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14 MECHANICAL EQUIVALENT OF HEAT (ELECTRICAL METHOD) with solar power optimization competition OBJECT To measure the mechanical equivalent of heat by an electrical method. APPARATUS Heating coil, calorimeter and stirrer, DC voltmeter and ammeter, switch, connecting wires, temperature sensor (brass or plastic), resistor boxes (1 kilo-ohm step, 100 ohm and 10 ohm step), distilled water, ice, balance, cork, computer temperature and time program. THEORY Potential difference is defined as work per unit charge given by the expression V = W/Q (1) where W is the work done in moving the charge Q through the circuit. In the practical (mks) system V is expressed in volts, W in joules, and Q in coulombs. Equation (1) may be written as W = VQ (2) And recalling that I = dQ/dt or Q t I (3) V = I R (4) we may rewrite equation (1) using these substitutions as W = VQ = VIt = IR(I)t = I 2 Rt (5) This equation indicates that if an electric current of 1 ampere is sent through a coil of wire of resistance 1 ohm for 1 second, then 1 joule of work has been expended in maintaining this current. This energy is transformed into heat. If the coil is submerged in a calorimeter containing water, the number of calories of heat produced can be obtained by the usual method of calorimetry. In a circuit containing only resistance, a direct proportion exists between the expenditure of the electric energy W and the heat H developed. This fundamental law is represented by the conservation of energy equation W = JH (6)
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15 where J is the proportionality factor called the mechanical equivalent of heat, or the number of joules required to produce one calorie of heat. By referring to the experiments on calorimetry you will derive an expression for H, the heat developed, so
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This note was uploaded on 08/25/2011 for the course PHYS 164 taught by Professor Johnjames during the Fall '09 term at MO St. Louis.

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