# heat_energy by pengtt

VIEWS: 135 PAGES: 38

• pg 1
***Heat equivalent…
Heat and modern technology are
inseparable
One of the first to demonstrate that heat is a form
of energy was James Prescott Joule (1818-1889)
Thermal energy is a form of kinetic energy
The good, the bad, and the ugly units
of heat
The SI unit of temperature
is the Kelvin

Is there an upper limit?
Is there a lower limit?
The driver of a 20,000-kg truck applies the brakes on a 10°
downhill run in order to maintain speed. What is the temperature
increase of 100 kg of brake material after the truck moves for
200 m? Assume an average specific heat of 800 J/kg·C° for the
brake fluid.

Q  mgh  20,000  9.8  200  sin 10
T  Q /(mc)  85 C 
How many stairs would you (75 kg) have to
run to work off 500 Calories?

mgh  500,000  4.18
h  2844 m
# steps  h / 0.2  14,218
Suppose a 65-kg person spends 8 hrs sleeping, 1 hr at moderate
physical labor, 4 hrs in light activity, and 11 hrs working at a desk or
relaxing. Is this person likely to gain weight if he maintains a 3500-Cal
daily diet?

Metabolic rates of an average 65-kg human

activity             Kcal/h    watts

Sleeping             60        70

Sitting upright      100       115

Light activity       200       230
(eating, dressing,
household chores)
Moderate work        400       460
(tennis, walking)
Running (15          1000      1150
km/h)
Bicycling (race)     1100      1270

(8·70+1·460+4·230+11·115)·3600=11.5 MJ=2800 Cal
Consider the apparatus that Joule used in his experiments on
the mechanical equivalent of heat. Suppose the block has a
mass of 0.65 kg and that it falls through a distance of 0.55 m.
Find the expected rise in temperature of the water given that
6200 J are needed for every 1.0°C increase.

T  mgh / 6200  5.7 10 4 C 
The 1.23 kg head of a hammer has a speed of 8.2 m/s just
before it strikes a nail and is brought to rest. Estimate the
temperature rise of a 13 g iron nail generated by twenty such
hammer blows done in quick succession. Assume the nail
absorbs all the energy.
An iron meteorite melts when it enters the Earth's
atmosphere. If its initial temperature, outside of the
atmosphere, was -135°C, calculate the minimum velocity the
meteorite must have had before it entered Earth's
atmosphere.
Water going over a waterfall drops through a height of about 62 m.
Suppose that all the gravitational potential energy of the water goes
into raising its temperature. Find the increase in water temperature at
the bottom of the waterfall as compared with the top.
Red blood in the tropics

Robert Mayer (1814-1878)
Heat Capacity…
Specific Heat Capacities of Some Solids
and Liquids
Substance                     Specific Heat Capacity, c, J/(kg · C°)b

Solids
Aluminum                                       900
Copper                                         387
Glass (common)                                 840
Human body (37 °C, average)                    3500
Ice (-15 °C)                                   2000
Iron or steel                                  452
Silver                                         235
Liquids
Benzene                                        1740
Ethyl alcohol                                  2450
Glycerin                                       2410
Mercury                                        139
Water (15 °C)                                  4186
Of these three metals, aluminum needs the most heat per gram
per degree when warmed, and releases the most heat when
cooled.
The temperature change depends on the amount of heat, on the
amount of substance, and on the heat capacity. Which has the
greater heat capacity, water or copper?
How big is a Btu?

0.252 kcal = 1055 J
Bomb calorimeter
Bomb calorimetry lab
Measuring the caloric value of food
A certain calorimeter cup is made from 0.15 kg of aluminum and contains
0.20 kg of water. Initially, the water and the cup have a common
temperature of 18.0 °C. A 0.040-kg mass of unknown material is heated to a
temperature of 97.0 °C and then added to the water. The temperature of
the water, the cup, and the unknown material is 22.0 °C after thermal
equilibrium is reestablished. Ignoring the small amount of heat gained by
the thermometer, find the specific heat capacity of the unknown material.
A caring husband, upon finding his stove out of order, decides to
boil the water for his wife's coffee by shaking it in a thermos
flask. Suppose that he uses 430 cm3 of tap water at 15 °C, and that
the water falls 1/3rd of a meter with each shake, at a rate of 20
per minute. Neglecting any loss of thermal energy by the flask, will
his wife make to work on time?

Q =m·4190·(100-15) = 153·m kJ
W = 20·t·m·9.8·0.3 = 58.8·m·t
Q = W or t = 2602 min = 43 hr
In order to maintain constant weight, we must
consume about 2000 kilocalories of food energy per
day of inactivity. How long could you live off your
fat?

30  4100 / 2000  61.5 days

•1 pound of fat contains about 4100 kilocalories
•On the average, 15%/22% of an adult male’s/female’s weight is
in the form of body fat (assume about 30 lb)
•In two days of starvation and inactivity, one would be able to
lose about 1 lb of fat
Most of the energy that we get from food goes into generating
heat energy. How much will the temperature of a 75-kg man
increase if he eats a cup of yogurt containing 350 kcal and does
not release this energy to the environment?

T = Q/mc = 350 kcal/(75 kg·0.83 kcal/kg·C°) = 5.6 C°
Suppose Dee Zertz just finished indulging herself with 2
servings of cheese cake, worth about 500 Cal. If all
“nutrients” in the cheese cake were immediately
metabolized and no heat were lost to the environment,
by how much would Dee’s body temperature rise?
Assume Dee’s body contains 38 liters of water.

500,000 = 1000·38·∆T
∆T=13.2 °C
Suppose 225 g of coffee at 80.3 °C and 12.2 g of cream at 5 °C are mixed
in a ceramic cup, m=116 g and c=1.09 J/(g·C°), initially at room temperature
(24 ºC). What is the equilibrium temperature of the mixture? (Assume that
no heat is exchanged with the surroundings and that the specific heat of
coffee and cream are roughly equal to that of water.) Does it matter which
you pour in first?

225  4.18  (80.3  T )  12.2  4.18  (T  5)  116 1.09  (T  24)
T  70.5 C
Consider a classroom containing 200 students. Assume that the
metabolic rate of generating heat is 130 W for each student and
that the heat accumulates during a 50-minute lecture. In addition,
assume that the air has a molar specific heat of CV =(5/2)·R and
that the room (volume = 1200 m3, initial pressure = 1.01 × 105 Pa, and
initial temperature = 21 °C) is sealed shut. If all the heat generated
by the students were absorbed by the air, by how much would the
air temperature rise during a lecture?
In a half-hour, a 65-kg jogger can generate 8.0 × 105 J of heat.
This heat is removed from the jogger's body by a variety of means,
including the body's own temperature regulating mechanisms. If
the heat were not removed, how much would the body temperature
increase?
Cold water at a temperature of 15 °C enters a heater, and the
resulting hot water has a temperature of 61 °C. If a person uses
120 kg of hot water in taking a shower, determine the cost of
heating the water. Assume that the utility company charges \$0.10
per kilowatt · hour for electrical energy.

\$\$\$  6.4  0.10  64 c
A 0.5-kg block of metal with an initial temperature of 30 °C is dropped
into a container holding 1.12 kg of water at 20 °C. If the final
temperature of the block-water system is 20.4 °C, what is the specific
heat of the metal? (Assume no heat is exchanged with the container or
environment.)
End
Burning money

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