Essential Physics

Section 1 review

In everyday life we might use the words temperature and heat interchangeably. In physics, however, they are different concepts. Temperature measures the average kinetic energy in random thermal motion per atom or molecule. Temperature is measured on the Celsius, Fahrenheit, and Kelvin scales. Both Celsius and Fahrenheit are based on the phase changes of water but the Kelvin scale is based on absolute zero. Matter takes different phases (solid, liquid, or gas) depending on its temperature. Heat, or thermal energy, is the total energy in random thermal motion for a whole collection of atoms or molecules. The strength of intermolecular bonds varies among materials. For this reason, equal amounts of different substances usually contain different amounts of heat even at the same temperature. The specific heat is the thermal energy (or heat) per unit mass for a substance, per degree Celsius. Read the text aloud

Read the text aloud

temperature, Brownian motion, thermometer, Celsius scale, Fahrenheit scale, absolute zero, Kelvin scale, Avogadro’s number, mole, kinetic theory, Boltzmann’s constant, phases of matter, gas, liquid, solid, heat, thermal energy, calorie, Calorie, specific heat

T_{C} = \frac{5}{9} (T_{F} - 32)

T_{F} = \frac{9}{5} T_{C} + 32

T_{K} = T_{C} + 273.15

N_{A} = 6.022 \times 10^{23}

E = \frac{3}{2} k_{B} T

\begin{matrix} Q = m c_{p} (T_{2} - T_{1}) \\ = m c_{p} Δ T \end{matrix}

Review problems and questions

An Italian exchange student living in the United States wants to set his apartment’s thermostat to 20°C. At what temperature in degrees Fahrenheit should he set the thermostat?

Answer: He should set his thermostat to 68°F.

Asked: convert temperature from Celsius to Fahrenheit
Given: T_C = 20°C
Relationships:

T_{F} = \frac{9}{5} T_{C} + 32

Solve:

T_{F} = \frac{9}{5} T_{C} + 32 = \frac{9}{5} (20 ° C) + 32 = 68 ° F

An American tourist in Paris, Goldie Locks, set her hotel room thermostat to 68°—not realizing that the thermostat works in degrees Celsius instead of degrees Fahrenheit.
1. In an hour or two, will her hotel room feel hot, cold, or just right?
2. At what temperature (in degrees Fahrenheit) did she set the thermostat?
3. Would you expect there to be some property of the thermostat that would prevent her from setting it at 68°? Explain.

Answer:

The room will feel hot.
She set the temperature to 154°F.
Yes; thermostats usually limit how high the temperature can be set. Typical limits are around 85°F or 29°C.

Solution:

The hotel room feels hot. This temperature of 68°C is about two-thirds of the way between freezing (32°F) and boiling (212°F), and so is much higher and hotter than 68°F.
Asked: the temperature (in degrees Fahrenheit) that she set the thermostat
Given: T_C = 68°C
Relationships: To solve the problem, you must convert the Celsius temperature she entered into the thermostat to Fahrenheit: $T_{F} = \frac{9}{5} T_{C} + 32$ Solve: $T_{F} = \frac{9}{5} T_{C} + 32 = \frac{9}{5} (68 ° C) + 32 = 154.4 ° F$ Answer: She set the thermostat to 154.4°F.
Yes; thermostats usually limit how high the temperature can be set. Typical limits are around 85°F or 29°C.

A racing cyclist burns 1,260 Calories in an hour, which go into powering his bicycle.
1. How many joules does he burn in an hour?
2. How many watts of power does he generate?
3. How many incandescent light bulbs rated at 100 W could he theoretically power with this energy?
4. How many fluorescent bulbs rated at 100 W could he power?

Answer:

The cyclist burns 5,266,800 J every hour.
The cyclist generates 1,463 W of power.
The cyclist could power 14 incandescent light bulbs.
The cyclist could power 63 fluorescent light bulbs.

Solution:

Asked: energy burned in one hour
Given: energy used = 1,260 Calories/hr
Relationships: 4,180 J = 1 Calorie
Solve: $(\frac{1, 260 Calories}{1 hr}) \times (\frac{4, 180 J}{1 Calorie}) = 5, 266, 800 J / hr$ Answer: The cyclist burns 5,266,800 J every hour.
Note: This problem uses Calories, not calories. (The Calorie is 1,000 times larger than the calorie.)
Asked: power generated in watts
Given: power generated = 5,266,800 J/hr
Relationships: unit conversions
Solve: $(\frac{5, 266, 800 J}{1 hr}) \times (\frac{1 hr}{60 min}) \times (\frac{1 min}{60 s}) = 1, 463 W$ Answer: The cyclist generates 1,463 W of power.
Asked: number of incandescent light bulbs powered
Given: power output = 1,463 W; power consumption of incandescent light bulb = 100 W
Solve: $(1, 463 W) \times (\frac{1 light bulb}{100 W}) = 14.63 light bulbs$ Answer: The cyclist could power 14 incandescent light bulbs
Asked: number of fluorescent light bulbs powered
Given: power output = 1,463 W; power consumption of fluorescent light bulb = 23 W
Solve $(1, 463 W) \times (\frac{1 light bulb}{23 W}) = 63.6 light bulbs$ Answer: The cyclist could power 63 fluorescent light bulbs.

Note: A bicyclist will usually only generate a few hundred watts of output power that actually go to moving the bicycle. The rest is lost to inefficiencies of the human body and the bicycle itself.

Three 30 g metal balls, one each of aluminum, copper, and lead, are placed into a large beaker of hot water for a few minutes. [The specific heats of aluminum, copper, and lead are 903, 385, and 130 J/(kg °C), respectively.]
1. Which, if any, of the balls will reach the highest temperature? Explain.
2. Which, if any, of the balls will have the most thermal energy? Explain.

What is the energy of a mole of carbon atoms at a room temperature of 20°C?

Answer:: 3.7 kJ
The temperature of the atoms is 20°C, which corresponds to 293 K. The energy of each carbon atom is

E = \frac{3}{2} k_{B} T = \frac{3}{2} (1.38 \times 10^{- 23} J/K)(293 K) = 6.07 \times 10^{- 21} J

A mole of carbon atoms contains N_A = 6.022×10²³ individual atoms, so their total energy is

E_{t o t a l} = (6.07 \times 10^{- 21} J/atom) (6.022 \times 10^{23} atoms) = 3, 650 J

Which of the following should you do if a mercury thermometer breaks in the classroom?
1. Tell your teacher about it at the end of the class period so that she can clean up the spill before the next class arrives.
2. Call 911 immediately.
3. Call the Environmental Protection Agency to have a hazmat crew sent to your school.
4. Tell your teacher immediately and help other students to exit the area until the spill is cleaned up.


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