Specific Heat of a Substance

 

When a hot object is added to cold water in a calorimeter, the heat lost by the hot object,

Δq _{hot object  is} equal to the heat gained by the cold water, Δq _{cold water} and the calorimeter,

 Δq _calorimenter  as predicted by the Law of Conservation of Energy.

 

Δq _{hot object  =}  Δq _{cold water}  +  Δq _calorimeter 

 

or

 

[ m • Δt • c_p ]_{hot object}  =  (calorimeter constant • Δt)_calorimeter  +  [ m • Δt • c_p ]_{cold water}

 

The purpose of this experiment is to compare the energy lost by a hot object with the energy gained by cold water and a calorimeter and to determine the specific heat of the hot object.

 

Procedure:

 

P1.  Heat about 300 mL of tap water in a 400 mL beaker using a hot, blue flame.  Mass the test tube and then fill it about one-half full of the material to be studied, and re-mass to the nearest 0.01 g.  Place the test tube containing the material in the warm water.  As soon as the water boils, reduce the flame so that the water barely boils. 

 

P2.  Mass a dry calorimeter, add 15 mL of cold tap water, and re-mass.  Record the temperature of both the water in the calorimeter and the temperature of the material in the test tube to the nearest 0.1 °C.  The temperature of the material in the test tube can be measured by pressing the thermometer against the material until the temperature is constant over several five-second intervals.

 

P3.  When the temperature of the material is constant, quickly pour the hot material into the cold water in the calorimeter.  Stir the mixture and record the temperature to the nearest

0.1°C when it is constant over several five-second intervals.

 

P4.  Drain the water from the material studied and return it to the collection point designated by the teacher.  Dry the calorimeter and repeat the experiment with another material.

 

Calculations and Questions:

 

Q1a.  Calculate the mass of the material in the test tube.

 

Q1b.  Calculate the mass of the water in the calorimeter.

 

Q1c.  Calculate the change in the temperature of both the water and calorimeter, Δt_water, by subtracting the initial temperature of the cold water from the final temperature of the water after the hot material was added to it, t_final.

 

Q1d.  Calculate the temperature change of the hot material in the test tube, Δt_material, by subtracting the initial temperature of the material while it was still in the boiling water from the final temperature of the mixture.

 

Q2a.  Calculate the change in the energy of the water, Δq_water , from its mass (Q1b), the specific heat of water (1.00 cal/g°C), and the change in its temperature (Q1c).

 

Δq _water  =  m_water  •  Δt_water  •  c_{p water}

 

Q2b.  Calculate the change in the energy of the calorimeter (Δq _cal) from the calorimeter constant and the change in temperature of the water (Q1c).

 

Δq _cal  =  calorimeter constant  •  Δt_water

 

Q2c.  Calculate the total energy lost by the hot material, Δq _material, from the energy gained by both the cold water (Q2a) and the calorimeter (Q2b).

 

Δq _material  =  Δq _water  +  Δq _cal

 

 

Q3.  Calculate the specific heat of the material studied, c_{p material},  from the energy lost by the hot material (Q2c), the mass of the material (Q1a), and the temperature change of the material (Q2d).

 

Δq _material  =  m_material • Δt_material • c_{p material}     (solve for c_p)

 

Note:  if multiple trials of the same material are used, average the results you have for the different trials at this time.

 

Q4.  Calculate the percent error by comparing your value for the material (Q3 or average of all Q3s) with the accepted value found of the chalkboard.

 

% error =  | c_p  -   c_{p­ theoretical} |  x 100

                                                          _______________

                                                                   c_{p theoretical}

 

 

 

Procedure 2

 

Using the final specific heat of the metal found above, repeat the experiment replacing the water in the calorimeter with ethylene glycol (antifreeze) and then a 50/50 mixture of ethylene glycol and water (prepared for you by the teacher).  Solve for the specific heat of the ethylene glycol (which is known to be 0.571 cal/g°C) and for the mixture (which is assumed to be

0.785 cal/g°C, the difference between 1.00 and 0.571 since the mixture was based on 50% by mass of water and ethylene glycol).  Complete the calculations for this section by doing % error calculations.

 

 

 

 

 

 

Analysis Questions:

1. Why use boiling water as the method for heating the metal samples each time?  Why not just hold the samples over a burner?
2. Using the three liquids, list their calculated specific heat capacities, in order from lowest to highest.  Next give the change in temperatures experienced by each liquid.  Assuming the metal samples transferred the same amount of heat to the three liquids (can this be checked?), is the ranking of the different changes in temperature correct?
3. How did the heat lost by the metal samples in each experiment compare?  Give values and explain their validity.
4. Which of the liquids would be the most effective coolant (during the summer) in a car’s radiator.  Why?  Which liquid is the most effective coolant for year round usage?  Why?
5. Explain how specific heat capacities be used to identify an unknown metal.
6. Given a true 50/50 mixture of the ethylene glycol and water, calculate the mass of the mixture (given the density of pure ethylene glycol as 1.1157 g/cm³)

 

 

Write-up Procedure:

1. Include all collected data in a table (use the P# and Q#s to help identify) including all appropriate units and significant figures.
2. Show all calculations required.  Include the appropriate formula, fill in all data with units, and solve.  Circle the final answer to all calculations (remember units and sig figs).
3. Answer all analysis questions fully.