3.4

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Videos: Conservation of energy Elastic potential energy Elastic potential energy in your bicep and tricep muscles Energy and work Gravitational potential energy Kinetic energy Physics of wind power Solar flare is a plasma in motion Steam rising out of cooling tower at a nuclear power plant

Investigations: 3A: Work and the force vs. distance graph (p. 113) 3B: Inclined plane and the conservation of energy (p. 118) 3C: Work and energy for launching a paper airplane (p. 122) 3D: Springs and the conservation of energy (p. 124) 3E: Conservation of momentum (p. 128) 3F: Collisions (p. 132) 3G: Shock absorbers and dampers (p. 139) 3H: Specific heat of water and steel (p. 144)

Science: Algebra derivation using the conservation of energy Brownian motion Choosing origin for potential energy reference frame Difference between heat and temperature Einstein's theory of relativity Elastic potential energy Elastic potential energy in your muscles Elastic potential energy in your muscles Energy and power for light bulb Energy and work Energy content of phases of matter Energy flow in open and closed systems Faster than light travel? Forms of energy Friction Galileo and the Leaning Tower of Pisa Gravitational potential energy Hooke's Law for springs Intensity of sunlight at Earth's surface Kelvin temperature scale and absolute zero Kinetic energy Law of conservation of energy Loose springs and stiff springs (BLM) Ordered and random kinetic energy Other conservation laws in physics Plasma in motion during a solar flare Plasma is a phase of matter Potential energy Power and radiant energy Power is the rate of doing work Radiant energy Relationship between momentum conservation and Newton's third law Symmetry in the physics of collisions Units of work and energy van der Waals forces

Technology: Batteries and electrical power Calories on food labels Conserving energy in everyday life Converting units and understanding energy content from food Efficiency in technology Energy content of everyday goods Energy flow in clothing manufacture Energy transformations in an internal combustion (piston) engine Energy transformations in technology usually produce heat Everyday objects that store energy Everyday technology in our age of energy Friction from brake pads in a car's wheel Hydroelectric dam Objects with elastic potential energy Power in everyday technology Power, wattage, and the light bulb Radiant power and the light bulb Technology and agriculture over the last century

Engineering: Calculating energy production for the Hoover Dam Design a wind turbine power plant Efficiency Electric current Electromagnetic spectrum Open and closed systems Siting constraint for power plants Specific heat Springs Volts, amps, and power

Mathematics: Algebra derivation using the conservation of energy Calculating energy production for the Hoover Dam Changes in a quantity represented by Greek symbol Δ Choosing origin for potential energy reference frame Converting units and understanding energy content from food Deducing a physical equation Different rates of change Hooke's Law for springs Non-linear relationships Proportional relationships Using algebra to derive temperature conversion formula Using algebra to solve for a variable

Interactive Simulations Interactive simulation of motion down an inclined plane Motion down an inclined plane Interactive simulation of an oscillating spring Spring-loaded carts simulation Elastic collisions between two balls Inelastic collisions between two balls Interactive simulation of an oscillating spring Interactive simulation of an oscillating spring Wind power design simulation Interactive Calculators Work equation calculator Kinetic energy equation Potential energy equation Elastic potential energy equation Efficiency equation Conservation of momentum in collisions equation Power equation calculator
Electric power equation Temperature conversion equation Specific heat equation

1 - Science of Physics
2 - Forces and Motion 3 - Energy Transformations Chapter 3 at a glance 3.1 - Energy 3.2 - Conservation of energy 3.3 - Flow of energy 3.4 - Temperature and the kinetic theory of matter 3.5 - Chapter review4 - Waves and Sound
5 - Electricity and Magnetism
6 - Light and Optics
7 - The Atom
8 - Linear Motion
9 - Vectors and Forces
10 - Forces
11 - Newton's Laws and Gravitation
12 - Circular Motion and Gravitation
13 - Torque and Static Equilibrium
14 - Momentum and Collisions
15 - Angular momentum
16 - Power and Machines
17 - Harmonic Motion
18 - Waves
19 - Sound
20 - Electricity
21 - Electric and Magnetic Fields
22 - Electromagnetism and Induction
23 - Light and Color
24 - Geometrical Optics
25 - Electromagnetic Radiation
26 - The Properties of Matter
27 - Thermodynamics and Heat Transfer
28 - The Atom
29 - The Quantum Theory
30 - TBD
31 - TBD
32 - TBD
33 - TBD
34 - TBD
35 - TBD
36 - TBD
37 - The atomic nucleus and radioactivity
38 - Nuclear reactions
39 - Relativity
40 - Particle physics and the standard model
41 - Electronics (semiconductors)
42 - Nuclear technology
43 - Lasers and photonics
44 - Metals, alloys and materials science
45 - Communications technology
46 - Buildings and structures
47 - Energy technology
48 - Biophysics
49 - Matter and Energy, Space and Time
50 - Energy Transformations
51 - Nanotechnology
52 - Website Videos
53 - ExtraStuff
55 - Modeling Motion, Friction, and Center of Mass
56 - Work and the Conservation of Energy

3.4 - Heat and thermal energy

Nearly every day we talk about hot and cold, heat and temperature. In physics, the concepts of hot and cold do not refer to heat per se, but instead describe the sensation of temperature. Hot is high temperature and cold is low temperature. Thermal energy is a form of energy that relates to temperature and is measured in joules, the same units as other forms of energy. Heat, on the other hand, represents the transfer of thermal energy from a hotter body to a colder one, such as from hot tap water to your hand. This section will discuss thermal energy, heat, temperature, the differences between them, and how we can understand each of them at the atomic or molecular level.

Different ways to measure temperature: digital mouth thermometer; infrared ear thermometer; alcohol thermometer; bi-metallic strip in an outdoor disk thermometer; and indoor thermostat.

You have probably measured temperature many times throughout your life. A thermometer inserted into your mouth measures your body temperature and can indicate if you are running a fever. A thermometer in a weather station indicates the outside air temperature. A thermostat in a house both measures the inside air temperature and sets the minimum temperature for the heater to turn on.

In those cases you used a relative scale, such as degrees Fahrenheit or Celsius, to measure the temperature. In a relative scale, two different physical conditions are used to set the scale. The Celsius scale defines zero degrees as the freezing point of water and 100 degrees as the boiling point of water. The Fahrenheit scale defines 32 degrees as the freezing point of water and 212 degrees as the boiling point of water. Show Absolute scale to measure temperature

Show Absolute scale to measure temperature

In scientific applications, a different kind of temperature scale is often used: the absolute Kelvin scale. In an absolute scale, zero is defined as the minimum possible temperature that matter can have. In the relative Celsius scale, it is possible to have temperatures below zero—such as the temperature outside when it is snowing—but it is impossible to have a temperature below absolute zero in the Kelvin scale. Absolute zero corresponds to −273.15°C (although it is often rounded off as −273°C) or −459.7°F:

T_{k e l v i n} = T_{c e l s i u s} + 273.15

T_kelvin	=	temperature in kelvins (K)
T_celsius	=	temperature in degrees Celsius (°C)

Kelvin
temperature
scale

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Two vertical thermometers for Celsius and Fahrenheit temperature scales

The Fahrenheit scale has

212 - 32 = 180

degrees between the boiling and freezing points of water. The Celsius scale, however, has 100 degrees between the same two points, so a change of 180°F is equivalent to a change of 100°C. If we want to convert from degrees Celsius to degrees Fahrenheit, then we will need to multiply by a factor of

180 / 100 = 9 / 5

; we also must add 32 degrees, because the Fahrenheit scale sets the freezing point of water 32 degrees higher than the Celsius scale does.

\begin{array}{l} T_{c e l s i u s} = \frac{5}{9} (T_{f a h r e n h e i t} - 32) \\ T_{f a h r e n h e i t} = \frac{9}{5} T_{c e l s i u s} + 32 \end{array}

T_celsius	=	temperature in degrees Celsius (°C)
T_fahrenheit	=	temperature in degrees Fahrenheit (°F)

Celsius and Fahrenheit temperature scales

Show Deriving one formula from the other

Let's say that you want to convert a temperature from degrees Celsius into degrees Fahrenheit, but that the only equation you remember—or the equation provided in a written exam—converts from degrees Fahrenheit into degrees Celsius. What do you do? Use algebra to derive the equation you need! Starting with the equation you are given:

T_{c e l s i u s} = \frac{5}{9} (T_{f a h r e n h e i t} - 32)

multiply both sides by

\frac{9}{5}

and then cancel out terms in the numerator and denominator:

\frac{9}{5} \times T_{c e l s i u s} = \frac{9}{5} \times \frac{5}{9} (T_{f a h r e n h e i t} - 32) = \frac{9}{5} \times \frac{5}{9} (T_{f a h r e n h e i t} - 32) = T_{f a h r e n h e i t} - 32

Now add 32 to both sides:

\frac{9}{5} T_{c e l s i u s} + 32 = T_{f a h r e n h e i t} - 32 + 32 = T_{f a h r e n h e i t}

and you have the equation you need:

T_{f a h r e n h e i t} = \frac{9}{5} T_{c e l s i u s} + 32

In a physics exam, you may sometimes be required to use algebra to manipulate a given equation into another one in order to calculate the answer. Hide me!

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Which temperature is hotter, 200°F or 95°C? Show

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