Temperature and Heat

Temperature.  This is another everyday quantity, like time, that we are constantly aware of.  Also like time in that we want control over it.  Hot, warm, cold, freezing: these are some words we use to describe our environment, or how we may feel at any particular time.  Our perception of temperature, however, is influenced by the rate of heat conduction between our skin and some object or substance we’re in contact with, not just the temperature of the object or substance.  So temperature as sensed by us is relative.

If heat is conducted rapidly by an object to our skin, the object feels hot.  If heat is conducted rapidly away from our skin, the object feels cold.  Bread in the oven:  the air in the oven, surface of bread, and metal rack are all at the same temp, but you feel different “temperatures” when you touch any one of these.  The metal oven rack will burn you immediately!  Heat conduction and heat capacity of the substances is what that’s all about.

TEMPERATURE

What is temperature, and how can it be measured accurately?   Temperature is a measure of the average kinetic energy of the molecules of a substance.   A single  molecule doesn’t have a temperature, but it does have a kinetic energy.  If you could measure the KE of each molecule in a cup of coffee, then add those KE’s up and divide by the number of molecules, you’d have the temp of the coffee.  In the oven example, the molecules of the air, the bread, and the metal rack all have the same average kinetic energy.  We need a device that can somehow measure average kinetic energy.  What is often used is thermal expansion.  Liquid-in-glass thermometer uses mercury, or alcohol colored with red dye (safer if broken).  (What do the digital thermometers use?)

How does a thermometer work?  Over time, kinetic energy of the substance is transferred to the thermometer.  May be slow or fast (depends on the “time constant” of the particular thermometer), but physical contact insures transfer will happen.  Three minutes for in-the-mouth thermometer?  In the case of the oven, metal transfers heat rapidly, bread less rapidly, and air even least rapidly, but thermometer will read the same in each case, given enough time.

Thermometers, like other measuring devices, need to have two reference points and a choice of unit.  In other words, thermometers need to have a scale that can be assigned numerical values.  Freezing point and boiling point of water at atmospheric pressure are often chosen as reference points for a thermometer scale.

Fahrenheit: Freezing point is assigned value of 32º and boiling point a value of 212º.  Where did that come from?  Supposedly to start with Fahrenheit assigned 100º to the human body by measuring his wife’s body temperature. Then he had to choose the increments of the scale. He came up with the idea of having 180 degrees between freezing and boiling.  Each 1º increment of Fahrenheit scale is thus 1/180 of the temp change between boiling and freezing.

(A professor from Russia who was teaching a thermodynamics class I was in at the University of Texas at Austin told the class about Fahrenheit measuring his wife’s body temperature and choosing that temperature, which he assumed to be the normal temperature of the human body, to be 100º on his scale.  Since 98.6º is the actual normal human body temp, the professor from Russian said of Fahrenheit’s wife: “I guess she had a fever.”  The question of where on or in his wife’s body Fahrenheit used his primitive thermometer wasn’t discussed in the class.)

Celsuis:  0º and 100º, freezing and boiling, so each increment on the scale is 1/100^th of the temp change between boiling and freezing.

Kelvin scale: units are same size as Celsius, but start at absolute zero.  Freezing point at atmospheric pressure of water is 0º C is 273.15 K.  The Kelvin unit doesn’t have a degrees symbol º  associated with it.

Given Celsius temp, how to find Fahrenheit?  T_f = 9/5 T_c + 32.  Subtract 32 from both sides, multiply both sides by 5, divide both sides by 9 and have T_c = 5/9(T_f –32). 

Human body:  98.6º F.  Find Celsius.  T_c = 5/9 (98.6 – 32) = 5/9 (66.6) = 37º C.

HEAT

Total energy or INTERNAL ENERGY in a substance is Ek + Ep.  Rotational and vibrational states of molecules have potential energy.  Does internal energy thus depend on the amount?  Yes.  Does temperature depend on amount of substance?  No.  Average means energy per molecule.

Heat is “net energy transferred from one object to another because of a temperature difference.”  When an object receives heat, it’s internal energy increases.   Some may go into increasing the temp and some may go into vibration or rotation of molecules.

(From fall 2009 class: A student named Savannah said:  “the heat due to friction doesn’t seem to come from a temperature difference.”  I hadn’t thought of that myself, or encountered it otherwise, before.)

Several different units are used for heat measurement.  Heat is a form of energy so the joule is one unit.  A more common one for measuring heat is the calorie.  1 cal = 4.186 joule.  1 cal is amount of heat necessary to raise the temp of one gram of pure water by one Celsius degree (at 1 atm of pressure).  Also, a food calorie, the unit you see most often, is equal to 1000 calories or 1 kcal  = 4186 J.

Food calorie, kcal:  the amount of energy released when a given amount of the particular food is completely burned.  Give me the numbers:   Gram of fat, gram of protein, gram of carbohydrate, gram of alcohol.  How many kcal in each?

(Chapt 5 says 100 Watts is average power output of human body.  How many kcal per minute is this?  How many kcal per day?  About 2,000 as most nutrition labels say.)

Also have the Btu, which is the amount of heat necessary to raise one pound of water one F degree at 1 atm.   Ratings of AC and heating units are Btu’s per hour, often abbreviated to just Btu.

Thermal expansion/contraction.   Freezing of water:  less dense at 0º C than at 4º C. 

Specific Heat and Latent heat.   As already mentioned, when energy is transferred as heat to an object, some of the energy goes into Ek, some into Ep.  Iron and aluminum are given as examples in the book—have to add more than twice as much heat to Al to get the same temp rise as in Fe.  Specific Heat --  “of a substance is the amount of heat necessary to raise the temperature of one kg of the substance by one Celsius degree.”  Since it’s 1º kcal for 1 kg of water. Specific heat of water is 1 kcal/kg Cº. 

Originally “specific heat capacity”.  If substance has high specific heat, can store more energy (heat) for a particular temp change.  Water has high heat cap/ specific heat.

Amt of heat to change the temp by a given amount = mass x specific heat x temp change.

H = mcΔT.   This is true as long as the object/substance is not undergoing a change of phase.

What is a change of phase?  Look at example of ice- water- steam.

Latent heat:  hidden heat, like hidden talent.  The heat released or absorbed when there is a phase change.

Heat needed to melt a substance = mass x latent heat of fusion.

Heat needed to boil a substance = mass x latent heat of vaporization.

Heat transfer.  Three ways heat can be transferred from one object to another:  Conduction, Convection, and radiation.

Conduction: the transfer of heat by molecular collisions.  Example:  when you touch something, heat is conducted to your skin.  In the case of the bread in the oven, air is a poor thermal conductor, bread is a better thermal conductor, but both are no comparison to metal—it is an excellent thermal conductor.  See table 5.3

Convection:  the transfer of heat by the movement of a substance or mass from one position to another.

Radiation: the process of transferring energy by means of electromagnetic waves.  EM waves travel through empty space (vacuum), but they carry energy.  As you can feel from the sun’s radiation (some of that is hot air around you)