Mechanical Equivalent of Heat
Mechanical Equivalent of Heat :- In early days heat was not recognized as a form of energy. Heat was supposed to be something needed to raise the temperature of a body or to change its phase. James Prescott Joule first experimentally found that the “heat produced in a system is directly proportional to the mechanical work done on it”.
If mechanical work W produces the same temperature change as heat H, then
The proportionality constant J is known as Joule’s Mechanical Equivalent of Heat or Joule’s Constant, after the name of James Prescott Joule. The value of the constant J is calculated through a unique experiment, which is described below.
Joule’s Experiment to calculate Mechanical Equivalent of Heat (J)
Joule’s experiment setup to find out Joule’s constant is as shown in figure below:
In above figure, two masses are attached with a rope and a paddle wheel as shown in Figure. When these masses fall though a distance h due to gravity, both the masses lose potential energy equal to 2mgh. When these masses fall, the potential energy stored in the masses during lifting of weights, is released as kinetic energy which turn paddle wheels. Due to the turning of wheels inside calorimeter filled with water, the temperature of water increases due to frictional force between water and the paddle wheels.
Two vertical scales measure the vertical movements of the weights and the thermometer on the top cover of the calorimeter measures the rise of temperature of the water. This experiment is done until there is a measurable temperature difference indicated on the thermometer.
Let total n repetitions of weight movements increased the temperature of water through ΔT. Hence, total work done will be
W = 2 nmgh
If M is the mass of the water in the calorimeter and W’ is the water equivalent of the calorimeter, then total heat produced for ΔT rise in temperature,
Q = (M + W’)ΔT
Now, mechanical equivalent of heat
By putting the values of m, g, h, n, M, W’ and ΔT, we get,
J = 4.186 kJ/kcal.