Experiment 10

#### Specific Heat Measurement

Objective:

The objective is to measure the specific heat of a selected material or substance.

Equipment:

A calorimeter, a piece of metal (aluminum, brass, copper, zinc, or iron), a mass scale, two thermometers, a water heater, and a calculator

Theory:

Although the SI unit for any type of energy is Joule; however,  the commonly used units for heat are calorie (cal), kilocalorie (kcal), and Btu.

1cal is the amount of heat that can raise the temperature of 1gr of pure water by 1oC.

{On the average, the best range is from 58.5 to 59.5oC}.

1kcal is the heat that can raise the temperature of 1kg of pure water by 1oC.

British Thermal Unit (Btu):

1Btu is the heat that can raise the temperature of 1lbm of pure water by 1oF.

Definition of Specific Heat:

The specific heat c of a substance is the # of kcal that 1kg of that substance absorbs to warm up by 1oC.  The specific heat of water is therefore:

 cwater = because of the way 1cal is defined, or cwater = because of the way 1kcal is defined, or cwater = because of the way 1Btu is defined.

The specific heat for other materials may be found in physics texts or handbooks.

 In this experiment, since mass will mainly be expressed or measured in grams,  we will use the unit shown on the right for specific heat. On this basis,  cAl = 0.215 Note that in general, metals take less heat for their temperature to increase by a certain amount compared to water; therefore, metals have lower specific heats than water.

Procedure:

1.  Use a mass scale to measure the mass of the inner aluminum pot of the calorimeter you have after making sure it is clean and dry.  Record the mass of aluminum.

2.  Fill it to 1/4 with tap water and measure its mass again.  The difference is the mass of water.

3.  Select a piece of metal for which the specific heat is known.  For example a 200-gram piece of copper, zinc, or brass.  You may obtain its specific heat from your text or a handbook.  Such value is the accepted value for this experiment.  Measure the mass of the sample you select.

4.  Connect the sample to a string and place it in the already filled water-heater and let the water come to boil.  With the sample in boiling water, the initial temperature of the sample will be very close to 100.0oC.   Have a thermometer in the boiling water to measure the initial temperature of the sample.   As you know the boiling point of a pure substance (such as water) is a function of its pressure as well.  The atmospheric pressure is taken to be 1 atmosphere at ocean level with no winds blowing.

5.  A thermometer must be placed in the calorimeter through its cap's hole to measure the initial temperature of the calorimeter.  This is the initial temperature of water and aluminum.

6.  After a few minutes, when the initial temperature of the calorimeter is stabilized and at the same time the initial temperature of the sample (while in boiling water) is also stabilized, in a quick and careful motion, the sample must be withdrawn from the boiling water and placed in the calorimeter.  All safety measures must be observed when working with any electric heater and boiling water to avoid burns and injuries.

7.  The temperature of the calorimeter will keep increasing for a while.

8.  The calorimeter could be given a mild shake (while holding its outer container in hand and lifting it slightly above the table surface).  This helps a better mixing of water in the calorimeter and a faster thermal equilibrium reach.  The thermometer must be repeatedly checked in order to record the highest possible temperature.  Record the highest possible temperature you read as the equilibrium temperature Teq .

9.  The gathered data must then be inserted in the thermal equilibrium equation in order to solve for the unknown.  Let the unknown be the specific heat of the metal piece (sample).  The value you calculate for the unknown from the equation will be the measured value in this experiment.

10. Calculate a % error for your measurement.

Data:

 Given: Measured: Substance Specific Heat (Accepted) cal /(gr oC) Specific Heat (Measured)  cal /(gr oC) MAl =              gr. MW =              gr. Sample (Alum.) 0.215 cS = TiAl =             oC Sample (Brass) 0.091 cS = TiW =              oC Sample (Iron) 0.108 cS = TiS =               oC Sample (Copper) 0.091 cS = Teq  =             oC

Calculations:

Equation:

- [The heat loss by hot object(s)]  =  [The heat gain by cold object(s)]

or,  - MScS (Teq - TiS =  Mwcw (Teq - Ti  +  MAlcAl (Teq - Ti )

or,  - MScS (Teq - TiS =  [ Mwcw  +  MAlcAl ] (Teq - Ti ).

Treat cS as an unknown in this equation and solve for it.  The result will be the measured value.

Comparison of the Results:

## The accepted and measured values ofcS may be used in the following equation to calculate a percent error.

Conclusion:   To be explained by students

Discussion:    To be explained by students