Specific Heat Capacity Measurement and Calibration

Specific Heat Capacity Measurement and Calibration

1.0 Introduction

Calorimetry is the technique used to measure the amount of heat exchange between two different substances at different temperatures (Ribeiro, 1984). A calorimeter comprises an insulated container, a mass of water, the thermometer, a lid, and the system to be investigated. The use of the Styrofoam cup allows an assumption that there is no heat exchange through the calorimeter walls. This particular experiment is focused on the determination of the heat capacity of the adiabatic calorimeter to measure heat changes at constant pressure. The experiment involves the use of a calorimeter with water and a metal sample to find the specific heat capacity of the metal sample. According to Chang (1984), the specific heat capacity refers to the amount of heat energy required by an object to absorb a unit increase in temperature for a given unit of the mass.

Theoretical background

The calorimeter contains a suitable liquid which creates a good thermal contact with the process being investigated. If the process generates heat energy, then the energy exchanged to the liquid, as well as the material of the calorimeter, results in an increase in the temperature of the liquid. Change in temperature is calculated as the change in temperature between the initial temperatures of the liquid and the final temperatures of the calorimeter..

Heat exchange is expressed as:

–qhw= qcw+ qcal

Where qhw,qcw, and qcal are the heat lost by the hot water, gained by cold water, and gained by the calorimeter, respectively.

Quantity of heat is calculated as:

Mass x specific heat capacity x change in temperature

Plucking in the above formula in equation one results in the equation:

–mhwCpwΔThw= mcwCpw∆Tcw+ Ccal∆Tcw

Also, density = (mass/volume) and therefore mass = (density x volume). Replacing the mass value in the above equation gives the equation:

𝐶𝑐𝑎𝑙=−𝜌𝑤𝐶𝑝𝑤[𝑉ℎ𝑤(∆𝑇ℎ𝑤/∆𝑇𝑐𝑤) + 𝑉𝑐𝑤]

This experiment will, therefore, be focusing on two major activities. The first one is the calibration of the calorimeter, followed by the determination of the specific heat capacity of the sample.

Experimental objectives

1. To construct the calorimeter and demonstrate how it can be calibrated
2. To determine the specific heat capacity of a metal sample, compare it with standard heat capacity data in the literature, and determine the material basing on the specific heat

2.0 Experimental Procedure

Materials and equipment

• Thermometer
• Styrofoam cups
• Beaker
• Heating oven
• Tongs
• Distilled water
• Measuring cylinder
• Stirring rod
• Stopwatch
• Weighing balance

Calorimeter calibration

Two Styrofoam cups stacked inside each other were used to make a calorimeter and the calorimeter inserted into the beaker. A 50ml cold distilled water was added to the empty calorimeter and a lid placed on the cup, followed by the insertion of the thermometer probe via the lid until the thermometer immersed into the water. It was ensured that the thermometer does not touch the walls of the calorimeter in the course of the experiment. The calorimeter was allowed to stabilize for five minutes, followed by the creation of a blank similar to Table 1. The temperature of the cold water, T_cwi, was obtained and recorded. 120ml of hot water, T_hwi, was measured into the Styrofoam cups followed by removal of calorimeter’s lid and the hot water poured into the calorimeter, and then the lid closed as soon as possible. The water was gently stirred, and its temperature measured at every 20 seconds intervals for five minutes. This experiment was repeated thrice for accuracy.

Investigation of the Cp of the metal sample

Two Styrofoam cups were stacked together to make a calorimeter, which was later placed inside the beaker. 30ml of cold distilled water was added into an empty calorimeter. The lid was placed on top of the cup and a thermometer probe inserted via the lid down until it immerged into the water. The calorimeter was allowed to stabilize for five minutes, and the initial temperature of the cold water, Tcwi, was recorded. The lid was removed off the calorimeter, and a required sample was s removed from the oven using tongs and later placed into the calorimeter. The calorimeter’s lead was replaced as soon as possible, and the ware gently stirred, followed by measurement of its temperature after every 10 seconds interval for five minutes. The metal sample was removed using the tongs, dried using a blue roll, and weighed. This experiment was repeated two times for accuracy. Also, the experiment was repeated for five different samples to establish the specific heat capacity as well as the type of material.

3.0 Results

Specific heat capacity measurement and calibration

Table 1: Calorimeter calibration data set

Table 2: Investigation of the cp of a metal sample

Table 3: Samples weights

The initial temperature of cold water is 19.5^oC

The temperature of cold water for this experiment is 18.4 ⁰C

Figure 1: A graph of temperature vs. Time for calorimeter calibration

Figure 2: A graph of temperature vs. time for sample A

Figure 3: A graph of temperature vs. time for sample B

Figure 4: A graph of temperature vs. time for sample E

Figure 5: A graph of temperature vs. time for sample F

Calculation of the calorimeter constant, C_cal

𝐶𝑐𝑎𝑙=−𝜌𝑤𝐶𝑝𝑤[𝑉ℎ𝑤(∆𝑇ℎ𝑤/∆𝑇𝑐𝑤) +𝑉𝑐𝑤]

Where:

V_hw is the volume of hot water

V_cw is the volume of cold water

Vhw =100 ml

Vcw= 50 ml

Cp = 4.184 j/g^oC

∆𝑇𝑐𝑤=𝑇𝑚𝑖𝑥−𝑇𝑐𝑤𝑖 and ∆𝑇ℎ𝑤=𝑇𝑚𝑖𝑥−𝑇ℎ𝑤𝑖

∆𝑇𝑐𝑤= 56.7 – 18.4 = 38.3 ^OC

∆𝑇ℎ𝑤= 100 -56.7 = 43.3 ^OC

𝐶𝑐𝑎𝑙=−𝜌𝑤𝐶𝑝𝑤[𝑉ℎ𝑤(∆𝑇ℎ𝑤/∆𝑇𝑐𝑤) +𝑉𝑐𝑤]

= – 1g/ml x 4.184 j/g^oC [100ml (43.3/38.3) + 50ml]

= 4.184 x 163.05

= 682.2 Joules

Specific heat capacity of metal samples

Cpms=− (M𝑐𝑤Cp𝑤∆𝑇𝑐𝑤+𝐶𝑐𝑎𝑙∆𝑇𝑐𝑤/ M𝑚𝑠∆𝑇𝑚𝑠)

Sample A

Cpms = – ((100 x 4.184 x 38.3 + 682.2 x 38.3)/ (7.126 x (100-18)))

= – (42152.98/584.332)

= 72.14 j/g^oC

Sample B

= – ((100 x 4.184 x 38.3 + 682.2 x 38.3)/ (19.108 x (100-19.8)))

= 27.51 j/g^oC

Sample E

= – ((100 x 4.184 x 38.3 + 682.2 x 38.3)/ (23.985 x (100-21.6)))

= 22.42 j/g^oC

Sample F

= – ((100 x 4.184 x 38.3 + 682.2 x 38.3)/ (19.137 x (100-20.0)))

= 27.53 j/g^oC

Discussion and Questions

Calorimeter calibration

From the results obtained, the calorimeter constant after calibration is 682.2 joules. Heat and temperature are different quantities. According to Martin, (1960), heat is a form of energy that is exchanged between a cold and hot body, while the temperature is the degree of coldness and hotness of a body. Heat is measured in joule, while the temperature is measured in kelvin. Also, heat is the total potential and kinetic energy gained by molecules in an object, while the temperature is the average kinetic energy of molecules within a substance (Rossini & Skinner, 1956). In this experiment, Styrofoam cups are used in designing the calorimeter because Styrofoam is a fairly good insulating material. A Styrofoam cup makes a good a fairly good adiabatic wall and keeps the heat absorbed or released by the reaction within the cup so it can be measured (Waples & Waples, 2004). However, it is an ideal calorimeter, and despite the insulation property, it still allowed some heat to escape from the calorimeter and therefore resulting in the experimental error. The hole at the top of the calorimeter had a slightly bigger diameter than that of the thermometer, and therefore, the system was not perfectly insulated. Another source of error is that the thermometer has a tendency of rounding and therefore changing the actual value of the temperature recorded. There was an instability in the temperature readings and, therefore, the graphs indicating irregular changes in the temperature, particularly in the initial moment of temperature stabilization.

From the calculations, the calorimeter constant was 682.2 Joules. This value was slightly lower than the theoretical value. This variation is an indication of some inefficiencies in the calorimeter. Each trial showed a variation in the results of the temperatures obtained, and therefore average values were used for accuracy purposes.

Cp of the metal sample

In this section, the specific heat capacity of the metal samples was established, and a comparison made with the online literature to establish the kind of material based on the specific heat capacity obtained. In this particular procedure, the heat capacity calculated was higher than expected due to inaccurate measurements obtained on the thermometer as well as poor calibration. Also, a considerable amount of heat was lost as a result of inefficiency in the transfer of metal samples from the heating chamber into the water. The non-uniform heating of the water in the calorimeter resulted in hot and cold spots caused by the uneven distribution of heat. In addition, spending more time to shift the metal sample from the oven to water will result in energy loss and thus poor results.

The values brained were relatively high than required and easy difficulty in identifying the exact type of the sample being investigated. The specific heat capacity specifies the quantity of heat that was required to be added in a kilogram mass to increase its temperature by a unit temperature (Myers, 2003). For all samples, the specific heat capacity decreased by a decrease in the temperature. The variation was, however, relatively small, and therefore, it is possible to regard the specific heat capacity values as a constant for a given temperature interval.

Conclusion

With regard to the observations made in this experiment, the sample metals had the property of absorbing and emitting heat. This particular property is the characteristic specific heat capacity of the material that is dependent on the type of metal, mainly copper and aluminum. Specific heat capacity can be determined only from temperature-sensitive materials due to the very minimal actual values which cannot be easily established on other metals. In the future experiment, it is necessary to take into consideration some factors to avoid more repeats. The first consideration is that some materials such as aluminum have higher conductivity of heat compared to others such as copper. Also, metals with relatively lower specific heat capacity tend to emit more heat. In summary, the calorimetry experiment was successfully performed, and the specific heat capacity of the metal samples identified.

References

Martin, D. L. (1960). THE SPECIFIC HEAT OF COPPER FROM 20° TO 300 deg; K. Canadian Journal of Physics, 38(1), 17-24.

Chang, S. S. (1984). Thermodynamic properties and glass transition of polystyrene. In the Journal of Polymer Science: Polymer Symposia (Vol. 71, No. 1, pp. 59-76). New York: Wiley Subscription Services, Inc., A Wiley Company.

Ribeiro. S. M. A. V. (1984). Thermochemistry and Its Applications to Chemical and Biochemical Systems: The Thermochemistry of Molecules, Ionic Species, and Free Radicals in Relation to the Understanding of Chemical and Biochemical Systems. Dordrecht: Springer, Netherlands.

International Union of Pure and Applied Chemistry., In Rossini, F. D., & In Skinner, H. A. (1956). Experimental thermochemistry: Measurement of heats of reaction. New York: Interscience Publishers.

Myers, R. L. (2003). The basics of chemistry. Westport, Conn: Greenwood Press.

Waples, D. W., & Waples, J. S. (2004). A review and evaluation of specific heat capacities of rocks, minerals, and subsurface fluids. Part 2: fluids and porous rocks. Natural resources research, 13(2), 123-130.