# Joule Equivalent of Electrical Energy

## Physics 231 with Jones at University of Tennessee - Knoxville *

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Joule Equivalent of Electrical Energy Justin Boyd Billy Stack Austin Lee Physics 231, Savan Kharel February 24, 2009-March 3, 2009 Objectives: The objectives of this experiment are: 1) to understand the equivalence of electrical energy and heat energy, 2) to learn techniques of calorimetry, 3) to learn how to measure electrical energy, and 4) to measure the Joule equivalent of electrical energy. Apparatus: The apparatus includes 1) an assembly with a resistive heating coil, stirrer, and electrical connector posts, 2) a double-wall aluminum calorimeter, 3) a low voltage, high current power supply with a digital voltmeter and ammeter, 4) electrical leads, 5) a digital multimeter, and 6) a Pasco 750 Science Workshop data acquisition system with a temperature sensor. Theory: Electrical and mechanical energy use the same units of energy. This is because both were developed by the same principles of energy and power. Heat energy is measured in quantities separately defined from the principles of electricity, magnetism, and mechanics. Due to this inconvenience, Sir James Joule developed a constant of proportionality between the two forms of energy which is now called the Joule equivalent of electrical energy. This constant allows for an understanding relationship between the two forms of energy. Error Analysis: In the experiment there is a measure of error that could not be avoided given the equipment and the parameters of the experiment. Error in the data is brought on by one primary reason. Since water is a poor conductor of heat, failure to stir properly causes thermal equilibrium to be tougher to obtain. With the water and the container not in complete thermal equilibrium, the slope of the Temperature versus time graph will be lower than its theoretical equivalent causing inaccurate joule equivalence constant to be calculated. Conclusion: It was determined that the units for heat energy could be successfully converted to the units for electrical and mechanical energy. By using our calculated heat energy we successfully proved the joule equivalence constant with an average percent error of less than 5 percent. These calculations are supported by the data as well as by the known joule equivalence calculated first by Sir James Joule as 4186 Joules/kilocalorie. The data collected can also be proven true by the equations of heat energy and heat energy relationships to mechanical and electrical energy. Questions: 1) 313.95 seconds 2) 178.9515 seconds Power is defined as the rate of doing work, and electrical power is defined as the amount of electrical energy being expended per unit of time. An explanation of this is: work is the mechanical energy required to move an electrical charge through a potential difference (W=QxV) therefore power, P, is given by (P=W/t = VxQ/t) so that power is equal to potential difference times current. Heat energy is measured in kilocalories as opposed to mechanical and electrical energy which is measured in joules. The change in heat energy of a material is directly proportional to the change in temperature of the material and depends on the type of material and its mass. The change of heat energy for a given change of temperature is equal to mass of the material times specific heat of the material times the change in temperature (Q=mcT). When electrical energy is transformed into heat energy, then the equivalence of the electrical energy and heat energy is given by multiplying the joule equivalent constant of 4186 Joules/kilocalorie times the change in heat energy (W=JxQ). With this in mind, throughout the experiment a constant current and voltage will be maintained causing the resistance to increase and therefore the heat energy. This heat energy will increase the temperature of a quantity of water and the container in which it is kept. The change in heat energy of the container and water will be the sum of the heat energies of each and will be given by Q=(m’c)(c’c)T + (m’w)(c’w)T , where m’c and m’w are masses of the container and water and c’c and c’w are specific heats of the material of the container and water. With our previous equations for work and energy, we can deduce that our joule equivalence calculated for the experiment will be given by the following equation: J = {(VI) / [ (m’c)(c’c) + (m’w)(c’w) ]} x [ 1 / (T/t) ]. In this equation, temperature, T, is a function of time, t. Data/Results: (see attached)

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