Figure 1 Cut Away of Double-Cone Calorimeter
Energy occurs in many forms in nature, and we observe these all about us. Mechanical energy is associated with the motion of a body, or its position in a gravitational field. Electrical energy is associated with electric or magnetic fields, or the change of potential of electrical currents (moving charges) through generators, motors, resistors, or other devices. Heat energy in a substance is due mostly to microscopic motion of atoms and molecules composing the material. The generalized law of energy conservation states that, while energy may neither be created or destroyed, it may be converted from one form to another through a transfer process.
Like energy itself, the process of energy transfer can be observed continually in the environment. For example, water, at a high elevation, possess potential energy, which may be converted to kinetic energy in a waterfall. Upon striking the rocks at the bottom of a gorge, this kinetic energy may be converted to heat, thereby raising the water temperature. Alternatively, the falling water may be directed against the blades of a turbine producing rotational mechanical energy. The turbine may be connected to a generator, which transfers mechanical energy to electrical energy, used to heat and light our homes and power the machines of industry. Throughout these events, the transfer of energy between mechanical, electrical and heat occurs in a continual series of processes.
Historically, the understanding of heat and thermal processes was developed independently of mechanics. Heat was thought to transfer from one substance to another through a flow of quantity called "caloric", which was determined by temperature differences. It was Count Rumford who in 1798 observed that cannon casting increased their temperature while being bored, then realized mechanical energy was being converted into heat energy, and conjectured heat was really microscopic motions. Later Sir James Joule quantified the relationship between mechanical and various types of heat energy and laid the foundations of thermodynamics.
A change in the heat energy content results in a change of temperature of a substance, and it is through observations of this process that energy in the form of heat is defined. A given material has heat capacity, a thermodynamic quantity which relates the change of heat energy to the change in temperature. All materials have a heat capacity, which depends on the details of the atomic and molecular structure of the material, its physical state, and often the temperature and pressure to which the material is subject. The Calorie was originally defined as the amount of heat required to raise a gram of water from 14.5 to 15.5 C, i.e. a change of temperature of 1 C at 15 C.
After the realization that heat and mechanical energy were related, experiments of Joule and Thompson (1823) found that:
1 Calorie (heat energy) = 4.18 Joules (mechanical energy).
The quantity J = 4.18 joules/calorie is called the "mechanical equivalent of heat". Because the Calorie is a very small unit of energy, the relation in mks units is usually expressed as:
J = 4.18 x 103 joules/kilocalorie,
which is the accepted value today.
Here we perform an experiment not unlike those of Rumford, Joule and Thompson, and determine, via an energy transfer process, the mechanical equivalent of heat.
The Mechanical Equivalent of Heat
In this experiment, we determine the mechanical equivalent of heat by turning two brass cones against each other and comparing the mechanical work done against this friction with the gain in heat of the system. This is known as the "Cavendish method" of determining J.
Figure 1 Cut Away of Double-Cone Calorimeter
A large disk is attached to the top of an inner cone as shown in Figure 1. A cord is attached to a point on the side of the disk, and leads through a pulley to a spring balance which indicates the force exerted on it. When the outer cone is rotated with the hand-operated crank, it drags along the inner cone until the force exerted by the spring balance on the inner cone through its lower arm equals the frictional torque between the two cones. From the relation between the torque, the rate at which the cones are rotating, and the total time, we can determine the mechanical energy input against friction, which we assume is entirely converted to heat.
The torque on the inner cone with respect to the axis of the cone is a constant which may be evaluated using
= RF,
where F is the force registered on the spring balance, and R is the radius at which force is measured. The total mechanical work done against friction is
W = 
where is the angle through which the inner cone is turned against the
torque .
Thus, if the apparatus is turned through N revolutions as recorded on a counter at the base of the apparatus, we have
W = 2
N R F.
This energy is converted to heat via friction and is absorbed by the brass cone calorimeter system. Assuming no other energy losses, this results in a temperature increase of the system. The heat input Q, can be expressed in terms of the temperature increase through
Q = C 
T ,
where C is the heat capacity of the system (Cal/C). The latter can be computed if we know the specific heats, masses, and volumes of each component of the system, and assume a simple, or linear relationship:
c = m1c1 + m2c2 + . . .
Here m1 and c1 are the masses and specific heats (Cal/gm-C) of each component of the system.
Finally J is determined from:
J = W/Q (joules/calorie).