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Chapter 15Heat Capacity

Thermal ExpansionChapter 16

Heat Transfer

Lecture 17

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Internal EnergyInternal energy of an

object depends on:• Temperature• Mass• Material

1 kg

Temperature InternalEnergy

300 K 120,000 J

200 K 80,000 J

100 K 40,000 J

0 K 0 Joules

Iron

Temperature InternalEnergy

300 K 120 J

200 K 80 J

100 K 40 J

0 K 0 Joules

Iron

1 gram

Temperature InternalEnergy

300 K 1,200,000 J

200 K 800,000 J

100 K 400,000 J

0 K 0 Joules

Water

1 kg

1000 grams

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Specific Heat CapacitySpecific heat capacity is the amount of heat

energy required to raise the temperature of one unit mass of a material by one degree.

SI Unit: J/(kg•K) or J/(kg•°C)Other Units: cal/(g •°C)

Heat energy needed to raise temperature of material by ∆T is:

(Specific heat cap. of material)•(mass)•∆T

Some specific heat capacity values.Specific heats of gases are complicated.

Example• How much heat energy is needed to raise the

temperature of 2 kg of copper (s.h.c. = 387 J/kg-K) from 10° to 30°C?

• Q = (s.h.c.)•m•∆T = (387 J/kg-K)(2kg)(20K)= 1.55 x 104 J

• How long would it take for a 1000 W heater to do this? Power = (Energy provided)/∆t

∆t = (Energy needed)/(Power) = 15500J/(1000 J/s)= 15.5s

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Check Yourself

Why does a piece of watermelon stay cool for a longer time than sandwiches do when both are removed from a cooler on a hot day?

Why is it that the climate in the desert is so hot during the day yet so cold at night?

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Thermal Expansion

Due to increased molecular motion, most materials expand as temperature increases.

Sidewalk buckles and cracks due to expansion on a hot summer day

Space allows for expansion

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Demo: Expansion of a Ring

Metal ball barely fits past the metal ring.

Not surprising that heated ball won’t pass through cold ring.

Will cold ball pass through heated (expanded) ring?

Coefficients of Linear Expansion

Thermal Expansion DifferencesA bimetallic strip has two metals of different coefficients of thermal expansion, A and B in the figure. It will bend when heated or cooled.

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Demo: Heat, Cool, Break

COOL (quickly)

HEAT

Glass expands when heated. If hot glass is cooled quickly, exterior cools before the interior. Exterior contracts faster than the interior, cracking the glass.Pyrex glass expands much less than regular glass.

GLASS

Cracks form

Thermal ExpansionThe amount of thermal expansion of length L is:

∆L = (expansion coefficient)•L•∆TAn area gets linear expansion in both directions.

Holes expand as well:

You have a (glass) jar and you can’t get the metal lid off. What should you do:

a) ask your friendb) run the jar & lid under cold water

c) run the jar & lid under hot water

You have a (glass) jar and you can’t get the metal lid off. What should you do:

a) ask your friendb) run the jar & lid under cold waterc) run the jar & lid under hot water

Because the metal has a substantially higher coefficient of thermal expansion than the glass, heating them will make both of them bigger, but the metal will be ‘more bigger’.

Water Density vs. Temperature

This explains why lakes freeze from the top.

Heat Transfer(Flow of Heat Energy)

Three Methods•Conduction - Thermal kinetic energy passed

from particle-to-particle along a length ofmaterial.

•Convection - Thermal energy carried bymoving fluid.

•Radiation - Thermal energy carried byelectromagnetic waves.

Heat Transfer: ConductionHeat conduction can be visualized as occurring through molecular collisions. Thermal kinetic energy is passed along as “hotter” particles collide with “colder” ones.

L

Q

Cross-sectional area

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Conduction

Conduction is heat flow by direct contact.

Some materials are good thermal conductors, others are insulators.

98º

75º

98º

75ºWood is an

insulatorTile is a

conductor

Tile floor feels colder than wood floor

ConductionExperimentally, it is found that the amount of heat Q that flows through a piece of material:

• Increases proportionally to the cross-sectional area A

• Increases proportionally to the temperature difference ∆T from one end to the other

• Increases steadily with time t

• Decreases with the length L of the piece

• Depends on the “thermal conductivity” of the material. More conductive → more heat flows

Thermal Conductivity

Some typical thermal conductivities:

Substances with high thermal conductivities are good conductors of heat; those with low thermal conductivities are good insulators.

Vacuum has a thermal conductivity = 0.

Convection

Convection is flow of fluid due to difference in temperatures, such as warm air rising. Fluid “carries” heat with it as it moves.

“Natural” convection: Warm fluid will rise because it is less dense then cold fluid.

Heat Transfer: ConvectionConvection occurs when heat flows by the mass movement of molecules from one place to another. It may be natural or forced (fans); both these examples are natural convection.

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Convection

Heat transfer in a fluid often occurs mostly by convection.

Buoyancy causes warm air to rise, which carries thermal energy directly by its motion.

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Convection OvenConvection oven has a fan to enhance the circulation of the air, increasing the transfer of heat.

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Fiberglass Insulation

Air is a poor thermal conductor but easily transfers heat by convection.

Fiberglass insulation is mostly air, with the fibers disrupting the convection flow.

RadiationAll objects give off energy in the form of radiation, as electromagnetic waves – infrared, visible light, ultraviolet – which, unlike conduction and convection, can transport heat through a vacuum.

Objects that are hot enough will glow visibly –first red, then yellow, white, and blue as temperature increases. Objects at body temperature radiate in the infrared, and can be seen with night vision binoculars.

3-Oct-10 Physics 1 (Garcia) SJSU

RadiationRadiation has many

different wavelengths, most of which are not visible to the eye.

All radiation carries energy, and thus transfers heat. Heat Lamp

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Emission of Radiant Energy

All objects radiate; higher the temperature, the higher the frequency.

At room temperature, the radiated light is at frequencies too low for our eyes to see.

Special cameras are sensitive to this infrared radiation.

Attics in this house were kept warm for growing marijuana.

70

98º

75º

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Reflection of Radiant EnergyWhite and “silver” objects reflect light, black objects

and “holes” don’t.

Hole in a box with white interior looks black because almost none of the light entering the hole reflects back out.

White tubes look black inside.

Black objects are also the best emitters of radiation. White objects emit less radiation, and perfectly reflective objects don’t emit at all. (Space blanket.)

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Controlling Heat TransferThermos bottle eliminates conduction

and convection by having double-walled sides with vacuum.

Silvered interior walls minimize heat transfer by radiation.

RadiationIf you are in sunlight, Sun’s radiation will warm you. The intensity of solar radiation is 1000 W/m2. In general, you will not be perfectly perpendicular to the Sun’s rays, and will absorb energy at a rate that depends on your angle to the sun’s rays.

SeasonsThis angle effect is also responsible for the seasons.

3-Oct-10 Physics 1 (Garcia) SJSU

Greenhouse EffectGlass is transparent to sunlight (short-wavelength).

Glass is opaque to infrared radiation (long-wavelength) produced by objects inside greenhouse, trapping the heat.

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Earth’s Greenhouse Effect

Earth’s atmosphere acts as a greenhouse, trapping solar energy.

Most of the trapping is due to carbon dioxide and water vapor, which is why they’re called “greenhouse gasses.”

Key Points of Lecture 17Key Points of Lecture 17

Before Friday, read Hewitt Chap. 16.

Homework Assignment #12 is due before 11:00 PM on Friday, Oct. 8.

• Specific Heat Capacity• Thermal Expansion• Transfer of Heat by Conduction• Transfer of Heat by Convection• Transfer of Heat by Radiation