8.2: Measuring Energy and Heat Capacity – Chemistry LibreTexts

Теперь введем два понятия, полезные для описания теплового потока и изменения температуры. Теплоемкость (C) of a body of matter is the quantity of heat (q) it absorbs or releases when it experiences a temperature change (ΔT) of 1 degree Celsius (or equivalently, 1 kelvin)

Heat capacity is determined by both the type and amount of substance that absorbs or releases heat. It is therefore an extensive property—its value is proportional to the amount of the substance.

For example, consider the heat capacities of two cast iron frying pans. The heat capacity of the large pan is five times greater than that of the small pan because, although both are made of the same material, the mass of the large pan is five times greater than the mass of the small pan. More mass means more atoms are present in the larger pan, so it takes more energy to make all of those atoms vibrate faster. The heat capacity of the small cast iron frying pan is found by observing that it takes 18,150 J of energy to raise the temperature of the pan by 50.0 °C

The larger cast iron frying pan, while made of the same substance, requires 90,700 J of energy to raise its temperature by 50.0 °C. The larger pan has a (proportionally) larger heat capacity because the larger amount of material requires a (proportionally) larger amount of energy to yield the same temperature change:

The specific heat capacity (c) of a substance, commonly called its “specific heat,” is the quantity of heat required to raise the temperature of 1 gram of a substance by 1 degree Celsius (or 1 kelvin):

Specific heat capacity depends only on the kind of substance absorbing or releasing heat. It is an intensive property—the type, but not the amount, of the substance is all that matters. For example, the small cast iron frying pan has a mass of 808 g. The specific heat of iron (the material used to make the pan) is therefore:

The large frying pan has a mass of 4040 g. Using the data for this pan, we can also calculate the specific heat of iron:

Although the large pan is more massive than the small pan, since both are made of the same material, they both yield the same value for specific heat (for the material of construction, iron). Note that specific heat is measured in units of energy per temperature per mass and is an intensive property, being derived from a ratio of two extensive properties (heat and mass). The molar heat capacity, also an intensive property, is the heat capacity per mole of a particular substance and has units of J/mol °C (Figure (PageIndex)).

Figure (PageIndex): Из-за большей массы большая сковорода имеет большую теплоемкость, чем маленькая сковорода. Поскольку они сделаны из одного и того же материала, обе сковороды имеют одинаковую удельную теплоемкость. (кредит: Марк Блазер).

Liquid water has a relatively high specific heat (about 4.2 J/g °C); most metals have much lower specific heats (usually less than 1 J/g °C). The specific heat of a substance varies somewhat with temperature. However, this variation is usually small enough that we will treat specific heat as constant over the range of temperatures that will be considered in this chapter. Specific heats of some common substances are listed in Table (PageIndex).

Table (PageIndex): Specific Heats of Common Substances at 25 °C and 1 bar

Если мы знаем массу вещества и его удельную теплоемкость, мы можем определить количество теплоты, q, entering or leaving the substance by measuring the temperature change before and after the heat is gained or lost:

In this equation, (c) is the specific heat of the substance, m is its mass, and ΔT (which is read “delta T”) is the temperature change, T_{окончательный} – T_{начальный}. Если вещество приобретает тепловую энергию, его температура увеличивается, его конечная температура выше его начальной температуры, T_{окончательный} – T_{начальный} имеет положительное значение, а значение q is positive. If a substance loses thermal energy, its temperature decreases, the final temperature is lower than the initial temperature, T_{окончательный} – T_{начальный} has a negative value, and the value of q отрицательно.

Example (PageIndex): Measuring Heat

A flask containing (mathrm) of water is heated, and the temperature of the water increases from 21 °C to 85 °C. How much heat did the water absorb?

Решения

To answer this question, consider these factors:

• the specific heat of the substance being heated (in this case, water)
• the amount of substance being heated (in this case, 800 g)
• the magnitude of the temperature change (in this case, from 21 °C to 85 °C).

The specific heat of water is 4.184 J/g °C, so to heat 1 g of water by 1 °C requires 4.184 J. We note that since 4.184 J is required to heat 1 g of water by 1 °C, we will need 800 times as much to heat 800 g of water by 1 °C. Finally, we observe that since 4.184 J are required to heat 1 g of water by 1 °C, we will need 64 times as much to heat it by 64 °C (that is, from 21 °C to 85 °C).

This can be summarized using the equation:

Because the temperature increased, the water absorbed heat and (q) is positive.

How much heat, in joules, must be added to a (mathrm) iron skillet to increase its temperature from 25 °C to 250 °C? The specific heat of iron is 0.451 J/g °C.

 Ответ

Обратите внимание, что взаимосвязь между теплотой, удельной теплоемкостью, массой и изменением температуры можно использовать для определения любой из этих величин (не только теплоты), если остальные три известны или могут быть выведены.

Example (PageIndex): Determining Other Quantities

A piece of unknown metal weighs 348 g. When the metal piece absorbs 6.64 kJ of heat, its temperature increases from 22.4 °C to 43.6 °C. Determine the specific heat of this metal (which might provide a clue to its identity).

Решения

Since mass, heat, and temperature change are known for this metal, we can determine its specific heat using the relationship:

[q=c times m times Delta T=c times m times (T_ce−T_ce)]

Substituting the known values:

Comparing this value with the values in Table (PageIndex), this value matches the specific heat of aluminum, which suggests that the unknown metal may be aluminum.

A piece of unknown metal weighs 217 g. When the metal piece absorbs 1.43 kJ of heat, its temperature increases from 24.5 °C to 39.1 °C. Determine the specific heat of this metal, and predict its identity.

 Ответ

(c = mathrm); the metal is likely to be iron from checking Table (PageIndex).

Solar Thermal Energy Power Plants

The sunlight that reaches the earth contains thousands of times more energy than we presently capture. Solar thermal systems provide one possible solution to the problem of converting energy from the sun into energy we can use. Large-scale solar thermal plants have different design specifics, but all concentrate sunlight to heat some substance; the heat “stored” in that substance is then converted into electricity.

The Solana Generating Station in Arizona’s Sonora Desert produces 280 megawatts of electrical power. It uses parabolic mirrors that focus sunlight on pipes filled with a heat transfer fluid (HTF) (Figure (PageIndex)). The HTF then does two things: It turns water into steam, which spins turbines, which in turn produces electricity, and it melts and heats a mixture of salts, which functions as a thermal energy storage system. After the sun goes down, the molten salt mixture can then release enough of its stored heat to produce steam to run the turbines for 6 hours. Molten salts are used because they possess a number of beneficial properties, including high heat capacities and thermal conductivities.

Figure (PageIndex): This solar thermal plant uses parabolic trough mirrors to concentrate sunlight. (credit a: modification of work by Bureau of Land Management)

The 377-megawatt Ivanpah Solar Generating System, located in the Mojave Desert in California, is the largest solar thermal power plant in the world (Figure (PageIndex)). Its 170,000 mirrors focus huge amounts of sunlight on three water-filled towers, producing steam at over 538 °C that drives electricity-producing turbines. It produces enough energy to power 140,000 homes. Water is used as the working fluid because of its large heat capacity and heat of vaporization.

Figure (PageIndex): (a) The Ivanpah solar thermal plant uses 170,000 mirrors to concentrate sunlight on water-filled towers. (b) It covers 4000 acres of public land near the Mojave Desert and the California-Nevada border. (credit a: modification of work by Craig Dietrich; credit b: modification of work by “USFWS Pacific Southwest Region”/Flickr)

Заключение

Video (PageIndex): A video summary of Energy and Chemistry.

Energy is the capacity to do work (applying a force to move matter). Kinetic energy (KE) is the energy of motion; potential energy is energy due to relative position, composition, or condition. When energy is converted from one form into another, energy is neither created nor destroyed (law of conservation of energy or first law of thermodynamics). Matter has thermal energy due to the KE of its molecules and temperature that corresponds to the average KE of its molecules. Heat is energy that is transferred between objects at different temperatures; it flows from a high to a low temperature. Chemical and physical processes can absorb heat (endothermic) or release heat (exothermic). The SI unit of energy, heat, and work is the joule (J). Specific heat and heat capacity are measures of the energy needed to change the temperature of a substance or object. The amount of heat absorbed or released by a substance depends directly on the type of substance, its mass, and the temperature change it undergoes.

Ключевые уравнения

• (q=c×m×ΔT=c×m×(T_ce−T_ce))

Словарь трейдера

calorie (cal) unit of heat or other energy; the amount of energy required to raise 1 gram of water by 1 degree Celsius; 1 cal is defined as 4.184 J endothermic process chemical reaction or physical change that absorbs heat energy capacity to supply heat or do work exothermic process chemical reaction or physical change that releases heat heat (q) transfer of thermal energy between two bodies heat capacity (C) экстенсивное свойство тела материи, представляющее собой количество теплоты, необходимое для повышения его температуры на 1 градус Цельсия (или 1 кельвин) джоуль (Дж) единица энергии в СИ; 1 джоуль – это кинетическая энергия тела массой 2 кг, движущегося со скоростью 1 метр в секунду, 1 Дж = 1 кг м 2 /с и 4.184 Дж = 1 кал кинетическая энергия движущегося тела, в джоулях , равно (где m = mass and v = velocity) potential energy energy of a particle or system of particles derived from relative position, composition, or condition specific heat capacity (c) intensive property of a substance that represents the quantity of heat required to raise the temperature of 1 gram of the substance by 1 degree Celsius (or 1 kelvin) temperature intensive property of matter that is a quantitative measure of “hotness” and “coldness” thermal energy kinetic energy associated with the random motion of atoms and molecules thermochemistry study of measuring the amount of heat absorbed or released during a chemical reaction or a physical change work (w) energy transfer due to changes in external, macroscopic variables such as pressure and volume; or causing matter to move against an opposing force

Авторы

Пол Флауэрс (Университет Северной Каролины – Пембрук), Клаус Теопольд (Университет Делавэра) и Ричард Лэнгли (Государственный университет Стивена Ф. Остина) с соавторами. Контент учебника, созданный OpenStax College, находится под лицензией Creative Commons Attribution License 4.0. Загрузите бесплатно по адресу http://cnx.org/contents/85abf193-2bd. a7ac8df6@9.110).

8.2: Измерение энергии и теплоемкости распространяется по незаявленной лицензии и был создан, изменен и/или курирован LibreTexts.

Heat Transfer? Can you Measure it? How is it Done?

To determine how one can measure the transfer of heat?

Вопросы исследования:

• In your experiment, why is it important to use foam cups? In your experiment, what are some possible sources of heat loss?
• How can they affect your results?

On the information level, this experiment serves to acquaint students with basic information on the process of heat transfer and the conditions under which the transfer will occur. It becomes evident that heat is energy that flows between two objects as a result of a difference in temperature. In brief, heat flows from a warmer body to a cooler body. Heat also moves as a result of direct contact as well as by processes such as convection and radiation. The student also learns about the specific heat of different materials. When heat flows into an object its thermal energy increases and so does its temperature. The amount of heat depends on the size of the object and the material of which it is made. The student is learning about the specific heat of the various materials used in this project recognizing that the specific heat of any substance is defined as the amount of energy that must be added to the material to raise the temperature of a unit mass by one temperature unit. In performing this experiment the concepts are being internalized. They are “seeing” the specific heat of different materials.

This science fair experiment also serves to acquaint students with the essential processes of sciencing such as the importance of the use of a control when required, of identifying dependent and independent variables, of selecting a large enough sample of subjects when applicable to the objective, of accurate and organized data collection, of pictorial and or graphic presentation of data and of being able to make better judgments as to the validity and reliability of their findings. They take on the role of scientists and in the process they learn to act as scientist.

Материалы по теме:

• 2 plastic foam cups
• ручка
• карандаш
• a thermometer(Celsius)
• щипцы
• a Bunsen burner or a large can of sterno
• большой горшок
• a bolt
• скрепка
• a clock with a second`s hand

These materials can readily be obtained from a local hardware store and from home.

Experimental Procedure:

1. Gather all of the materials that you need for your project.
2. Put on your safety glasses, apron and gloves.
3. Reproduce the chart provided on the next page so that you can readily record your observations.
4. Exercise care if you are using a Bunsen burner in lieu of a stove and have long hair tie it back!
5. Start with the cups and label them #1 and #2.
6. Using the graduated cylinder, Start by measuring 75 mol of tap water and and put it into the cup#1
7. With a sharp pencil make a small hole on the rim of cup#2.Place the thermometer carefully into the hole.
8. Now place cup # 2 upside down on top of cup#1 so that the rims meet and matctch. Make certain that the thermometer is in the water in cup #1.
9. Record the temperature of the water in your data chart.
10. Light the Bunsen burner or the large sterno can. Take the bolt, use tongs, and hold it in the flame for ten seconds.
11. Теперь осторожно снимите чашку № 2 и осторожно опустите горячий болт в воду в чашке № 1 и накройте чашкой № 2. Прочтите температуру воды.
12. Подождите 30 секунд, снова считайте температуру. Запишите температуру, которая была самой высокой, в диаграмму данных.
13. Замените воду в стакане № 1 водопроводной водой. Начните снова, повторите шаги с 8 по 12, используя гайку, а затем скрепку.
14. Use the formula heat = mass of the water X temperature change X specific heat. With the specific heat of water being 4186 J/kg times degrees C.
15. Review your data. Explain why the temperature of the water rose. What were your results with the nut and the paper clip? How do you explain these results?
16. Write up your report. Make certain that you include your research and your bibliography.

Chart for Data Collection

Terms/Concepts: Heat, thermal energy, specific heat, conduction, convection, radiation.

Ссылки:

Lafferty,Peter. Burning and Melting . New York: Gloucester Press, 1990 Heat.Mac, Dos. ESI.

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