Heat and Heat Transfer

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

Water has a very high specific heat

Example : 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 : 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 : 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.

Heat of transformation Heat needed to change a substance from solid to liquid or liquid to gas. Depends on substance Q= ML M is mass of substance Lf or LvHeat of fusion f, heat of vaporization v Lf for water =3 x 105 J/kg Lv (water) = 20 x 105 J/kg Evaporation is similar to vaporization

Thermal expansion Most objects including liquids and solids expand when their Temperature increases

An object’s length after its temperature has changed is  is the coefficient of linear expansion. It is usually very small T = TT0 and L0 is the length of the object at a temperature T0. The fractional change in volume due to a temperature change is: For solids  = 3

Heat Transfer Conduction Convection (evaporation) Radiation

Conduction

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/L is the temperature gradient, the temperature change per unit distance.  depends on the material. Some materials conduct heat better than others

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.

Example : 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 L ∆T Rate of ice melting which is related to rate of heat transfer Find κ

Example : 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.

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

Thermal Radiation 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. Heat gets here by radiation

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

Examples of radiation All bodies emit electromagnetic (EM) radiation. 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 C) radiation D) all of the above

The rate of energy emission by a body is (Stefan’s Law) where A is the surface area of the emitting body, T is its temperature, and e is the emissivity; e ranges from 0 to 1 (perfect emitter).  = 5.670108 W/m2 K4 is the Stefan-Boltzmann constant.

The net energy gained or lost by a body at a temperature T is where Ts is the temperature of the surroundings.

Question • Which of the following do not emit radiant energy? • A) Sun • B) Earth • C) Cup of hot chocolate • D) Ice cube • E) all of the above emit radiation

Heat and Heat Transfer