded with hot water to smooth out the ice? Wouldn’t cold water work better?

Above 800C, hot water freezes faster than warm water. For a large surface area like an ice skating rink, the rate of cooling by rapid evaporation is very high because each gram of water that evaporates, draws at least 540 cals/gram from the water left behind.

This is huge compared with the 1 cal/g/0C that is drawn for each gram of water that cools by thermal conduction.

Phase Changes

Latent Heat of Fusion:

The quantity of heat needed per kg to melt a solid (or solidify a liquid) at constant temperature and atmospheric pressure.

Change in heat = (mass)(heat of fusion)

Q = m Lf Lf units: J/kg

Lf,water = 80 cal/g or 3.35 x 105 J/kg

Latent Heat of Vaporization:

The quantity of heat needed per kg to vaporize a liquid (or liquefy a gas) at room temperature and atmospheric pressure.

Change in heat = (mass)(heat of vaporization)

Q = m Lv Lv units: J/kg

Lv,water = 540 cal/g or 2.26 x 106 J/kg

More than 6x’s Lf for water

Phase Changes

Latent Heat of Fusion:

The quantity of heat needed per kg to melt a solid (or solidify a liquid) at constant temperature and atmospheric pressure.

Change in heat = (mass)(heat of fusion)

Q = m Lf Lf units: J/kg

Lf,water = 80 cal/g or 3.35 x 105 J/kg

Latent Heat of Vaporization:

The quantity of heat needed per kg to vaporize a liquid (or liquefy a gas) at room temperature and atmospheric pressure.

Change in heat = (mass)(heat of vaporization)

Q = m Lv Lv units: J/kg

Lv,water = 540 cal/g or 2.26 x 106 J/kg

More than 6x’s Lf for water

Gas Laws

Atmospheric Pressure

The weight of 30km of air on each square meter at the earth’s surface is about 100 000 N (105 N).

A Pascal is 1 N/m2 so the pressure is reported as 100 000 Pa or 100 kPa. It is actually 101.3 kPa.

The earth’s atmosphere has density therefore it has weight. At sea level (200C) it has a density of 1.2 kg/m3

Barometers and pumps rely on the atmospheric pressure to push a liquid up an evacuated tube.

The pressure at the bottom of a mercury barometer must be the same as the atmospheric pressure (otherwise liquid would keep on being pushed up the tube).

Similarly, a vacuum pump can only raise water up a height of 10.3m as mercury is pushed up 76 cm and is 13.6 times more dense as water (13.6 x 0.76m = 10.3m)

Gas Laws

Robert Boyle (1627-1691)

V 1/ P (constant T) PV = constant P1V1 = P2V2

Kinetic Theory Interpretation The pressure exerted on the wall of a container is due to the constant bombardment of molecules. If the volume is reduced (say in half), the molecules are closer together and twice as many will be striking a given area of the wall per second, hence the pressure will be twice as great.

The volume of a gas is inversely proportional to the pressure applied when the temperature is kept constant.

Gas Laws

Archimedes Principle (Buoyancy)

FB = F g V (for submerged portion of the object placed in the fluid)

Any object that has a mass less than the mass of an equal volume of the surrounding fluid (air or liquid) will rise.

Buoyant forces are caused by a difference in pressure on the top and bottom surfaces of a submerged object.

The buoyant force on a body immersed in a fluid is equal to the weight of the fluid displaced by the object.

In other words for air if any object is less dense than the surrounding air around it, it will rise. Heating air in a hot air balloon has this effect.

Gas Laws

P1 = 2.00 x 105 Pa V1 = 5.00 cm3 P2 = 1.01 x 105 Pa V2 = ?

1. To capture its prey a whale will create a cylindrical wall of bubbles beneath the surface of the water, trapping the confused fish inside. If an air bubble has a volume of 5.0 cm3 at a depth where the water pressure is 2.00 x 105 Pa, what is the volume of the bubble just before it breaks the surface of the water?

V2 = P1V1 / P2 = (2.00 x 105 Pa)(5.00 cm3) / (1.01 x 105 Pa)

Examples

V2 = 9.90 cm3

Gas Laws

P1 = 1.01 x 105 Pa V1 = 6.0 x 10-7 m3 P2 = 1.00 x 105 Pa V2 = ?

2. In a jet liner ascending from sea level where the cabin pressure starts off at 1.01 x 105 Pa to flying altitude where the cabin pressure drops slightly to 1.00 x 105 Pa despite pressurized conditions. A person will feel a strange sensation in their middle ear, whose volume is 6.0 x 10-7 m3. What is the new volume of air inside the person’s middle ear and what can they do to compensate for this change in volume?

Examples

P1V / T1 = P2V / T2

V2 = P1 V1 / P2 = (1.01) (6.0 x 10-7 m3) / (1.00)

= 6.1 x 10-7 m3

Swallowing or yawning clears the Eustachian tube by reducing the volume of air.

Gas Laws

P1 = 3.06 x 105 Pa P2 = 1.01 x 105 Pa V2 / V1 = ?

3. Mr. Fawcett is diving at a dept of 20m off the coast of Mexico where the density of water is 1025 kg/m3 and the pressure is 3.06 x 105 Pa. If he foolishly hold s his breath as he ascends to the surface, how many times would the volume of his lungs change (assuming the water temp stays constant)? Would his lungs be crushed or would they expand? What is the best way to ascend after diving?

Examples

V2 / V1 = P1 / P2 = (3.06 x 105 Pa) / (1.01 x 105 Pa) = 3.03 times bigger

His lungs would blow up like a balloon

He could continue releasing air from his lungs while ascending

* Note pressure with depth is calculated using: P = gh + atmos pressure P = (1025 kg/m3)(10 N/kg)(20m) + 101.3 x 103 N/m2 P = 3.06 x 105 N/m2 (Pa)

Gas Laws

F = 1.21 kg/m3 V = 5450 m3 g = 10 N/kg H = 0.178 kg/m3

4. A 5450 m3 blimp circles Fenway Park during the Word Series, suspended in earth’s 1.21 kg/m3 atmosphere. The density of the helium in the blimp is 0.178 kg/m3.

a) What is the buoyant force that suspends the blimp in the air?b) How does this force compare to the blimp’s weight?c) How much weight in addition to helium, can the blimp carry and still continue to maintain a constant altitude?

Examples

a) FB = F g V = (1.21 kg/m3) (10 N/kg) (5450 m3) = 65 945 N = 65 900 N

b) The blimp is suspended so it is the same

c) Weight of Helium = H g V = (0.178 Kg/m3)(10 N/kg)(5450 m3) = 9701 N

Therefore weight that can be added is 65 945 N – 9701 N = 56 200N

Gas Laws

F = 1025 kg/m3 s = 980 kg/m3 g = 10 N/kg V = 0.060 m3

5. Floating on her back in the beautiful Caribbean during her spring break a student has a density of 980 kg/m3 and a volume of 0.060 m3. What buoyant force supports her in the sea, which has a density of 1025 kg/m3?

Examples

FB = Wt = s g V = (980 kg/m3) (10 N/kg) (0.060 m3) = 588N = 590N

Note: Buoyant force can’t be more than her weight because she is floating. She is not submerged as he density is less than that of sea water.

Gas Laws

F = 1000 kg/m3 g = 10 N/kg V = 0.9000 m3

6. Swimming in her backyard pool, a student attempts to hold a 0.9000 m3 inner tube under the water. If submerged what buoyant force will be exerted? If the tube is then let go and pops up with a force of 8990N, what is the weight of the inner tube?

Examples

FB = F g V = (1000 kg/m3) (10 N/kg) (0.9000 m3) = 9000 N

Wt = FB – F = 9000N – 8990N = 10N