Chapter 7: Heat
The unit for specific heat capacity is
(calories/gram oC)
Evaporation...
removes heat
Thermal Conductivity Problem: A thermostat in a house keeps the inside temperature of a room at 23o C. The temperature outside the house is 0o C. How much energy is lost (by conduction) through a glass window in 60 seconds if the glass window is 0.5 cm. thick, and measures 100 cm. high by 200 cm. wide?
ΔH = (k x ΔT x A x Δt) / d .Where ΔH= total heat loss by conduction through the given object k= thermal conductivity of the material ΔT= temperature difference between the hot and cold sides of the material A= area of the material through which heat conduction occurs Δt= time for which heat conduction is considered d= thickness of material through which heat conduction occurs. In this problem k= 0.0020 cal/sec cm oC ΔT= 23oC - 0o C = 23o C A= 100 cm x 200 cm = 20,000 cm2 Δt= 60 s d= 0.5 cm. Then ΔH= (k x ΔT x A x Δt ) / d ΔH= (0.0020 cal/s cm oC x 23o C x 20,000 cm2 x 60 s) / (0.5 cm) ΔH= 110,400 calories. By comparison, it takes about 18,217 calories to heat an 8 oz cup of water from room temperature to boiling. In other words, our example window is losing enough energy to heat approximately six 8 oz cups of water to the boiling point every minute.
Calculate the amount of heat loss for a copper wall. The temperature changes from 0 oC to 45 oC. A = 50 cm x 50 cm. Δt = 60 s d = 2.54 cm.
ΔH = (k x ΔT x A x Δt) / d .Where ΔH= total heat loss by conduction through the given object k= thermal conductivity of the material ΔT= temperature difference between the hot and cold sides of the material A= area of the material through which heat conduction occurs Δt= time for which heat conduction is considered d= thickness of material through which heat conduction occurs. YOU WOULD USE THERMAL CONDUCTIVITY FOR HEAT LOSS In this problem k= 0.9200 cal/sec cm oC ΔT= 0oC - 45o C = 45o C A= 50 cm x 50 cm = 2,500 cm2 Δt= 60 s d= 2.54 cm. ΔH=(0.9200*45*2,500*60)/2.54 cm ΔH=2,444,881.889
One food calorie is equal to
1 kilocalorie and is designated with a capital C.
For water, the heat required to change one gram of ice into water is
80 cal/g, and 540 cal/g additional heat is needed to change water into water vapor
Heat is taken in by what?
A: conduction B: convection C: radiation D: All of the above
What happens when you use a toaster?
A: you heat the bread B: you heat the air around the bread C: A and B
thermal expansion
An increase in the size of a substance when the temperature is increased All gases (and most liquids and solids), expand when heated. But they do not expand equally. If a gas, liquid, and solid receive enough heat to raise their temperatures the same amount, the gas will expand the most, the liquid much less, and the solid the least. Thermometers, thermostats, and many other devices work on this principle of expansion and contraction. Many thermometers contain a liquid (such as alcohol or mercury), which expands and contracts evenly as the temperature changes
A metal rod is in a fire. __________ is the transfer of heat from atom to atom between two parts of a stationary system, caused by a temperature difference between the parts.
Conduction
Calculate the specific heat capacity of an unknown substance, and identify that substance using the chart provided where: Mass = 100 g, Change in temperature = 60oC, Heat = 6000 calories.
H = heat energy, m = mass of the sample, ΔT = change in temperature of the specimen. In this problem H = 6000 cal m = 100 g ΔT = 60 C Then c = H / (m x ΔT) c = 6000 cal/ (100g x 60o C) c = 1.0 cal/g oC. This substance would be water
Heat Energy Problem: Let us determine the amount of heat energy transferred to or from a sample. Let us assume the mass (m), is 60 grams, the temperature of the sample changes from 20o C to 220o C, (that is: ΔT = 200o C), and the specific heat capacity is 1.00 cal/g oC. To determine the number of calories of heat energy: In this problem m = 60 g ΔT = 200o C c = 1.00 cal/g oC. Then ΔH = m x ΔT x c ΔH = 60g x 200 oC x 1.00 cal/g oC ΔH = 12,000 calories.
Heat Energy: H = m x ∆T x c Where ΔH = heat energy m = mass of the sample, ΔT = change in temperature of the specimen. c = the specific heat capacity of the material.
Determine the heat energy needed to raise 100 grams of lead from a temperature of 30oC to 100oC. Note: You may need to reference Table 1.
Heat Energy: H = m x ∆T x c Where ΔH = heat energy m = mass of the sample, ΔT = change in temperature of the specimen. c = the specific heat capacity of the material. Then ΔH = m x ΔT x c ΔH = 100g x 70 oC x 0.030 cal/g oC ΔH = 210 calories.
Determine the number of calories needed to raise 10 grams of water from a temperature of 10oC to boiling: Note: You may need to reference Table 1.
Heat Energy: H = m x ∆T x c Where ΔH = heat energy m = mass of the sample, ΔT = change in temperature of the specimen. c = the specific heat capacity of the material. Then ΔH = m x ΔT x c ΔH = 10g x 90 oC x 1.00 cal/g oC ΔH = 900 calories. H=1.00 m=10 ΔT =90 900 calories
Heat Measurement: Heat is different than temperature. Temperature measures the random motion of the molecules of the material being measured by the thermometer.
Heat describes the relationship among mass, temperature change, and the specific heat of the substance. Heat is measured in calories and is determined by multiplying the mass by the change in temperature by the specific heat of the material.
Characteristics of Heat Every body of matter, whether solid, liquid or gas, consists of atoms or molecules which are in constant motion. Their motion gives every object internal kinetic energy. The level of internal kinetic energy in an object depends on how rapidly its atoms or molecules move
Heat is a form of energy, which, when added to a body of matter, increases its internal kinetic energy content, and causes its temperature to rise. Temperature is an indication of an object's internal kinetic energy level
Thermal Conductivity:
Heat is transferred by three methods: (1) conduction, (2) convection, and (3) radiation.
Latent heat real term
Instead, the disorder of the atoms in the object increases, causing the material to change states. The heat needed to change a material from a solid to a liquid to a gas
At present, there are three commonly used scales available to measure temperature:
Kelvin (or absolute), Centigrade (or Celsius), and Fahrenheit. We will use the Celsius scale for our measurements of temperature.
Specific Heat Capacity Problem: *You will be asked to measure the specific heat capacity of several samples using the expression c = H / (m x ΔT), which can also be expressed as H = m x c x ΔT. This can also be interpreted as the heat (H), injected into an object of mass (m). Specific heat (c) can be determined by multiplying the mass (m), by the specific heat (c), and then by the change in temperature (ΔT), which resulted from putting that much heat (H) into the object.
Let us take one of the various samples and run a test: assume the mass, is 60 grams, and that by heating it in the oven with 120 calories of heat, the temperature of the sample changes from 20o C to 220o C, (that is: ΔT = = Tf - Ti = 200o C). To determine the specific heat capacity which is the amount of heat energy stored per gram for each 1oC change in the formula: c = H / (m x ΔT) Where H = heat energy, m = mass of the sample, ΔT = change in temperature of the specimen. In this problem H = 120 cal m = 60 g ΔT = 200o C Then c = H / (m x ΔT) c = 120 cal / (60g x 200o C) c = 0.01 cal/g oC.
As more heat is added to an object, the motion of its atoms becomes even more disorderly
The addition of heat to an object will always increase its internal kinetic energy.
Info regarding thermal expansion
The expansion and contraction of the materials in bridges, buildings, and other structures can cause serious problems unless builders allow for this. For example, the steel beams in a building will bend or break if they do not have enough room to expand. For this reason, structures have expansion joints. Expansion joints provide space for the expansion and contraction of building materials as the temperature changes, without damaging the structure itself. Engineers can determine how much the length of any material will be increased by a rise in temperature, if they know the coefficient of linear expansion of the material. The coefficient of linear expansion indicates how much longer each meter of a material will become if its temperature is increased by one degree.
A law that describes the relationship between heat gained and the heat lost in a thermal reaction:
The law of conservation of energy
Calculate the thermal expansion of aluminum. The temperature changes from 25 oC to 65 oC and L = 3000 m.
Thermal Expansion: ∆L = ∂ x L x ∆T Where: ΔL = change in length as a result of temperature change ∂ = coefficient of linear expansion of the given material L = length of the given material ΔT = temperature change of the given material in this problem. ∆L = 0.000026 x 3000m x 40c ∆L=3.12m BUT SHOULD BE CONVERTED TO CM SO, ∆L=312 cm
Specific Heat Capacity At home, a simple thermal analysis would consist of taking the sample, heating it by giving it so many calories of heat (which we will call H), and observing its change in temperature. This change we will call ΔT (remember Δ means change in), one way to determine how the various samples are thermally different is by obtaining the ratio of heat to temperature change, H/ΔT. This ratio will be different for the different samples, thus distinguishing the samples from one another.
This ratio does not take into account the mass of the sample (a real goof-up). To correct this, we simply divide the ratio H /ΔT by the mass, (m), or H/ (m x ΔT). Such a ratio is a measure of the specific thermal characteristics of a sample, and it is assigned the symbol (c), and given the name Specific Heat Capacity. c = ΔH / (m x ΔT)
The Law of Conservation of Energy: When two systems or objects of different temperatures come into contact, energy (in the form of heat) is transferred from the warmer system into the cooler one.
This transfer of heat raises the temperature of the cooler system, and lowers the temperature of the warmer system (provided that no changes of states of matter occur in either system). Eventually, the two systems reach a common, intermediate temperature, and the heat transfer stops. This transfer of heat from the warmer (warm front) to the cooler (cold front) can be related to the weather Warm and cold air masses are always trying to bring one another into equilibrium, and this struggle causes wind.
Latent Heat
When heat is continuously added to a solid, it grows hotter and hotter, and finally begins to melt. While it is melting, the material remains at the same temperature, and the absorbed heat goes into changing the state of the substance from a solid to a liquid After all of the solid has melted, the temperature of the resulting liquid then increases as more heat is supplied, until it begins to boil. Now the material again stays at a constant temperature until all of it has become a gas, after which the temperature of the gas rises. This is explained by realizing that under certain circumstances, the addition of heat causes no increase in temperature.
Calculate the specific heat capacity of a 625 gram unknown substance if it undergoes a 105oC change in temperature when 13,125 calories of energy are added. Identify that substance, using the chart provided:
Where H = heat energy, m = mass of the sample, ΔT = change in temperature of the specimen. In this problem H = 13,125 cal m = 625 g ΔT = 105 C Then c = H / (m x ΔT) c = 13125 cal/ (625g x 105o C) c = 0.2 cal/g oC. The substance is Sand
Insulation is
a way to control the movement of heat by keeping it in or out of a place. People commonly use three methods of insulation because heat can travel in the three different ways discussed. Certain materials, such as plastic and wood, make good insulators against the movement of heat by conduction. The movement of heat through the air by convection can be controlled by blocking the space between hot and cold areas. Surfaces that reflect infrared rays can insulate against heat traveling by radiation.
It is important to recognize that temperature and heat _______
are not the same thing.
Heat is the transfer of energy from one object to another
as a result of temperature differences
Water____________as heat enters it.
expands
When heat enters a copper water pipe, it
expands
The Unit of heat energy
the calorie
The standard unit for measuring heat transfer is
calorie
A thermometer under your tongue shows that you have a high fever. _______ (You are touching the thermometer.)
conduction
When heat moves through a material by passing the energy from atom to atom it is called?
conduction
You place a spoon into a cup of cocoa and it gets hot over time. _________(The spoon touches the cocoa.)
conduction
This is a material that transfers heat energy easily.
conductor
When warm water rises in a lake and cold water descends, what is happening?
convection
Heat radiating out of an object will always
decrease the internal kinetic energy of that object -The heat loss also usually lowers the temperature of the object.
Heat is the transfer of _____________ between substances of different temperatures.
energy
Cold air
falls
As heat raises the internal kinetic energy of an object
its atoms or molecules move faster
Warm air rises because it is
less dense
Heat is the random movement of what?
molecules Situations that produce heat involve motion either observable, such as activity-based (human or mechanical), or electrical.
On cloudless nights, heat escapes from our planet and goes into space.
radiation
Which of the following is responsible for bring heat to our planet?
radiation Sunlight is a form of radiation that is radiated through space to our planet without the aid of fluids or solids.
Brownies bake in a GLASS pan using these 2 methods.
radiation and conduction
Pressure is proportional to...
temperature
When something is heated, this changes.
temperature
Which of the following can be measured with a thermometer?
temperature
Temperature is simply an indication of
the level of internal kinetic energy found in objects
Conduction is
the movement of heat through a material. When heat travels by conduction, it moves through a material without carrying any of the material with it. For example, the end of a copper rod placed in a fire quickly becomes hot; the atoms in the hot end begin to vibrate faster, causing adjoining atoms to vibrate faster. In this way, the heat travels from atom to atom until it reaches the other end of the rod.
Convection is
the transfer of heat by the movement of the heated material. For example, when a hot stove heats the air around it by conduction, this heated air expands, and thus becomes lighter than the colder air surrounding it. The heated air rises, and cooler air replaces it. This movement of heated air away from a hot object, and the flow of cooler air toward that object, is called convection current.
Infrared radiation is
the transfer of heat energy through empty space. In any object, the moving atoms or molecules create waves of radiant energy. These waves are also called infrared rays. Hot objects give off more infrared rays than colder objects. When radiant energy strikes an object, it speeds up the atoms or molecules in that object. Most of the energy from the sun travels through space to the Earth by this means.
Heat always moves from __________ objects to ___________ objects.
warmer, cooler
Thermal Expansion Problem: Workers place steel railroad rails exactly end-to-end for a distance of 10 kilometers on a day when the temperature is 5o C. How much will the railroad track expand on a day when the temperature reaches 35o C? If you observed the rails you would note that the workers leave a small gap between the rails to allow for expansion or contraction of the steel due to temperature changes.
ΔL = ∂ x L x ΔT Where: ΔL = change in length as a result of temperature change ∂ = coefficient of linear expansion of the given material L = length of the given material ΔT = temperature change of the given material in this problem. In this problem ∂ = 0.000011 cm/cm oC L = 10 km x 1000 m/1 km x 100 cm/ 1 m = 1,000,000 cm ΔT = 35o C - 5o C = 30o C. Then ΔL = ∂ x L x ΔT ΔL = 0.000011 cm/cm(degree sign)C x 1,000,000 cm x 30(degree sign) C = 330 cm.
