heat capacity

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Heat Capacity

Heat capacity and calorimetry

Heat capacity and the law of conservation of energy

Resources

Heat capacity (often abbreviated Cp) is defined as the amount of heat required to raise the temperature of a given mass of a substance by one degree Celsius. Heat capacity may also be defined as the energy required to raise the temperature of one mole of a substance by one degree Celsius (the molar heat capacity) or to raise one gram of a substance by one degree Celsius (the specific heat capacity).

Heat capacity is related to a substances ability to retain heat and the rate at which it will heat up or cool down. For example, a substance with a low heat capacity, such as iron, will heat and cool quickly, while a substance with a high heat capacity, such as water, heats and cools slowly. This is why on a hot summer day the water in a lake stays cool even though the air above it (which has a low heat capacity) heats quickly, and why the water stays warm at night after the air has cooled.

Heat capacity and calorimetry

Calorimetry is the study of heat and heat energy. A calorie is a unit of heat energy in the British system of measurement. In the metric system, energy is measured in joules, and one calorie equals 4.184 joules. When any substance is heated, the amount of heat required to raise its temperature will depend on the mass of the object, the composition of the object, and the amount of temperature change desired. It is the temperature change, and not the individual starting and final temperatures, that matters when considering heat. The equation that relates these quantities is:

q = m Cp ΔT

where q is the quantity of heat (in joules), m is the mass of the object (usually in grams), Cp is the heat capacity (usually in joules/gram degree) and ΔT is the change in temperature (in degrees Celsius).

The amount of heat required depends on the mass to be heated (i.e., it takes more heat energy to warm a large amount of water than a small amount); the identity of the substance to be heated (water, for example, has a high heat capacity and heats up slowly, while metals have low heat capacities and heat up quickly); and the temperature change (it requires more energy to heat up an object by 60 degrees than by 20 degrees).

Heat capacity and the law of conservation of energy

Calculations using heat capacity can be used to determine the temperature change that will occur if two objects at different temperatures are placed in contact with each other. For example, if a 50 g piece of aluminum metal (Cp = 0.9 J/g C) at a temperature of 100°C is put in 50 g of water at 20°C, it is possible to calculate the final temperature of the aluminum and water. The aluminum will cool and the water will warm up until the two objects have reached the same temperature. The water will gain all of the heat lost by the aluminum as it cools. This is a result of law of conservation of energy, which states that energy can neither be created nor destroyed. The heat lost by the metal will be

qlost = (50 grams) x (0.9J/g°C) x (100-T)

and the heat gained by the water will be

qgained = (50 grams) x (4.184J/g°C) x (T-20)

These two equations are equivalent since heat lost equals heat gained; the final temperature of the mixture will be 27.8°C. This final temperature is much closer to the initial temperature of the water because water has a high heat capacity and aluminum a low one.

Significance of the high heat capacity of water

Water has one of the highest heat capacities of all substances. It takes a great deal of heat energy to change the temperature of water compared to metals. The large amount of water on the Earth means that extreme temperature changes are rare on the Earth compared to other planets. Were it not for the high heat capacity of water, human bodies (which also contain a large amount of water) would be subject to a great deal of temperature variation.

Resources

BOOKS

Goldick, Howard D. Mechanics, Heat, and the Human Body.Upper Saddle River, NJ: Prentice Hall, 2001.

Goldstein, Martin, and Inge Goldstein. The Refrigerator and the Universe: Understanding the Laws of Energy.Harvard University Press, 1993.

Maxwell, James Clerk. Theory of Heat. Mineola, NY: Dover Publications, 2001.

Young, Hugh D. Sears and Zemanskys University Physics.San Francisco, CA: Pearson Addison Wesley, 2004.

Louis Gotlib

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Heat capacity

Heat capacity (often abbreviated Cp) is defined as the amount of heat required to raise the temperature of a given mass of a substance by one degree Celsius. Heat capacity may also be defined as the energy required to raise the temperature of one mole of a substance by one degree Celsius (the molar heat capacity) or to raise one gram of a substance by one degree Celsius (the specific heat capacity). Heat capacity is related to a substance's ability to retain heat and the rate at which it will heat up or cool. For example, a substance with a low heat capacity, such as iron , will heat and cool quickly, while a substance with a high heat capacity, such as water , heats and cools slowly. This is why on a hot summer day the water in a lake stays cool even though the air above it (which has a low heat capacity) heats quickly, and why the water stays warm at night after the air has cooled.

Heat capacity and calorimetry

Calorimetry is the study of heat and heat energy. A calorie is a unit of heat energy in the British system of measurement. In the metric system , energy is measured in joules, and one calorie equals 4.184 joules. When any substance is heated, the amount of heat required to raise its temperature will depend on the mass of the object, the composition of the object, and the amount of temperature change desired. It is the temperature change and not the individual starting and final temperatures that matters. The equation that relates these quantities is

where q is the quantity of heat (in joules), m is the mass of the object (usually in grams), Cp is the heat capacity (usually in joules/gram degree,) and DELTAT is the change in temperature (in degrees Celsius). The amount of heat required depends on the mass to be heated (i.e., it takes more heat energy to warm a large amount of water than a small amount), the identity of the substance to be heated (water, for example, has a high heat capacity and heats up slowly, while metals have low heat capacities and heat up quickly), and the temperature change (it requires more energy to heat up an object by 60 degrees than by 20 degrees).

Heat capacity and the law of conservation of energy

Calculations using heat capacity can be used to determine the temperature change that will occur if two objects at different temperatures are placed in contact with each other. For example, if a 50 g piece of aluminum metal (Cp = 0.9 J/g C) at a temperature of 100°C is put in 50 g of water at 20°C, it is possible to calculate the final temperature of the aluminum and water. The aluminum will cool down and the water will warm up until the two objects have reached the same temperature. All of the heat lost by the aluminum as it cools will be gained by the water. This is a result of law of conservation of energy, which states that energy can neither be created or destroyed. The heat lost by the metal will be
and the heat gained by the water will be

These two equations are equivalent since heat lost equals heat gained; the final temperature of the mixture will be 27. 8°C. This final temperature is much closer to the initial temperature of the water because water has a high heat capacity and aluminum a low one.

Significance of the high heat capacity of water

Water has one of the highest heat capacities of all substances. It takes a great deal of heat energy to change the temperature of water compared to metals. The large amount of water on Earth means that extreme temperature changes are rare on Earth compared to other planets. Were it not for the high heat capacity of water, our bodies (which also contain a large amount of water) would be subject to a great deal of temperature variation.

Resources

books

Goldstein, Martin, and Inge Goldstein. The Refrigerator and the Universe: Understanding the Laws of Energy. Harvard University Press, 1993.

Pitts, Donald R., and Leighton E. Sissom. Schaum's Outline of Heat Transfer. 2nd ed. Whitby, Ontario: McGraw-Hill Trade, 1998.

periodicals

Hendricks, Melissa. "Plant Calorimeter May Pick Top Crops." Science News 134 (September 17, 1988): 182.

Louis Gotlib

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heat capacity or thermal capacity, ratio of the change in heat energy of a unit mass of a substance to the change in temperature of the substance; like its melting point or boiling point, the heat capacity is a characteristic of a substance. The measurement of heat and heat capacity is called calorimetry. In the metric system, heat capacity is often expressed in units of calories per gram per degree Celsius (cal/g-°C); in the English system, British thermal units per pound per degree Fahrenheit (Btu/lb-°F) are often used. Because of the definitions of the calorie and Btu, these two heat capacity units are equivalent; the heat capacity of pure water is 1 cal/g-°C and 1 Btu/lb-°F. Other units are used also; for example, the heat capacity of pure water is 4.184 joules/g-°C and 1.16x10-6 kilowatt-hours/g-°C. The heat capacity of a system such as a calorimeter refers to the ratio of the change in heat energy of the system as a whole to the change in its temperature and is expressed in such units as calories per degree Celsius. See also specific heat.

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heat capacity (thermal capacity) Ratio of the heat supplied to an object to the rise in its temperature. It is measured in joules/kelvin. See also specific heat capacity

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heat capacity The energy required to increase the temperature of a given mass of material by one degree Celsius.