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#### Specific Heats of MetalsIntroduction: Different substances require different quantities of heat to produce a given temperature change

###### Physics

Specific Heats of MetalsIntroduction: Different substances require different quantities of heat to produce a given temperature change. For example, about three and one-half times as much heat is needed to raise the temperature of 1 kg of iron through a given temperature interval ΔT as is needed to raise the temperature of 1 kg of lead by the same amount. This material behavior is characterized quantitatively by specific heat, which is the amount of heat necessary to raise the temperature of a unit mass of a substance by one unit temperature interval, e.g., 1 gram or 1 kilogram of a substance 1 degree Celsius. Thus, in the previous example iron has a greater specific heat than lead.

The specific heat of a material is specific or characteristic for that material. As can be seen from the definition, the specific heat of a given material can be determined by adding a known amount of heat to a known mass of material and noting the corresponding temperature change. It is the purpose of this experiment to determine the specific heats of some common metals by the calorimetric method.

Equipment needed:

1.                  Calorimeter

2.                  Boiler and stand

3.                  Bunsen burner and striker, or hot plate

4.                  Two thermometers (0 to 119º C) or the Venier Computer Thermometer

5.                  Two kinds of metal (shot form or slugs with at­tached strings)

6.                  Laboratory balance or digital scales

7.                  Ice

Theory:

The change in temperature ΔT of a substance is pro­portional to the amount of heat Q added (or re­moved) from it:

In equation form, we may write

(Eq 1)

where the constant of proportionality C is called the heat capacity of the substance.

However, the amount of heat required to change the temperature of an object is also proportional to the mass of the object. Hence, it is convenient to define a specific heat capacity "c" (or simply specific heat)

(Eq 2)

which is the heat capacity per unit mass of a substance. Thus, Eq 1 becomes

or solving for the specific heat c,

(Eq 3)

In common units the specific heat is then the amount of heat (in calories) required to change the tempera­ture of 1 g of a substance 1ºC. The calorie unit of heat is defined as the amount of heat required to raise the temperature of 1 g of water 1ºC. By definition, then, water has a specific heat of 1 cal/g-ºC.

[A kilocalorie (kcal) is the unit of heat defined as the amount of heat required to raise the temperature of 1 kg of water by 1 ºC. In these units, water has a spe­cific heat of 1 kcal/kg-ºC or 4.18 X 103 J/kg-ºC.]

The specific heat of a material can be determined experimentally by measuring the temperature change of a given mass of material produced by a quantity of heat. This is done indirectly by a calorimetric procedure known as the method of mixtures. If several substances at various temperatures are brought together, the hotter substances will lose heat and the colder substances will gain heat until all the substances reach a common equilibrium temperature. If the system is insulated so that no heat is lost to the surroundings, then by the conservation of energy, the heat lost is equal to the heat gained.

In this experiment, hot metal is added to water in a calorimeter cup and the mixture is stirred until the system is in thermal equilibrium. The calorimeter insulates the system from losing heat (Figure). In mathematical form, we may write

heat lost = heat gained

Qmetal = Qwater + Qcup and stirrer

mmcm(Tm-Tf) = mwcw(Tf - Tw) + mcsccs(Tf - Tw)

mmcm(Tm-Tf) = (mwcw + mcsccs)(Tf - Tw)

(Eq 4)

where Tf is the final intermediate equilibrium temperature of the system. The other subscripts indicate the masses, specific heats, and initial temperatures of the respective components. Hence, Eq 4 may be used to determine the specific heat cm of the metal if all the other quantities are known.

Specific Heats of Metals

Introduction:

Different substances require different quantities of heat to produce a given temperature change. For example, about three and one-half times as much heat is needed to raise the temperature of 1 kg of iron through a given temperature interval ΔT as is needed to raise the temperature of 1 kg of lead by the same amount. This material behavior is characterized quantitatively by specific heat, which is the amount of heat necessary to raise the temperature of a unit mass of a substance by one unit temperature interval, e.g., 1 gram or 1 kilogram of a substance 1 degree Celsius. Thus, in the previous example iron has a greater specific heat than lead.

The specific heat of a material is specific or characteristic for that material. As can be seen from the definition, the specific heat of a given material can be determined by adding a known amount of heat to a known mass of material and noting the corresponding temperature change. It is the purpose of this experiment to determine the specific heats of some common metals by the calorimetric method.

Equipment needed:

1.                  Calorimeter

2.                  Boiler and stand

3.                  Bunsen burner and striker, or hot plate

4.                  Two thermometers (0 to 119º C) or the Venier Computer Thermometer

5.                  Two kinds of metal (shot form or slugs with at­tached strings)

6.                  Laboratory balance or digital scales

7.                  Ice

Theory:

The change in temperature ΔT of a substance is pro­portional to the amount of heat Q added (or re­moved) from it:

In equation form, we may write

(Eq 1)

where the constant of proportionality C is called the heat capacity of the substance.

However, the amount of heat required to change the temperature of an object is also proportional to the mass of the object. Hence, it is convenient to define a specific heat capacity "c" (or simply specific heat)

(Eq 2)

which is the heat capacity per unit mass of a substance. Thus, Eq 1 becomes

or solving for the specific heat c,

(Eq 3)

In common units the specific heat is then the amount of heat (in calories) required to change the tempera­ture of 1 g of a substance 1ºC. The calorie unit of heat is defined as the amount of heat required to raise the temperature of 1 g of water 1ºC. By definition, then, water has a specific heat of 1 cal/g-ºC.

[A kilocalorie (kcal) is the unit of heat defined as the amount of heat required to raise the temperature of 1 kg of water by 1 ºC. In these units, water has a spe­cific heat of 1 kcal/kg-ºC or 4.18 X 103 J/kg-ºC.]

The specific heat of a material can be determined experimentally by measuring the temperature change of a given mass of material produced by a quantity of heat. This is done indirectly by a calorimetric procedure known as the method of mixtures. If several substances at various temperatures are brought together, the hotter substances will lose heat and the colder substances will gain heat until all the substances reach a common equilibrium temperature. If the system is insulated so that no heat is lost to the surroundings, then by the conservation of energy, the heat lost is equal to the heat gained.

In this experiment, hot metal is added to water in a calorimeter cup and the mixture is stirred until the system is in thermal equilibrium. The calorimeter insulates the system from losing heat (Figure). In mathematical form, we may write

heat lost = heat gained

Qmetal = Qwater + Qcup and stirrer

mmcm(Tm-Tf) = mwcw(Tf - Tw) + mcsccs(Tf - Tw)

mmcm(Tm-Tf) = (mwcw + mcsccs)(Tf - Tw)

(Eq 4)

where Tf is the final intermediate equilibrium temperature of the system. The other subscripts indicate the masses, specific heats, and initial temperatures of the respective components. Hence, Eq 4 may be used to determine the specific heat cm of the metal if all the other quantities are known.

Figure: Apparatus for specific heat measurements. Metal shot or a solid piece of metal (right) is heated and then placed in an amount of water in a calorimeter, which insulates the system from losing heat. The inner calorimeter cup is shown with its dark insulating ring. Data: Type of Metal Mass of Mass of Specific Cs Mass of Metal, Calorimeter heat of Water, and Stirrer Calorimeter T metal T water T final ms and Stirrer Aluminum 0.0647 0.0435 0.0823 95.7 23.1 32.5 Steel 1.762 0.0435 0.077 86.6 23.1 36.3 Lead 0.243 0.0435 0.074 88.0 25.5 31.3 Cooper 0.219 0.0435 0.087 95.6 25.3 36.4 Calculations: Type of Metal Cm experimental Cm accepted Percent Error Aluminum 920 Steel 510 Lead 125 Cooper 380 Experimental Procedure: 1. Weigh out 400 to 500 g (0.4 to 0.5 kg) of one kind of dry metal shot. [Do this by first determining the mass of the empty boiler cup (in which the metal shot is heated) and then adding an appropriate amount of metal shot to the cup and reweighing. ] Record the mass of the metal