Paddle wheel Joule

One can also do work by stirring, e.g. by driving a paddle wheel as in the Joule experiment above. If tire paddle is taken as part of the system, the energy input (as work) is detemiined by appropriate measurements on the electric motor, falling weights or whatever drives the paddle. 

A picture of the paddle-wheel apparatus used by Joule can be seen at http //www.sciencemuseum.0rg.uk/galleryguide/E3011.asp). 

Once water has entered the pond, it loses its identity as stream or rain water. The pond does not contain any identifiable stream water or rain water, simply water. Similarly systems do not contain so much heat or work, just energy. Just as the water level in the pond can be raised either by stream water alone or by rain water alone. Joule showed in the nineteenth century that a temperature rise in a water bath of so many degrees can be caused either by heating (transferring energy due to a temperature difference) or by thrashing a paddle wheel about... 

The first law is based mainly on the series of experiments carried out by Joule between 1843 and 1848. The most familiar of these experiments is the one in which he raised the temperature of a quantity of water, almost completely surrounded by an adiabatic wall, by means of a paddle which was operated by a falling weight. The result of this experiment was to show an almost exact proportionality between the amount of work expended on the water and the rise in its temperature. This result, considered on its own, is not very significant the really important feature of Joule s work was that the paddle-wheel experiments gave the same proportionality as was obtained in several other quite different methods of transforming work into the temperature rise of a quantity of water. These were as follows ... 

Joule s apparatus contained the paddle wheel shown in Fig. 3.12. It consisted of eight sets of metal paddle arms attached to a shaft in a water-fiUed copper vessel. When the shaft rotated, the arms moved through openings in four sets of stationary metal vanes fixed inside the vessel, and churned the water. The vanes prevented the water from simply moving around in a circle. The result was turbulent motion (shearing or viscous flow) in the water and an increase in the temperature of the entire assembly. 

This problem guides you through a calculation of the mechanical equivalent of heat using data from one of James Joule s experiments with a paddle wheel apparatus (see Sec. 3.7.2). The experimental data are collected in Table 3.2. 

For the purposes of the calculations, define the system to be the combination of the vessel, its contents (including the paddle wheel and water), and its lid. All energies are measured in a lab frame. Ignore the small quantity of expansion work occurring in the experiment. It helps conceptually to think of the cellar room in which Joule set up his apparatus as being effectively isolated from the rest of the universe then the only surroundings you need to consider for the calculations are the part of the room outside the system. 

The paddle wheel vessel had no thermal insulation, and the air temperature was slighter warmer, so during the experiment there was a transfer of some heat into the system. From a correction procedure described by Joule, the temperature change that would have occurred if the vessel had been insulated is estimated to be -1-0.317 K. 

Here we have used 1 cal = 4.184 J (a calorie is worth many jewels ) due to some amazing work by James Prescott Joule. Joule [3] performed a careful experiment measuring the increase in temperature of water caused by a rotating a paddle wheel driven by falling weights in a measurable way. Modem recreations of the experiment produce the value of 4.184 J/cal. Note the work on the gas is negative. Then we use the first law equation to find the heat change. 

Joule s falling-weight-paddle wheel-tank device was one of the first calorimeters, devices for measuring heat quantities by measuring the temperature increase of a known mass of some reference substance, almost often water. Most of our data for the changes of u and s with changes in temperature are based on measurements made in more refined versions of Joule s calorimeter. We most often report such information in terms of the heat capacity,... 

In the following year (1845) Joule read, to the British Association meeting at Cambridge, an account of a new method of determining the mechanical value of heat. A paddle-wheel, driven by the same mechanism of falling weights that he had used tb provide power for his dynamo in 1843, rotated horizontally in a calorimeter full of water. A comparison of the heat generated with the work performed yielded a mechanical value... 

The way ahead was now, at last, clear for Joule. He had soldiered on and had won through to recognition and acceptance. In 1850 the Royal Society published his account of new and very accurate paddle-wheel experiments which gave the figure of 772 ft.lbs for the mechanical value of a unit of heat. From this time onwards Joule could extend and consolidate his theory, devise even more accurate methods for determining his constant, and find further instances of the great principle of the convertibility of energy in nature." (Cardwell, pp.232-236)... 

To get some idea about the experimental difficulties, and required accuracy, in the temperature measurements of Joule s work, let us assume that in the paddle-and-wheel experiment (Figure 2.2) ... 

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