T5: Calorimetry

The sensation of hot or cold that we feel when we touch an ice cube, or walk outside under the sun, is related to temperature and heat. Atoms have kinetic energy. This energy is transferrable between objects through contact; this is seen as an ice cube melts in a glass of water, or as a pan heats up when you place it on a stove. When these atoms interact, kinetic energy is transferred. This flow of energy is known as heat.

Heat is quantified through the following relationship:

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Where Q is heat measured in joules, m is mass, c is the specific heat capacity, and ΔT is change in temperature of the object. The objective of the experiment is to find the specific heat capacity of two metals, namely aluminum and copper, by exploiting this relationship.

Another phenomenon is essential to finding specific heat capacity: The Zeroth Law of Thermodynamics. The Zeroth Law of Thermodynamics states that if A is in contact with B, and B is in contact with C, is A and B are in thermal equilibrium, then A and C are in thermal equilibrium as well.

The experimental set-up consisted of an isobaric coffee-cup calorimeter filled with tap water. The metal, which was originally immersed in boiling water, was placed in the calorimeter. The change in temperature of the water is measured using a thermocouple. After this, using the known specific heat capacity of water, the heat of the water is calculated. By the Zeroth Law of Thermodynamics,

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when there is a metal present. The heat of both the calorimeter and the water must be known to be able to calculated the heat of the metal. By extension, the heat capacities of each are needed to calculate their respective values for heat. When there is no metal, a calibration curve may be obtained to calculate the heat capacity of the calorimeter. This is done by mixing hot and lukewarm water. Change in temperature is tracked with reference to time, and a calibration curve is formed by linearizing the following relationship:

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The y-intercept of the curve is equal to the exponential of the final temperature as time approaches infinity.  Once the change in temperature of both the tap and hot water have been calculated, their heats may be obtained, and therefore the heat capacity of the calorimeter. Once this value is known, any change in temperature in the water in the calorimeter due to an immersed metal may be used to calculate the heat capacity of that metal.

Three calibration trials were done. 60 mL of both tap and hot water were used for each trial. Knowing the density of water, this means that the mass of each was 60g, for a total of 120 g. The specific heat capacity of water is also known to be 1 Jg 0C-1. Below is a representative calibration curve.

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The heat capacities calculated for the three trials were the following:

Trial Heat Capacity of the Calorimeter (J/g • 0C)
1 26.16
2 38.07
3 48.75

The average value obtained was 37.66. This result was far from precise as manifested by the large range in values, which had the experimenters quite confused. Still, this average value was determined to be the heat capacity of the calorimeter.

Knowing the mass of the metal, the volume of the water in the calorimeter, the density of water, and the specific heat of water, and measuring the changes in temperature in the water using the thermocouple, the specific heat capacity of the metals was then calculated. The following results were obtained:

Metal Aluminum Copper
Calculated Specific Heat Capacity 1.003 0.3895
Percent Error 11.52% 0.9002%

From these results, it is safe to say that the specific heat capacities of both metals were accurately calculated, even with the imprecise measurement of the heat capacity of the calorimeter. Still, error may have arisen from a multitude of sources: the makeshift nature of the coffee-cup calorimeter and the fact that it was not a sealed system and that heat may have escaped, the fact that the thermocouple could only measure accurately to the ones digit, inaccuracies in the measurement of the water since it cannot be transferred perfectly from vessel to vessel, and many more.

In conclusion, the experiment has been deemed a success, and the method used valid.







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