• Questions at the end of standards-based textbook readings and/or activities cited in the right-hand column after each standard/benchmark can be considered as potential standards based assessment questions for quarter "mid-terms" or semester "end-of-term" finals.·
• YELLOW is used to draw attention to core instructional vocabulary.
• BLUE is used to draw attention to instructional "experiences" that students should have.
• GREEN is used to draw attention to expected student opportunities (some requiring the application student initiated metacognitive skills) based on state framework suggestions.
• RED is used to draw attention to issues that might affect the scope and sequence of how the standard based material is presented.
• PINK is used to draw attentions to items that can be used for "cross-curricular" integration of "Language Arts" standard-based items.
• GRAY is used to draw attentions to items that can be used for "cross-curricular" integration of "Mathematics" standard-based items.
• Notations like "Q 2" beside a standard or benchmark mean that the standard or benchmark in question will be covered during the 2nd Quarter. L means late in the quarter and E means early in the quarter.
• The "Content Standard Summary " and annotations after each standard and benchmark are from the California Science Framework (scroll through this document to the High School Physics Standards)
• A * benchmark means it is not considered an "Essential Standard" (Standards considered "essential" are those that are included in the state CST blueprint for a given subject area test).
• "(13% - 8 items) " means that 13% or 8 questions on the HS PHYSICS CSS CRT have been written using framework descriptions for this standard and its benchmarks (Physics CST Blueprint, 2002).
• NE - Considered a Non-Essential Standard (Standards considered "essential" are those that are included in the state CST blueprint for a given subject area test)
• Corelation between State Standards and the textbook currently in use ( Physics, 5th Edition 2003, Wilson & Buffa):
  • I- the page number were the standard is first introduced in the text.
  • P- the page number were the student has an opportunity to Practice their application of the standard.
  • TM -means the page number were the studen/teacher as an opprtunity to determine their level of Mastery of the standard.
• Resources used:

Course:Hybrid Physics AP/Regular Ed

Text: Physics, 5th Edition 2003, Wilson & Buffa

Criteria: California Science Content Standards for High School Physics

1^st Content Standard

Motion deals with the changes of an object’s position over time. Inherent in any useful study of motion is the concept of force, which represents the existence of physical interactions. Although Newton’s laws provide a good platform from which to analyze forces, those laws do not address the origin of forces. Fundamental forces in nature govern the physical behavior of the universe. One of these fundamental forces, gravity, influences objects with mass but acts at a distance, or without any direct contact between the objects. The electromagnetic force is also a fundamental force that operates across a distance. These standards on motion and forces provide the foundation for understanding some key similarities. And differences between these two forces. A working knowledge of basic algebra and geometry is an essential prerequisite for studying these concepts.

Motion deals with the changes of an object’s position over time. Inherent in any useful study of motion is the concept of force, which represents the existence of physical interactions. Although Newton’s laws provide a good platform from which to analyze forces, those laws do not address the origin of forces. Fundamental forces in nature govern the physical behavior of the universe. One of these fundamental forces, gravity, influences objects with mass but acts at a distance, or without any direct contact between the objects. The electromagnetic force is also a fundamental force that operates across a distance. These standards on motion and forces provide the foundation for understanding some key similarities. And differences. Between these two forces. A working knowledge of basic algebra and geometry is an essential prerequisite for studying these concepts.

Text Page Numbers

I- Introduced

P- Practiced

TM -Taught to Mastery

Physics Motion and Forces (20% of CST: 12 items) - Q 1 - 2

[12 items] 1. Newton's laws predict the motion of most objects. As a basis for understanding this concept:

- Q 1

a. Students know how to solve problems that involve constant speed and average speed.

• p. 32-38
• p. 37, 56-58
• p. 38,56, 58-63

The rate at which an object moves is called its speed. Speed is measured in distance per unit time (e.g., meters/second). Velocity v is a vector quantity and therefore has both a magnitude---the speed—and a direction. If an object travels at a constant speed, a simple linear relationship exists between the speed, or rate of motion r; distance traveled d; and time t, as shown in

d = rt. (eq. 1)

If speed does not remain constant but varies with time, average speed can be defined as the total distance traveled divided by the total time required for the trip.

- Q 1

b. Students know that when forces are balanced, no acceleration occurs; thus an object continues to move at a constant speed or stays at rest (Newton’s first law).

• p. 103-106
• p. 132-133
• p. 124-129, 137-138

If an object’s velocity v changes with time t, then the object is said to accelerate. For motion in one dimension, the definition of acceleration a is

a = Dv/Dt , (eq. 2)

where the Greek capital letter delta (D) stands for “a change of." Acceleration is defined as change in velocity per unit time. (Another way to state this definition is that acceleration is a change in distance per unit time per unit time, producing acceleration units of, for example, m/s² [meters per second squared or meters per second per second].) Acceleration is a vector quantity and therefore has both magnitude and direction. A push or a pull (force) needs to be applied to make an object accelerate. Force is another vector quantity.

A vector quantity, such as force, can be resolved into its x, y, and z components, Fx , Fy , and Fz . More than one force can be applied to an object simultaneously. If the forces point in the same direction, their magnitudes add; if the forces point in opposite directions, their magnitudes subtract. The net (overall) force can be calculated by adding forces along a line algebraically and keeping track of the direction and signs. If an object is subject to only one force, or to multiple forces whose vector sum is not zero, there must be a net force on the object. How- ever, if there is no net force on an object already in motion, that object continues to move at a constant velocity. An object at rest remains at rest if no net force is applied to it. This principle is Newton’s first law of motion.

- Q1

c. Students know how to apply the law F =ma to solve one-dimensional motion problems that involve constant forces (Newton’s second law).

• p. 106-109
• p. 109-111, 133-135
• p. 112, 115- 120, 135-137, 139-140

If a net force is applied to an object, the object will accelerate. The relationship between the net force F applied to an object, the object’s mass m, and the resulting acceleration a is given by Newton’s second law of motion

F = ma . (eq. 3)

If mass is in kilograms (kg) and acceleration is in meters per second squared (m/s²), then force is measured in Newtons, with 1 Newton = 1 kilogram-meter per second squared (1 kg-m/s²).

If the net force on an object is constant, then the object will undergo constant acceleration. When studying constant force, students should be able to make use of the following equations to describe the motion of an object in one dimension at any elapsed time t by calculating its velocity v and distance from the origin d:

v = v0 + at , (eq. 4)

d =d0 + v0t + 12 at 2 . (eq. 5)

In these equations m is the mass, v0 is the initial velocity, d0 is the initial position (distance from origin) of the object, and t is the time during which the force F is applied.

- Q1

d. Students know that when one object exerts a force on a second object, the second object always exerts a force of equal magnitude and in the opposite direction (Newton’s third law).

• p. 113-114
• p. 135
• p. 136

Newton’s third law of motion is more commonly stated as, “To every action there is always an equal and opposite reaction." The mutual reactions of two bodies are always equal and point in opposite directions. Mathematically stated, if object 1 pushes on object 2 with a force F₁₂ then object 2 pushes on object 1 with a force F₂₁ such that

F₂₁ = - F₁₂ . (eq. 6)

This universal law applies, for example, to every object on the surface of Earth. Trees, rocks, buildings, and cars, even the atmosphere, are all subject to the downward force of gravity. In all cases Earth exerts an equal and opposite upward push on the objects. Stars exist because of the balance between the inward force of gravity and the outward pressure of their hot interior.

- Q 1

e. Students know the relationship between the universal law of gravitation and the effect of gravity on an object at the surface of Earth.

• p. 236-237
• p. 237-238,257
• p. 237, 249-252, 258

Since the time of Galileo’s reputed experiment of dropping objects from the tower of Pisa, it has been understood that in the absence of air resistance, all objects near Earth’s surface, regardless of their mass or composition, accelerate downward toward Earth’s center at 9.8 m/s². Through Newton’s second law, this principle can be expressed as

F = w = mg (where g = 9.8m/s² is the acceleration due to gravity). (eq. 7)

The gravitational force pulling on an object is called the object’s weight w and is measured in Newtons.

- Q 1

f. Students know applying a force to an object perpendicular to the direction of its motion causes the object to change direction but not speed (e.g., Earth’s gravitational force causes a satellite in a circular orbit to change direction but not speed).

• p. 226-227
• p. 248, 254
• p. 243-249, 257-258

A force that acts on an object may act in any direction. The component of the force parallel to the direction of motion changes the speed of the object, and the components perpendicular to the motion change the direction in which the object travels.

- Q 1

g. Students know circular motion requires the application of a constant force directed toward the center of the circle.

• p. 226-227
• p. 227-233, 254-255
• p. 233-235, 219-226, 256-257

An object moving with constant speed in a circle is in uniform circular motion. The direction of motion continuously changes because of a force that always points inward toward the center of the circle. Such a centrally directed force is called a centripetal force. If the mass of the object is m, its speed is v, and the radius of the circle in which the object travels is r, then the magnitude of the force causing the circular

Fc = mv²/r . (eq. 8)

Examples of centripetal forces are the tension in a string attached to a ball that is swung in a circle, the pull of gravity on a satellite in orbit around Earth, the electrical forces that deflect electrons in a television tube, and the magnetic forces that turn a charged particle.

NE- Q 1

h.* Students know Newton’s laws are not exact but provide very good approximations unless an object is moving close to the speed of light or is small enough that quantum effects are important.

• p. 843
• p. 870
• p. 844-869, 870-874

Newton’s laws are not exact but are excellent approximations valid in domains involving low speeds and macroscopic objects. However, when the speed of an object approaches the speed of light (3 x 10⁸ m/s), Einstein’s theory of special relativity is required to describe the motion of the object accurately. Among the major differences between Einstein’s and Newton’s theories of mechanics are that (1) the maximum attainable speed of an object is the speed of light; (2) a moving clock runs more slowly than does a stationary one; (3) the length of an object depends on its velocity with respect to the observer; and (4) the apparent mass of an object increases as its speed increases.

The other domain in which Newtonian mechanics breaks down is that of very small objects, such as atoms or atomic nuclei. Here the wavelike nature of matter becomes important, and quantum mechanics better describes the submicroscopic world. Newtonian mechanics assumes that if the motion of a particle is measured with great accuracy and all the masses and forces that are involved are also known, it is always possible to predict with equally great accuracy the future state of motion of the particle. Quantum mechanics shows that such certainty is not always possible. Sometimes only the probability of an outcome can be predicted.

NE- Q 1

i.* Students know how to solve two-dimensional trajectory problems.

• p. 84-85
• p. 85-86, 99-100
• p. 86-94,100-102

Students can consider the problem of a ball of mass m thrown upward into the air at some angle. The motion of the ball will have horizontal and vertical components that are independent of one another. If air resistance is ignored, there will be no horizontal force acting against the ball to slow it down. While the ball is in flight then, only a single vertical force, gravity, is acting on the ball (e.g., F = w =mg downward). If students know the angle and the height from which the ball is thrown and the ball’s initial velocity, they will be able to predict the path of the ball and to calculate how high the ball will go, how far it will travel before it strikes the ground, and how long it will be in the air.

NE- Q 1

j.* Students know how to resolve two-dimensional vectors into their components and calculate the magnitude and direction of a vector from its components.

• p. 64-69, 70- 76
• p. 69, 76-78, 94-97
• p. 79-84, 97-99

In a two-dimensional system, two quantities are needed to describe a vector. A vector r can be completely specified by a magnitude r and an angle f or by its x and y components (i.e., rx and ry ). Simple trigonometry can be applied to resolve a vector into its components (e.g., rx = r cos f and ry = r sin f) and to calculate the magnitude and direction of a vector from its components (r 2 = rx 2 + ry 2 and tan f = ry /rx ).

NE- Q 2

k.* Students know how to solve two-dimensional problems involving balanced forces (statics).

• p. 120-121
• p. 121-124
• p. 135-136

A body at rest that is subject to no net force is in static equilibrium. Examples of static equilibrium are a book resting on the surface of a table and a ladder leaning at rest against a wall. Because the book and table remain at rest does not imply that no forces act on these objects but does imply that the vector sum of all these forces is zero. In particular, the components of the forces in any particular direction sum to zero. Thus for an object that remains at rest,

S Fy = 0, (eq. 9)

where the Greek capital letter sigma (S) means to “sum over or add" and Fy represents the components in any chosen direction y of the forces acting on the object. One sample problem appears in Figure 2, “Calculation of Force." Students are given the weight of a hanging object, the lengths of the ropes holding it in place, and the distance between the anchors. The students are asked to calculate the forces, called tension, along ropes of equal length. Students find this problem difficult because the vector force diagram they should use to solve the problem is often confused with the physical lengths of the ropes.

NE- Q 2

l.* Students know how to solve problems in circular motion by using the formula for centripetal acceleration in the following form:a = v² / r

• p. 226-227
• p. 228-230, 254-255
• p. 231, 256-257, 259

The speed of an object undergoing uniform circular motion does not vary, but the object’s direction does and hence the object’s velocity. Thus the object is constantly accelerating. The magnitude of this centripetal acceleration is

ac = Fc /m = v²/r , (eq. 10)

and the direction of the centripetal acceleration vector rotates so that it always points inward toward the center of the circle.

NE- Q 2

m.* Students know how to solve problems involving the forces between two electric charges at a distance (Coulomb’s law) or the forces between two masses at a distance (universal gravitation).

• p. 236-237
• p. 257
• p. 258

Standard Set 5 for physics, “Electric and Magnetic Phenomena," which appears later in this section, shows that the origin of the force between two masses and between two electric charges is entirely different. However, the forces involved, the gravitational and the electromagnetic forces, are both inverse square relationships. Coulomb’s law (in a vacuum) is written

Fq = kq1q²/r² , (eq. 11)

where k = 9x10⁹ Nm²/coul², q1 and q2 are charges (positive [+] or negative [-]), r is the distance separating the charges, and Fq is the force resulting from the two charges. The force is repulsive if the charges are the same sign and attractive if they are different.

Newton’s law of universal gravitation states that if two objects have masses m1 and m2, with centers of mass separated from each other by a distance r, then each object exerts an attractive force on the other; the magnitude of this force is

Fg = Gm1m2/r² , (eq. 12)

where G is the universal gravitational constant, equal to 6.67 x 10^-11 newton-m²/kg². For the case of a small object falling freely near the surface of Earth, students should understand that

g = Gme /re 2 = 9.8 m/s² , (eq. 13)

where me and re are the mass and radius of Earth. Students might be interested to know that Henry Cavendish’s measurement of G, completed around the year 1800, was the last piece of information needed to calculate the mass of Earth.

2^nd Content Standard

The concept of energy was introduced and discussed several times in the lower grades, from the physical sciences through the life sciences. In fact, every process involves some transfer of energy. In Standard Set 2 energy is classified as kinetic, meaning related to an object’s motion, or as potential, meaning related to an object’s stored energy. The energy of a closed system is conserved. Another useful conservation law, conservation of momentum, is introduced and is shown to be a direct consequence of Newton’s laws. The power and importance of these conservation laws are that they allow physicists to predict the motion of objects without having to know the details of the dynamics and interactions in a given system.

Through the standard sets introduced in the lower grade levels, students should have learned about forces and motion and the idea of energy. They should have been taught the role of energy in living organisms and the effects of energy on Earth’s weather. The standards presented earlier also call for student exposure to energy conservation, a concept that is essential to the topics contained in the high school physics standard sets 3, 4, and 5 and in several standard sets in chemistry and earth sciences.

Test Page Numbers

I- Introduced

P- Practiced

TM -Taught to Mastery

Conservation of Energy and Momentum (20% of CST: 12 items) - Q 1l - 2

[12 items] 2. The laws of conservation of energy and momentum provide a way to predict and describe the movement of objects. As a basis for understanding this concept:

- Q 1- 2

a. Students know how to calculate kinetic energy by using the formula E = (1/2)mv ² .

• p. 150
• p. 153, 173
• p. 154, 174, 177

Kinetic energy is energy of motion. The kinetic energy of an object equals the work that was needed to create the observed motion. This work can be related to the net force applied to the object along the line of the motion. The work done on an object by a force is equal to the component of the force along the direction of motion multiplied by the distance the object moved:

W = Fd . (eq. 14)

The work needed to accelerate an object of mass m from rest to a speed v is ½ mv ². This quantity is defined as the kinetic energy E. The units of energy are joules, in which 1 joule = 1 kilogram-meter squared per second squared (1 kg-m²/s²) = 1 newton-meter. Energy is a scalar quantity, meaning that energy has a magnitude but no direction.

- Q 2

b. Students know how to calculate changes in gravitational potential energy near Earth by using the formula (change in potential energy) = mgh (h is the change in the elevation).

• p. 154-155
• p. 156, 174
• p. 156-159,174

Students can combine equations (3) and (14) to find the work done in lifting an object of weight mg through a vertical distance h, as shown in

W = mgh . (eq. 15)

Work and energy have the same units. Therefore, one can define mgh as the change in gravitational potential energy associated with the change in elevation h of the mass m.

- Q 1- 2

c. Students know how to solve problems involving conservation of energy in simple systems, such as falling objects.

• p. 159-160
• p. 161, 174-175
• p. 162-163,176-177

Equations (4) and (5) can be used to show that if the object dealt with in Standard 2.b is released from rest and allowed to fall freely, it will strike the ground with a speed v = (square root of ) 2gh , (eq. 16) and its kinetic energy at the instant of impact will be

E = 1/2 mv2 = 1/2 m(2 gh) = mgh . (eq. 17)

The total energy T of the object is then defined as the sum of kinetic plus potential energy

T = E + PE . (eq. 18)

This sum is conserved in a closed system for such forces as gravity and electromagnetic interactions and those produced by ideal springs. Thus,

DE + DPE = 0 . (eq. 19)

Therefore, the change in kinetic energy equals the negative of the change in potential energy. This principle is a consequence of the law of the conservation of energy. Energy can be converted from one form to another, but in a closed system the total energy remains the same.

- Q 2

d. Students know how to calculate momentum as the product mv.

• p, 179-180
• p. 181, 210-211
• p. 182, 211

The momentum p of an object is defined as the product of its mass m and its velocity v. Momentum is thus a vector quantity, having both a magnitude and a direction. The units of momentum are kg-m/s. The magnitude of the momentum is mv, the product of the object’s mass and its speed.

- Q 2

e. Students know momentum is a separately conserved quantity different from energy.

• p. 187-189
• p. 190, 213
• p. 191-193, 213-214

If no net force is acting on an object or on a system of objects, the momentum remains constant. That is, neither its magnitude nor its direction changes with time. Conservation of momentum is another fundamental law of physics.

- Q 2

f. Students know an unbalanced force on an object produces a change in its momentum.

• p. 185
• p. 186-187, 212
• p. 212-213

As discussed in the section for Standard 1.c, if the net force on an object is not zero, then its velocity and hence its momentum will change. Motion resulting from a constant force F acting on an object for a time Dt causes a change in momentum of FDt. This change in momentum is called an impulse. (Note that the units of impulse are the same as those of momentum [i.e., Newton-second = kg-m/s].) Depending on the direction of the force, the impulse can increase, decrease, or change the direction of the momentum of an object.

- Q 2

g. Students know how to solve problems involving elastic and inelastic collisions in one dimension by using the principles of conservation of momentum and energy.

• p. 193-195,197-199
• p. 196, 199, 214
• p. 200-202, 215-216

Momentum is always conserved in collisions. Collisions that also conserve kinetic energy are called elastic collisions; that is, the kinetic energy before and after the collision is the same. Billiard balls colliding on smooth pool tables and gliders colliding on frictionless air tracks are approximate examples. Collisions in which kinetic energy is not conserved are called inelastic collisions. An example is a golf ball colliding with a ball of putty and the two balls sticking together. Some of the kinetic energy in inelastic collisions is transformed into other types of energy, such as thermal or potential energy. In all cases the total energy of the system is conserved.

NE- Q 2

h.* Students know how to solve problems involving conservation of energy in simple systems with various sources of potential energy, such as capacitors and springs.

• p. 163, 559
• p. 169, 174, 561
• p. 175-176, 562, 574-575

An ideal spring is an example of a conservative system. The force required either to stretch or to compress a spring by a displacement x from its equilibrium (unstretched) length is

F = kx , (eq. 20)

here k is the spring constant that measures a spring’s stiffness. A graph of the magnitude of this force as a function of the compression shows that the force varies linearly from zero to kx as the spring is compressed. The area under this graph is the work done in compressing the spring and is equal to

½ (base)(height) = 1/2 kx ². (eq. 21)

This is also the potential energy stored in the spring.

A capacitor stores charge. The charge Q that is stored depends on the voltage V according to

Q = CV, (eq. 22)

where the constant C is called the capacitance. (Notice that this equation and the equation for a spring [eq. 20] have the same form.) The energy stored in a capacitor is given by the equation

E = 1/2 CV ², (eq. 23)

which also has the same form as the equation that gives the energy stored by a spring.

3^rd Content Standard

The concept of heat (thermal energy) is related to all scientific disciplines. Energy transfer, molecular motion, temperature, pressure, and thermal conductivity are integral parts of physics, chemistry, biology, and earth science. Thermodynamics deals with exchanges of energy between systems.

If students in high school have not yet covered the chemistry standards, the related topics from those standards should be introduced. (See the following standards for chemistry 4.a through 4.h, “Gases and Their Properties," and 7.a through 7.d, “Chemical Thermodynamics." Specific chemistry topics that are useful or necessary for promoting a more complete understanding of Standard Set 3 are specifically mentioned, when relevant, under the sections with detailed descriptions.

At the atomic and molecular levels, all matter is continuously in motion. For example, individual molecules of nitrogen, oxygen, and other gases which makes up the air inside a balloon move at varying speeds in random directions, vibrating and rotating. The collisions of these molecules with the inner surface of the balloon create the pressure that supports the balloon against atmospheric pressure.

Considerable confusion exists in scientific literature about the definitions of the terms heat and thermal energy. Some texts define heat strictly as “transfer of energy." These science content standards use the term heat interchangeably with thermal energy. However, it is less confusing to reserve the term heat for thermodynamic situations in which energy is transferred either because of differences in temperature or through work done by or on a system. In this sense both heat and work have meaning only as they describe energy exchanges into and out of the system, adding or subtracting from a system’s store of internal energy.

Students, just like scientists of the eighteenth century, might easily fall prey to the misconception that heat is a substance. Students should be cautioned that heat is energy, not a material substance, and that heat flow refers not to material flow but to the transfer of energy from one place to another. Confusion is most apt to arise when dealing with heat transfer by convection; that is, when heat is transferred through actual motion of hot and cold material along a thermal gradient. Heating a material such as air causes it to expand and leads to differences in density that drive the movement of heated material.

Students also often confuse temperature and heat. From a molecular viewpoint, temperature is a measure of the average translational kinetic energy of a molecule, as shown in equation (27). (See also Chemistry Standard Set 7.) Studies of the temperature of materials as they pass through phase transitions may also help students understand the differences and relationships between heat and temperature. A way to avoid confusion is to reserve the use of the word heat for situations in which heat transfer is involved, as described in the next section.

Text Page Numbers

I- Introduced

P- Practiced

TM -Taught to Mastery

Heat and Thermodynamics (15% of CST: 9 items) - Q 2l - 3

[9 items] 3. Energy cannot be created or destroyed, although in many processes energy is transferred to the environment as heat. As a basis for understanding this concept:

- Q 2l - 3

a. Students know heat flow and work are two forms of energy transfer between systems

• p. 404-408
• p. 408-410, 436
• p. 410-417, 437

Heat transfer is energy flow from one system to another because of differences in temperature or because of mechanical work. The energy that flows into a pot of cold water put on a hot stove is an example of heat transfer. This energy increases the kinetic energy of the random motion of the molecules of water and therefore the temperature of the water rises. When the water reaches 100 ^oC, a new phenomenon, a phase transition, occurs: the water vaporizes, or boils. Although energy continues to flow into the water, the kinetic energy of the water molecules does not increase; therefore the temperature of the water remains constant. As the water changes from a liquid to a gas, the energy goes instead into breaking the bonds that hold one molecule of liquid water to another. The energy required (per unit mass or mole of liquid) to change a particular liquid at its boiling temperature into a gas is called the liquid’s latent heat of vaporization.

Mechanical work can change temperature too (e.g., when the forces of friction heat objects or when a gas is compressed and so warms). Conversely, changes in temperature can do mechanical work (e.g., warming a container of gas that is sealed by a piston will cause the gas to expand and the piston to move). Heat is energy that moves between a system and its environment because of a temperature difference between them. Every system has its internal energy, that is, the energy required to assemble the system; and this energy is independent of any particular path or means by which the system is assembled. The transfer of internal energy from one system to another, because of a temperature difference, is known as heat flow. There are three basic kinds of heat flow: conduction, convection, and radiation. Students should have first learned about these processes in the sixth grade.

As heat is transferred to a system (object), the temperature of the system (object) may increase. Substances vary in the amount of heat necessary to raise their temperatures by a given amount. More mass in the system clearly requires more heat for a given temperature change. An expression that illustrates the relationship between the amount of heat transferred and the corresponding temperature change is shown in equation (24). The change in temperature DT is proportional to the amount of heat added. This relationship is specified by

Q = mCDT , (eq. 24)

where Q is the internal energy added by heat transfer to the system from the surroundings, DT is the difference in temperature between the final and initial states of the system, m is the system’s mass, and C is the specific heat of the substance (joules/gram-^oC or calories/gram-^oC). Specific heat is a characteristic property of a material. The unit of specific heat is energy divided by mass and temperature change (e.g., calories/gram-degree).

Water, which serves as a standard against which all other materials may be compared, has a specific heat of one calorie/gram-degree. In other words, one calorie of heat is required to raise one gram of water one degree Celsius. When a gram of water cools one degree, one calorie is liberated. This value is large compared with those of other substances. Therefore, it takes much more heat to warm water than it does to raise the temperature of the same amount of most other substances. This fact has important implications for weather and climate and is one reason the weather is “tempered" in coastal areas (e.g., summers are cooler and winters are warmer than they are in inland areas at a similar latitude).

Equation (24) makes the distinction between heat and temperature quite clear. It specifies that heat can flow in or out of a system because of temperature difference alone. There are, however, other situations in which the addition or removal of heat is not accompanied by changes in temperature. These situations occur when a substance undergoes a change of phase, or state, such as when water evaporates or freezes. During phase changes, the absorption or release of heat takes place while the system remains at a constant temperature. For example, when ice melts in a glass of water that is sufficiently well mixed, the temperature of the water remains at the freezing point of water. Additional heating of the water raises its temperature only after the ice has melted.

- Q 2l - 3

b. Students know that the work done by a heat engine that is working in a cycle is the difference between the heat flow into the engine at high temperature and the heat flow out at a lower temperature (first law of thermodynamics) and that this is an example of the law of conservation of energy.

• p. 424
• p. 426, 436-437
• p. 427-429, 439-440

The total energy of an isolated system is the sum of the kinetic, potential, and thermal energies. A system is isolated when the boundary between the system and the surroundings is clearly defined. Total energy is conserved in all classical processes. Thus, the law of conservation of energy can be restated as the first law of thermodynamics; that is, for a closed system the change in the internal energy DU is given by the expression

DU = Q - W , (eq. 25)

where Q is the internal energy added by heat transfer to the system from the surroundings and W is the work done by the system. The quantities DU, Q, and W in equation (25) can be negative or positive, depending on whether energy is converted from mechanical form into heat, as when work is done on the system, or on whether heat is transformed into mechanical energy, as when the system is doing work. By convention, Q is positive for heat added to the system and negative for heat transferred to the surroundings, and W is positive for work done by the system and negative for work done on the system. As a practical matter, energy that cannot be obtained as work is considered a loss to the system. Thus, the first law of thermodynamics indicates how much energy is available to do work.

A heat engine is a device for getting useful mechanical work from thermal energy. While part of the input heat energy QH , sometimes known as heat of combustion, is converted into useful work W, the remaining heat is lost to the environment as exhaust heat Q L. That is, the work done by a heat engine is the difference between thermal energy flowing in at higher temperature and heat flowing out at lower temperature, as shown in the following equation:

W =QH - Q L . (eq. 26)