# An experiment to determine the mechanical equivalent of heat

At the end of the 18th century the prevailing heat theory was the, obsolete now, caloric theory, according to which heat consists of a fluid called caloric that flows from hotter to colder bodies. Caloric was also thought of as a weightless gas that could pass in and out of pores in solids and liquids. The Mechanical Equivalent of Heat Purpose To verify the proportional relationship of mechanical to thermal energy, and to calculate the Joules constant. Prelab Homework The prelab homework must be done at home and handed to the lab TA before you start the lab.

Read the instructions for this lab. Question For the first apparatus described below, the string holding the mass M is assumed to be tangential to the perimeter of the disk while the crank is being turned.

Sketch a diagram showing a case when the string is not tangential and explain how to find the torque in this case. You may find that when you carry out your experiment, you will have to use this formula instead of that used for the ideal case of the tangential string.

Introduction Perhaps the most common evidence for a relation between mechanical and thermal energy is the heat produced by friction.

When two reasonably rough objects are rubbed together they tend to warm up. Consider, for example, two hands on a cold Rochester morning or two dry sticks in the care of a skillful Boy Scout. Joule devised elegant experiments that confirmed this relationship.

## Background

He also showed that W could be any form of mechanical energy, not just work against friction, provided it is all converted to heat. Mechanical work is the product of a force times the distance through which it acts, but how can one measure heat? Heat changes a body to which it is added; for instance, its temperature may rise or there maybe a phase change e.

As long as there is no change of phase and the temperature changes are small, to a first approximation, the change in heat of a body is directly proportional to the change in its temperature.

Furthermore, since a body can be conceptually broken up into smaller ones and the change in heat of the whole is the sum of the heat changes of the parts, a given temperature change should require an amount of heat directly proportional to the mass.

Therefore,2 where m is the mass and Ti and Tf are the initial and final temperatures, respectively. The constant of proportionality C, called the specific heat relates the temperature change of a given body to the quantity of heat that produces it.

It is a characteristic of the material of which the body is composed. This relationship C independent of temperature is an approximation that is good over small temperature ranges.

C at that temperature.

## Mechanical equivalent of heat - Wikipedia

The specific heats of other materials are determined by comparison with water and are tabulated for many common materials. For instance, the tabulated value of the specific heat of brass is,3 which you will need in analyzing your experiment.

The experiment consists of a moving part which rotates against a stationary brass mass containing a thermometer. These two parts exert frictional forces on each other which generate heat. The stationary mass is constrained from rotating only by a measured force F applied at a radius r from its center. This situation is shown in a schematic way below. Figure 1 The moving part is rotated at a rate so that the frictional force transmitted to the stationary part just balances a constant torque applied to it and keeps it from moving. Under these conditions, all the work done to keep the moving part rotating is converted to heat by friction.

What is the rate at which mechanical energy is converted into heat? Well, it does not matter which part moves and which is stationary except for the convenience of doing the experiment ; the relative motion is what produces the friction that balances the applied torque.

So, imagine that the moving part was stopped. The same balance would occur when the stationary part rotates under the influence of the applied torque such that the relative motion is the same as before; that is, at the same rate that the moving part was turning.

The rate at which work would be done by the applied force in this hypothetical situation is F s, where s is the linear displacement parallel to the direction of the force. When F is expressed in Newtons and r in meters then W is in Joules. This heat is absorbed by the friction producing assembly and raises its temperature.

By measuring the resulting change in temperature T with the thermometer, the heat absorbed by each of the parts is,5 where is the heat absorbed by the ith part with mass mi and specific heat Ci, can be accounted for. Now the thermometer itself consists of both mercury and glass, and these substances have different specific heats.

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However, by fortunate coincidence the product of density and specific heat is,6 and is nearly the same for both glass and mercury.Oct 27,  · Mechanical Equivalent of Heat James Prescott Joule found that the mechanical work done on a system was equal to the heat produced i.e., W is directly proportional to Q or w is equal to JQ.

Part 5A: Mechanical Energy into Heat.

## Prelab Homework

In this experiment you will convert mechanical energy into heat. The mechanical energy will come from friction. The heat will be observed by measuring the increase in temperature of known masses of known specific heat.

capacity.

## Experimental Determination of the Mechanical Equivalent of Heat

Experiment 6 Heat Equivalent of Mechanical Energy Objectives • Observetheconversionofmechanicalenergyintoheat. • Learn how to convert the units traditionally. THE MECHANICAL EQUIVALENT OF HEAT INTRODUCTION This is the classic experiment, first performed in by James Joule, which led to our modern view that mechanical work and. James Prescott Joule ( – ), an English physicist, calculated in , a few decades after Rumford’s cannon experiments, the mechanical equivalent of heat in a series of experiments.

In the most famous apparatus he built for this end, now called the Joule apparatus (see image below), a descending weight attached to a string caused a. joule on the mechanical equivalent of heat. little attention has hitherto been paid, is that in which he makes an estimate of the quantity of mechanical force required to produce a certain amount of heat.

The Mechanical Equivalent of Heat