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)

Work and Energy lecture

Remember what this class is all about: the big three: Force, Energy, and Work.  The FEW.  When dealing with work and energy, don’t have to calculate acceleration directly, and don’t have to deal with vectors.  Work and energy are magnitudes only, are scalars. 

Work.  Simple definition for a constant force. The WORK done on an object is equal to the constant force, F, applied along displacement, d, parallel to the direction of the force. 

W = Fd      (This is really a “dot product” or scalar product of the two vectors F and d.)

Force has what units in mks? Newtons. Distance?  Meters. So, work is newtons times meters, abreviated Nm.  This combination of units is important enough to have a name of it’s own:  Joule.  James Prescott Joule.  His family owned a brewery, don’t know which one, but he worked in it, experimented in it.  Among his other accomplishments, he invented arc welding.

Examples: 

Work against gravity. Force involved is the weight of the book. Raising a book a certain height, h, requires an amount of work W= weight x height = mgh.  Raise this book one meter.  What work is that?  (mass of book?)

Work against friction.  Push a book or a box across a table a distance d.  Let the force of friction be “little f”.  Work done = force x distance = fd.  

Mechanical Energy is either Kinetic Energy or Potential E.  The concept of energy is a unifying concept, applicable in all areas of physics, and also in other areas of science.  But it’s strictly a physics concept.  Energy is the ability to do work.  Can compare to money:  Energy is the payment for doing work. 

Work is “the process by which energy is transferred from one object to another.”  Like money from one person or entity to another.  

KE = ½ mv².  It is the energy of motion.  It also gives another way of calculating work:  When an object changes its velocity, the work done is

W =½ mv² - ½ mv².

Example of work against friction: Stopping distance and school zone;  fd = final KE minus initial KE = 0 – ½ mv²  .  Negative work is done on car to slow it down.  Friction does negative work on objects.   Main concept here is stopping distance is proportional to the square of the velocity.  For 20 mph it’s about 26 feet; for 40 mph, is four times that, about 104 ft.  This is rounded up to 105 in book.  Try calculating it yourself.

Potential Energy.  The energy an object has because of its position or location.  Same example as before:  W = mgh = PE2 – PE1 = change in potential energy in the gravitational field = work done on object to raise it by height h in gravity of earth (near earth’s surface).  This is gravitational potential energy.  Water stored behind a dam is another example of gpe.

Other standard example in physics is the compressed spring.  It  has potential energy that can be converted to work.

Conservation of Energy:  Energy can be neither created nor destroyed.  In changing from one form to another, it is always conserved.  Total amount in an isolated system is constant.

Is the earth an isolated system?  Very much not.

Example of conservation used to calculate speed of object falling height, h.  Draw picture.

½ mv² = mgh

The m’s cancel, come up with same equation as in chapter 2, but this is much easier!

Mass is also a form of potential energy, after Albert Einiesteinie.

Power   is the time rate of doing work.     The greater the power of engine or whatever, the faster it can do work.  P = Work/time or joules/sec in mks, which is called a  Watt.  Named for steam engine fellow, James Watt. Where do you see this unit used?  Electrical appliances. 

It is also time rate of energy production or energy usage.   Other units of power are BTU per hour and horsepower. Watt rated steam engines in equivalent horse power.

Now we can find the engine horsepower required to make a car go from 0 to 60 in 6 seconds.

Gotta multiply horsepower by seconds to get energy expended…. Also note kWh, or kilowatt-hour, your electrical bill’s units, are units of energy, not power.

A good exercise in energy understanding is to read your electric and gas meters, and based on your last month's bill, try to set an energy budget--which you try to adhere to by checking your meter every few days. That is a way to gain some power (over your utility costs). 

Newton's laws of motion & gravity; linear and angular momentum

In homework use full sentences.

Chapt 1 was about scientific methodology, measurement, about units, significant digits, unit conversions.  Chapt 2 was about motion, speed, velocity and acceleration.  Real motions that we observe and experience everyday are some combinations of constant speed, constant velocity, and acceleration. Last thing was projectile motion. Preview of chapt. 4:  if something is accelerating it must have a NET force acting on it.

Topics in Chapter 4:  Force: Newton’s laws of motion and law of gravity.  Momentum:  (a) momentum. (b) angular momentum and torque.

This is your first example of LAWS.  Scientists look for LAW and ORDER in the universe.   Recall from first class what a law is: a concise statement, in words or in a mathematical formula, about a fundamental relationship of nature. 

Force and Net force.  

WHAT is a force?  Let’s not use the long sentence in the book.  This is what I was taught and I haven’t found any reason why it shouldn’t be the definition of force.  A FORCE IS A PUSH OR A PULL.  Very common definition, but applies even to atoms, electrons, nuclei.  Four types of force have been discovered, only four.  Physicists have nearly unified them into one, but are having trouble putting gravity into the same theoretical framework as the supposedly unified three quantum field theory forces (electromagnetism, weak nuclear, strong nuclear).

Recall from previous chapter, most things aren’t moving out there—not visibly, anyway.  There’s some swaying of the tree limbs in the breeze, but the trees stay put.  Buildings and streets and signs also.  The traffic signal hanging out over the street.  Not moving.  Are any forces acting on these things that are not moving?  A building for instance?  Yes, gravity is one.  Gravity is trying to collapse all buildings to the ground.  What else?  The air!  Air can produce very powerful forces.

Just because something isn’t moving doesn’t mean there aren’t any forces acting on it. 

We’ve studied two kinds of motion:  velocity and acceleration.

If something isn’t moving at all or is moving at a constant velocity then there is no NET force acting on it.

IF a NET force acts on a body, then the body accelerates.   Another name: Net force = an unbalanced force.

When you push or pull on something, does that something move?  Only if you use enough force.

When a push or pull occurs, it must be in some direction.  VECtor!  Force is a vector.

External vs. internal forces – later, discussing momentum.

NEWTON’s  LAWS OF MOTION, and of Gravitation.

Aristotle thought and taught that an object in motion had to have a force acting on it—an earthly object.  Their natural state, he said, was being at rest. Heavenly objects were different, and their natural state was being in perfectly divine eternal motion.  Heaven and Earth, quite different realms.  Until Copernicus, Kepler, Galileo, and, especially, Newton.  Newton discovered universal gravitation. Heaven not so divinely different from earth!  Uh-oh.

Newton’ 1^st Law:  Inertia.  An object remains at rest or in uniform motion unless a net force acts on it.

Mass is a measure of amount of inertia.

2^nd Law: Newton, building on Galileo’s ideas of inertia, mass, and acceleration, claimed that acceleration is proportional to something he (Newton) called force, and also that the acceleration produced by a constant force is inversely proportional to the mass being accelerated.  These two relations can be expressed as

F=ma,

Or in words,   Net force equals mass times acceleration.

“Net force” means the sum of the forces acting on the object.  That’s shown in the example.  Show it. Page 53.

If the net force is zero, the object remains at rest or moves with a constant velocity.  When you use Newton ‘s 2^nd law, you isolate on object and only talk about the forces on it, not the forces it exerts on other objects. Examples:

Sitting in your chair.  The force of gravity is pulling down on you, the chair is pushing up.  But see Newton’s third law, below, for explanation…

Driving at constant speed—are there forces acting horizontally on your car?  Air resistance and friction in moving parts;  and force of the tires pushing back on the roadway.  The net force is zero when these forces balance.  To unbalance the forces, push down on or let off of the accelerator.  Acceleration will occur!  (Yeh, you can call the slowing down deceleration.)

Weight :  If you jump off the table, you accelerate according to F=mg, where m is the mass of your body and g is the acceleration due to gravity,  I’ll come back to this after we do Newton’s 3^rd law---

Newton’s 3^rd Law:  Forces always come in action/reaction pairs.  The action force acts on one object and the reaction force acts on another object.

Example:  What are all the action/reaction pairs for a person sitting in a chair?  First, earth’s gravity acting on you; the reaction force is your body pulling back on the earth!  What about the upward force the chair exerts on you? You exert a downward reaction force on the chair.  Draw it.

Horse and cart:   What constitutes an action/reaction pair?  A pair of forces that act on a pair of objects, not on just one object.  This is why action/reaction forces are equal and opposite but don’t cancel.

Law of Gravity:  before Newton, gravity was just an English word having to do with heaviness or seriousness, the opposite of the word levity, meaning lightness or humor.  Since the time Newton discovered universal gravitation, gravity also means

F= G m₁m₂/r²

which says two objects having masses m₁ and m₂ separated by a distance r attract each other with this force.

How does this reduce to F= mg?   Show.  What is the radius of the earth?

Momentum: Linear and Angular.  Are important because of the conservation laws associated with them.

Linear:  p=mv.  Can calculate with this using the law of conservation of linear momentum:

If no external unbalanced forces act on it, the total linear momentum of an isolated system is constant.  Ice skaters example.

Examples homework  p_final = p_initial

Angular momentum:  First have to define torque:  torque = lever arm times force.  Lever arm is distance to the center of motion from where the force is acting.  Wrench, figure 3-20.  Angular momentum of an object is its mass times its velocity times the distance from it to the axis of rotation:  L = mvr    The “lever arm” distance is r.

Law of conservation of angular momentum:  If no external unbalanced torque acts on an object the angular momentum of the object remains constant.  L_final = L_initial  Example of ice skater bringing in arms and increasing angular speed.