Chapter 2: Energy, Temperature, and Heat - …

1 2-1 Chapter 2: Energy, Temperature, and heat Energy The fundamental concept that connects all of the apparently diverse areas of natural phenomena is the concept of energy. Energy can be subdivided into well-defined forms such as: (1) mechanical energy, (2) heat energy, (3) electrical energy, (4) chemical energy, (5) atomic energy, etc. In any process that occurs in nature, energy may be transformed from one form to another. In its simplest form, energy can be defined as the ability of a body or system of bodies to perform work. Work is done whenever a force acting on a body causes that body to be moved through some distance. The unit of work is defined to be a joule, and is abbreviated as J.

2 Since energy is the ability to do work, the units of work will also be the units of energy. Gravitational Potential Energy Gravitational Potential Energy is defined as the energy that a body possesses by virtue of its position above the surface of the earth. If the parcel of air shown in figure , were lifted to a height h above the ground, then that parcel Figure Gravitational potential energy. Figure Water at the top of the falls has potential energy. would have potential energy in that raised position. That is, in the raised position, the parcel of air has the ability to do work whenever it is allowed to fall.

3 The most obvious example of gravitational potential energy is a waterfall, figure Water at the top of the falls has potential energy. When the water falls to the bottom, it can be used to turn turbines and thus do work. A similar example is a pile driver. A pile driver is basically a large weight that is raised above a pile that is to be driven into Chapter 2: Energy, Temperature, and heat 2-2 the ground. In the raised position, the driver has potential energy. When the weight is released, it falls and hits the pile and does work by driving the pile into the ground. As in all the concepts studied in physics, we want to make this concept of potential energy quantitative. That is, how much potential energy does a body have in the raised position?

4 How should potential energy be measured? Because work must be done on a body to put the body into the position where it has potential energy, the work done is used as the measure of this potential energy. That is, the potential energy of a body is equal to the work done to put the body into the particular position. Thus, the potential energy (PE) is PE = Work done to put body into position ( ) As you recall from your College Physics course, the work W done in displacing the body is defined as the product of the force acting on the body, in the direction of the displacement, times the displacement of the body. Mathematically this is W = Fx ( ) The unit of work or energy is the joule which is equal to a newton meter.

5 We can now compute the potential energy of the parcel of air in figure The applied force F necessary to lift the parcel is equal to the weight w of the parcel of air, and w = mg. The displacement x of the parcel is just the height h. Therefore, the potential energy of the parcel of air becomes PE = Work done = W = Fh = wh = mgh ( ) Therefore, whenever an object in the gravitational field of the earth is placed at a height h above the surface of the earth, that object will have potential energy because it has the ability to do work. The potential energy of the air parcel in figure is derived in equation as PE = mgh ( ) where m is the mass of the air in kilograms, abbreviated as kg; g is the acceleration due to gravity, which is equal to m/s2; and h is the height in meters, abbreviated as m, above the surface of the earth.

6 Air aloft in the atmosphere has potential energy because of its height above the surface of the earth. In general, if a parcel of air rises in the atmosphere (h increases), its potential energy increases; if the parcel of air descends in the atmosphere (h decreases), its potential energy decreases. When air aloft in the atmosphere descends it gives up that energy. That gravitational energy is converted into heat energy. Thus air will warm as it descends in the atmosphere. Chapter 2: Energy, Temperature, and heat 2-3 Example A kg parcel of air is raised to a height of 200 m above the surface of the earth. What is its potential energy with respect to the surface?

7 Diagram for example Since the mass of the air is m = kg and the height of the air is h = 200 m, the potential energy is found from equation as PE = mgh PE = ( kg)( m/s2)(200 m) PE = 1960 J To go to this Interactive Example click on this sentence. Kinetic Energy Besides having energy by virtue of its position, a body can also possess energy by virtue of its motion. The kinetic energy of a body is the energy that a body possesses by virtue of its motion. Because work had to be done to place a body into motion, the kinetic energy of a moving body is equal to the amount of work that must be done to bring a body from rest into that state of motion. Kinetic energy (KE) = Work done to put body into motion ( ) Consider a parcel of air at rest on the surface of the earth as shown in figure A constant net force F is applied to the parcel to put it into motion.

8 When it is a distance x away, it is moving at a speed v. What is its kinetic energy at this point? The kinetic energy, found from equation , is KE = Work done = W = Fx ( ) Solution Chapter 2: Energy, Temperature, and heat 2-4 Figure The kinetic energy of a parcel of air. But by Newton s second law, the force F acting on the parcel gives the body an acceleration a. That is, F = ma, and substituting this into equation we have KE = Fx = max ( ) But for a body moving at constant acceleration, the kinematic equation for the velocity v as a function of the displacement x was given by v2 = v02 + 2ax Since the parcel started from rest, v0 = 0, giving us v2 = 2ax Solving for the term ax, ax = v2 2 ( ) Substituting equation back into equation , we have KE = m(ax)

9 = 2 mv2 or KE = 1 2 mv2 ( ) Equation gives us the kinetic energy of a parcel of air that is in motion, where m is the mass of the body in kilograms and v is the speed of the body in meters per second, abbreviated m/s. Example A parcel of air has a mass m = kg and is moving at a speed of v = m/s. What is its kinetic energy? Chapter 2: Energy, Temperature, and heat 2-5 Diagram for example Using equation for the kinetic energy we obtain KE = 1/2 mv2 KE = 1/2 ( kg)( m/s)2 KE = kg m2/s2 KE = J To go to this Interactive Example click on this sentence.

10 Example If the speed of a parcel of air doubles, what happens to its kinetic energy? Let us assume that the air parcel of mass m is originally moving at a speed vo. Its original kinetic energy is (KE)o = 1/2 mvo2 If the speed is doubled, then v = 2vo and its kinetic energy is then KE = 1/2 mv2 = 1/2 m(2vo)2 = 1/2 m4vo2 KE = 4(1/2 mvo2) = 4(KE)o That is, doubling the speed results in quadrupling the kinetic energy. Increasing the speed by a factor of 4 increases the kinetic energy by a factor of 16. To go to this Interactive Example click on this sentence. As a further example of the application of the concept of kinetic energy to meteorology, suppose the normal wind speed in your area on a nice pleasant sunny day is 10 mph.