Page:Elementary Text-book of Physics (Anthony, 1897).djvu/210

196 in the calorimeter. The whole will soon come to a common temperature $$\theta.$$ The heat lost by the substance is $$Pc(t' - \theta)$$ calories. The heat gained by the calorimeter is the sum of that gained by the water and that gained by the materials of which the calorimeter is constructed. If $$p$$ represent the mass of water, and $$p'$$ the water equivalent of the calorimeter, or the mass of water which will rise by the same temperature interval as the calorimeter vessel does on the introduction of a given quantity of heat, the total heat gained by the calorimeter is $$(p + p')(\theta - t');$$ and hence from which $$c$$ may be determined. The water equivalent $$p'$$ is determined by experiment.

There is a source of error in the use of the instrument, due to the radiation of heat during the experiment.

This error may be nearly eliminated by making a preliminary experiment to determine what change of temperature the calorimeter will experience; then, for the final experiment, the calorimeter and its contents are brought to a temperature below the temperature of the surrounding air, by about half the amount of that change. The calorimeter will then receive heat from the surrounding medium during the first part of the experiment, and lose heat during the second part.

The rise of temperature is, however, much more rapid at the beginning than at the end of the experiment. The rise from the initial temperature to the temperature of the surrounding medium occupies less time than the rise from the latter to the final temperature. The gain of heat, therefore, does not exactly compensate for the loss. If greater accuracy be required, the rate of cooling of the calorimeter must be determined by putting into it warm water, the same in quantity as would be used in experiments for determining specific heat, and noting its temperature from minute to minute. Such an experiment furnishes the data for computing the loss or gain by radiation. To secure accurate results the body must be transferred from the bath to the calorimeter without sensible loss of heat.