Experiment 19

The Mechanical Equivalent of Heat

Objectives

To find an accurate value of the mechanical equivalent of heat.

Introduction

When an electrical current flows through a conductor, some of the electrical energy is transformed into heat.  The intent of this experiment, following in the footsteps of James Joule, is to find the amount of electrical energy which is equivalent to the one calorie of heat.

The energy dissipated by a resisting wire carrying a current I for a time t is

1)  E=VIt

where V is the voltage across the wire.  If the wire is immersed in water, the temperature change of the water in degree Celsius times the mass of the water is the heat gained by the water in calories.

Procedure

Wire the circuit of the figure.  Fill the inner cup of the calorimeter ½ full with a few degrees below room temperature water and replace it in the calorimeter.  Measure the temperature of the water.  Turn on the power supply.  Raise the voltage to give a power of about 10 W.  Monitor the temperature, voltage, and current to be sure they remain constant.  When the temperature is as much above room temperature as it started out below it, stop.  Record the total time of heating.

Remove and weigh the inner cup.  Now empty and dry the cup and weigh it again.

Evaluation

The mechanical equivalent of heat is calculated from the equation

2)  H=E/(m_w+m_cc_c + m_rc_r)(T_f - T_i)

where E comes from equation 1, T_f and T_i are final and initial temperatures, m_w is the mass of the water, m_c and c_c are the mass and specific heat of the cut and m_rc_r is the product of the mass and specific heat of the wire coil.  The specific heat of the cup should be given, stamped on the calorimeter.  If it is not given, get a different cup.

Make several runs of this procedure with varied starting temperatures, recording each set of data in a table.  Average the values of H thus obtained and calculate a percent error of your value from the accepted value of 4.186 J/cal.