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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)

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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

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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

3H: Specific heat of water and steel

What is the difference between temperature and heat?
How does the specific heat differ between water and steel?

In everyday conversation we often use the words heat, thermal energy, and temperature interchangeably. In physics, however, they are different, but related, quantities. Temperature is the measure of the average kinetic energy per atom or molecule in a substance. Thermal energy is a measure of how much total energy a substance contains. Heat is the flow of that thermal energy from a hotter to a colder material. In this investigation you will see that water and steel contain very different amounts of thermal energy for the same mass—even though they are at the same temperature.

Part 1: Specific heat of steel

Equipment for investigation on specific heat

Equipment for investigation on specific heat

Materials: Two foam cups (8 oz or larger); water; hot water from tap; ice; mass scale; ten or more steel washers (m≥100 g); string; temperature probe with ErgoDAQ (or other thermometer).

Tie the steel washers together with the string.
Tare the scale with one of the empty foam cups. Measure the mass of the steel washers. Choose a number of steel washers that will have a total mass close to 100 g.
Cover the washers with ice and cold water. Allow to equilibrate close to the freezing point. Measure the temperature of the cold water.
Measure 100 g of hot water into the other foam cup. Measure the temperature of the water.
Move the steel washers quickly from the ice water into the hot water. Stir them around for a minute or two until the temperature equilibrates. Measure the final temperature of the water containing the steel.
Repeat the experiment, but this time add 100 g of ice water to the cup containing 100 g of hot water.

Which caused a larger change in the temperature of the hot water, the 100 g of 0°C steel or the equal mass of ice water?

Which material do you think has a higher specific heat, steel or water? Why?

Using your data, calculate the specific heat of steel given the specific heat of water c_water=4.18 J g⁻¹ °C⁻¹. Was your prediction correct?

In the investigation, approximately equal masses (100 g each) of hot water and steel were mixed, yet the final temperature is not halfway between the hot and cold temperatures of the two materials. Why not?

Deriving the specific heat of steel from the investigation

The amount of thermal energy in a material is defined by the specific heat equation:

E_{t h} = m c_{p} Δ T

where m is the mass of the material, c_p is the specific heat of the material, and ΔT is the difference in temperature between the material and a reference temperature. In this investigation, we will use the temperature of the ice water T₀, which should be close to 0°C, as the reference temperature. The steel washers gained thermal energy when they changed temperature from T₀ to T₁, while the hot water lost an equal amount of thermal energy when it changed temperature from T₂ to T₁. Change in thermal energy of steel:

\begin{array}{l} E_{s t e e l} = m_{s t e e l} c_{s t e e l} (T_{1} - T_{0}) \end{array}

Change in thermal energy of hot water:

\begin{array}{l} E_{w a t e r} = m_{w a t e r} c_{w a t e r} (T_{2} - T_{0}) \end{array}

To solve this problem, set the thermal energy gained by the steel washers equal to the thermal energy lost by the hot water:

m_{s t e e l} c_{s t e e l} (T_{1} - T_{0}) = m_{w a t e r} c_{w a t e r} (T_{2} - T_{1})

Use algebra (and show your work) to solve this equation for the unknown quantity c_steel (the specific heat of steel). Hide me!

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