CALORIMETER

THE CALORIMETER

the water mass equivalent to the calorimeter

The calorimeter of Regnault (or of mixtures) is an instrument that it allows to measure the amounts of heat yielded or absorbed from a substance or a body during a physical or chemical process, and the thermal property of the substances (specific heat, heats of combustion,..).
It's constituted from a thermally isolated container, in which they are made to happen thermodynamic processes controlling the variations of the inner temperature in relation to the several ones is made of the same processes.
For example it can be used in order to determine the heat amounts, like that specific one, of the solid and the liquids.
The apparatus is composed from a vase of Dewar, container whose covering is constituted from three layers: that most external in wood, inside an insulating material like the fiber or the cotton, and a silver-plated covering that allows to limit the loss of heat, which it is not transmitted only for conduction but also for radiation.
The cover, in synthetic matter, introduces two holes that concur the passage with the inside of the system of a thermometer and a mixer; to the base of the thermometer the heat spillage is limited from a pierced rubber stopper, inserted perfectly in a practiced conical hole in the cover.
The little cruet of mercury is completely immersed in the liquid inside the calorimeter; the instrument is legible to the outside of the vase of Dewar. The use of an electronic thermometer would have been more indicated but also that thermometer used, of mercury, has one good precision (sensibility 0,1°C).
The agitator is fixed in a metallic girdle, to the inside of which it is free to slide towards the high and the bottom; moreover it is supplied inferiorly of a thin mesh gas mantle, of wire. The use of the agitator allows to maintain uniform the temperature inside the same vase.
Moreover the cover is supplied of two motivatings force of implantation, that they allow a greater adhesion of the cover with the rest of the object, if coupled opportunely to two eyelets screwed in the support, therefore ulteriorly diminish the loss of heat towards the surrounding atmosphere.
Inside there is a known volume of water in which a metal body is turn completely dipped .

MEASURE OF THE SPECIFIC HEAT

the instrument

specific heat

the water mass equivalent to the calorimeter

The observations on the thermal exchanges carry to the considerations that the increasing of the amount of heat yielded from a body increase its temperature;if two bodies of the same substance, but different mass, maintain the same temperature, they yield two various amount of heat (in particular the object biggest yields more heat), and therefore to equality of conditions, the quantity of heat yielded from a body depends on the nature of the same body. The specific heat is a specific property of the substances and it can be found through the following espression:

where Q is the heat yielded from the body of mass m when the temperature diminishes of Δt degrees, and c is a constant characteristic of the considered substance, that is the SPECIFIC HEAT of the body .
The specific heat is the amount of heat necessary in order to raise of 1°C, 1g of one determined substance. It is the number of calories that the body has. The specific heat of water is 1 cal/g°C. This is the unit of measure in the system cgs with which the specific heat is measured , in system S.I. we can use J/Kg°K. Instead, the thermal capacity is the amount of heat necessary in order to raise of 1°C the mass of one substance, C=Q/t (cal/°C in cgs, J/°K in S.I.).
In reality specific heat does not exist because it depends on the various conditions in which the object is. For solids and liquids we can suppose that the champion was to constant pressure ( 1 atm), instead the gases have various values in condition of constant pressure and volume. Therefore the use of the calorimeter of Regnault for the search of this value is right.

Considering inside of the instrument a water amount (ma), its temperature, called tf, is approximately 20°C. Moreover we used an object, whose mass is mc and whose temperature is tc.
After warm the champion in hot water, if we introduced it inside of the calorimeter, it will yield heat to the water, according to the second principle of the thermodynamic; the energy exchange will finish when the temperatures of the champion and the water coincide (te). The heat absorbed from the water is:

where te indicates the temperature of equilibrium to the term of the exchange of heat between the champion and the water. Moreover we know that the specific heat of the water is 1; therefore the formula will be reduced to

The heat yielded from the champion will be instead

According to the second principle of thermodynamic, the heats correspond to the same value therefore is possible campair all the two expression

Isolating the specific heat of the champion we will obtain:

THE WATER MASS EQUIVALENT TO THE CALORIMETER

the instrument

specific heat

the water mass equivalent to the calorimeter

The result obtained in the previous paragraph does not hold account of the dispersion of heat absorbed from the instrument. Therefore we must find how much the calorimeter influences the measure.
The correction is possible carrying out an other preliminary calculation.
Introducing inside of the system an amount of water (ma) at ambient temperature (tf), if as much water mass, mc, is added (mc=ma, convention that allows to simplify the calculation) at elevated temperature (tc), we will obtain a temperature of equilibrium, called te.
In this case the yielded heat will correspond to

While the absorbed heat will be

indicating with me the water mass represented the instrument that influences on the dispersion of the heat yielded from the warm water. Equaling the two formulas we will obtain that the mass equivalent to the calorimeter is

If we take different mass of water, indicating ma the hotter water mass and mb the other, and calling tc the first themperature and tf the second one, we can obtain me with:

(for a faster calculation is possible find me using the program

)

During the execution of the experiment it has not been possible to carry out such measure so we used the value of me that the manifacturing company associates to the instrument, that is of 5 g, to which we associated an error of 0,1 g, sensibility used also to the other masses considered during the execution of the experiment.