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# Question - PowerPoint PPT Presentation

Question . An ice cube is removed from the freezer and put in a cup of hot chocolate. Which statement is most accurate? A) Cold flows from the ice cube into the hot chocolate. B) Heat flows from the hot chocolate into the ice cube.

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Question

An ice cube is removed from the freezer and put in a cup of hot chocolate. Which

statement is most accurate?

A) Cold flows from the ice cube into the hot chocolate.

B) Heat flows from the hot chocolate into the ice cube.

C) The cold from the ice cube mixes with the heat from the hot chocolate.

Question

If the kinetic energy of an average ideal gas molecule in a sample at 20ºC doubles, its final temperature must be _______.

A) 10ºC

B) 40ºC

C) 313ºC

D) none of the above

Heat and Heat Transfer
• Where would you rather go for break, Montreal or Southern France?
Heat Capacity

Why do you burn your

mouth (but not your

hand) when you eat hot

pie or pizza?

Why do we go to the beach to cool off?

All because water has a high heat capacity!

Which heats up more quickly?
• Put a pot of water on the stove ~ 15 minutes to boil
• Put same mass of iron ~ 2 minutes to reach 100o C
• Substances have different ability to absorb or lose heat.
Heat Capacity and Specific Heat

For many substances, under normal circumstances TQ. Example: heat pot of water

Or Q = CT where C is the heat capacity.

Takes more Q to boil 2 cups than 1 cup

The specific heat capacity, or just specific heat, of a substanceis the heat capacity per unit mass.

or

• Which has a higher specific heat water or sand? A) water B) sand

Example (text problem 14.12): If 125.6 kJ of heat are supplied to 5.00102 g of water at 22 C, what is the final temperature of the water?

Example (text problem 14.19): A 0.400 kg aluminum teakettle contains 2.00 kg of water at 15.0 C. How much heat is required to raise the temperature of the water (and kettle) to 100 C?

Example (text problem 14.19): A 0.400 kg aluminum teakettle contains 2.00 kg of water at 15.0 C. How much heat is required to raise the temperature of the water (and kettle) to 100 C?

The heat needed to raise the temperature of the water to Tf is

The heat needed to raise the temperature of the aluminum to Tf is

Then Qtotal = Qw + QAl = 732 kJ.

The average kinetic energy of a molecule in an ideal gas is

And the total kinetic energy of the gas is

Define the molar specific heat at constant volume;

this is the heat capacity per mole.

Heat is allowed to flow into a gas, but the gas is not allowed to expand. If the gas is ideal and monatomic, all the heat goesinto increasing the average kinetic energy of the particles.

The amount of added heat is

If the gas is diatomic:

Rotational motions of a 2-atom molecule:

Internal energy will be distributed equally among all possible degrees of freedom (equipartition of energy). Each degree of freedom contributes ½kT of energy per molecule and ½R to the molar specific heat at constant volume.

Example (text problem 14.26): A container of nitrogen gas (N2) at 23 C contains 425 L at a pressure of 3.5 atm. If 26.6 kJ of heat are added to the container, what will be the new temperature of the gas?

T1 = 23 V1 = 425 L P1 = 3.5 atm Q = 26.6 T2 = ?

Change to standard units Absolute T, V in m3 and

P in N/m2

T =296oK V = 425 x 10-3 m3 P = 3.5 x 1.01 x105 N/m2

Example (text problem 14.26): A container of nitrogen gas (N2) at 23 C contains 425 L at a pressure of 3.5 atm. If 26.6 kJ of heat are added to the container, what will be the new temperature of the gas?

For a diatomic gas,

The number of moles n is given by the ideal gas law

The change in temperature is

The final temperature of the gas is Tf = Ti + T = 317 K = 44 C.

Thermal Conduction

Through direct contact, heat can be conducted from regions of high temperature to regions of low temperature. Energy is transferred by collisions between neighboring atoms or molecules.

The rate of energy transfer by conduction is

where  is the thermal conductivity, A is the cross-sectional area, and T/d is the temperature gradient, the temperature change per unit distance.

 depends on the material. Some materials conduct heat better than others

Also

where R is the thermal resistance.

This is convenient when heat is conducted through multiple layers because

Example (text problem 14.51): For a temperature difference of 20 C, one slab of material conducts 10.0 W/m2; another of the same shape conducts 20.0 W/m2. What is the rate of heat flow per m2 of surface when the slabs are placed side by side with a total temperature difference of 20 C?

For each slab, calculate the thermal resistance per square meter

Example continued:

When the materials are placed in series,

When the materials are placed in series, the rate of heat flow is

Final

Exam IV just like all exams. Covers all material since Thanksgiving including material covered only in lecture.

Final-Separate exam. Comprehensive, all material until Thanksgiving.

• 8 MC + 3 problems. Only from text material
• Recommend studying: HW most important +….

Curve exams and many lab grades +

• Promod’s lab – (3-5%)
• I am in my office T&W 2-5
Question

You are making macaroni and cheese for dinner, again. Which is the best choice for stirring the noodles in the pot of boiling water?

A) a wooden spoon

B) a metal spoon

C) any kind of spoon

D) your finger, but really fast

Example (text problem 14.48): A metal rod with a diameter of 2.30 cm and a length of 1.10 m has one end immersed in ice at 0 C and the other end in boiling water at 100 C. If the ice melts at a rate of 1.32 grams every 175 s, what is the thermal conductivity of the metal? Assume no heat loss to the surrounding air.

We are given geometrical information, A and d

∆T

Rate of ice melting which is related to rate of

heat transfer

Find κ

Example (text problem 14.48): A metal rod with a diameter of 2.30 cm and a length of 1.10 m has one end immersed in ice at 0 C and the other end in boiling water at 100 C. If the ice melts at a rate of 1.32 grams every 175 s, what is the thermal conductivity of the metal? Assume no heat loss to the surrounding air.

Heat is conducted to the ice at a rate of

Qc is the heat necessary to melt the ice.

The heat conducted to the ice in a time period t is

The heat needed to melt a given mass of ice is

Lf = 333 x 103 J/kg

Example continued:

Since all the heat conducted by the rod is absorbed by the ice,

Question

You are trying to transfer heat from a hot reservoir to a cold reservoir. You have at your disposal an aluminum rod and a copper rod of the same size. Which should you choose to have the highest rate of energy transfer?

A) The copper rod alone

B) The aluminum rod only

C) The rods in parallel.

D) The rods in series.

Question

You are in the doctor's office and notice that the metal instrument tray feels much colder than the exam table you are sitting on. This is because

A) the tray actually is colder than the table.

B) the exam table has a cushion inside, which is a good insulator.

C) the metal conducts heat away from your hand more quickly than does the table.

Thermal Convection

Hot air rises. We can see the ripples in the air above a

hot road. The rising air transfers heat.

Convection is the movement of heat by fluid currents. Material is transported from one place to another.

Convection can set up convection cells. Hot fluids rise and cool fluids sink. Important for cooking, weather, Sun, Ocean currents etc

The most important source of heat on Earth is

the Sun.

How can the heat get here?

There is nothing (vacuum between us and Sun)

Not by conduction or convection.

Radiation is a an electromagnetic (EM) wave.

Light is one example of EM radiation

Even if I turn out the lights this room is full of EM radiation

All bodies emit electromagnetic (EM) radiation. The perfect absorber and emitter of EM radiation is called a blackbody. The amount and type of radiation emitted depends on the temperature of the object.

Question

A wood-burning fireplace has a chimney which allows the heated air to rise and escape the

house. How then does a fireplace then heat the room?

A) convection

B) conduction

D) all of the above

where A is the surface area of the emitting body,

T is its temperature, and

 = 5.670108 W/m2 K4 is the Stefan-Boltzmann constant.

where e is the emissivity; e = 0 for a perfect reflector of EM radiation and e = 1 for perfect blackbody.

A spectrum shows the amount of radiation emitted at a particular wavelength. For a blackbody, the peak of the spectrum is determined only by its temperature.

Wien’s law

The net energy gained or lost by a blackbody at a temperature T is

where Ts is the temperature of the surroundings.

Example (R&S 14): A sphere with a diameter of 80 cm is held at a temperature of 250 C and is radiating energy. If the intensity of the radiation detected at a distance of 2.0 m from the sphere’s center is 102 W/m2, what is the emissivity of the sphere?

The power emitted by a point source is

This is the total power passing through a sphere of radius d

The emissivity is

Notice absolute T

Thermos bottle and heat transfer

Vacuum

Silvered surface

Thermos and heat transfer
• No Heat transfer by conduction. (Vacuum doesn’t conduct). Small losses through stopper.
• No convection (Vacuum)
• No heat transfer by radiation

Silvered surface reflects