Part 109

Since the materials of which the bomb is composed have a specific heat different from that of water, it is necessary to compute the water thermal value of each apparatus.

The hydrothermal equivalent of the whole apparatus is most simply determined by immersing it at a given temperature in water of a different temperature. With small apparatus this method is quite sufficient, but there are many difficulties attending its application to large systems weighing several kilograms. In these cases the hydrothermal equivalent may be calculated from the specific heats of the various components of the apparatus.

In calculating these values the specific heats of the various components of the apparatus are as follows:

Brass 0.093 Steel 0.1097 Platinum 0.0324 Copper 0.09245 Lead 0.0315 Oxygen 0.2389 Glass 0.190 Mercury 0.0332 Hard rubber 0.33125

Example.—It is required to calculate the hydrothermal value of a calorimeter composed of the following substances:

Hydrothermal value. Steel bomb and cover, 2850 grams × 0.1097 312.65 grams. Platinum lining, capsule and wires, 120 grams × 0.0324 3.89 ” Lead washer, 100 grams × 0.0315 3.15 ” Brass outer cylinder, 500 grams × 0.093 46.50 ” Mercury in thermometer, 10 grams × 0.0332 0.33 ” Glass (part of thermometer in water), 10 grams × 0.19 1.90 ” Brass stirring apparatus (part in water), 100 grams × 0.093 9.30 ” ------ Total water value of system 377.72 ”

When a bomb of 300 cubic centimeters capacity is filled with oxygen at a pressure of twenty-four atmospheres it will hold about ten grams of the gas, equivalent to a water value of 2.40 grams. Hence the water value of the above system when charged, assuming the bomb to be of the capacity mentioned, is 380.12 grams.

If the cylinder holding the water be made of fiber or other non-conducting substance, its specific heat is best determined by filling it in a known temperature with water at a definite different temperature.

It is advisable to have the water cylinder of such a size as to permit the use of a quantity of water for the total immersion of the bomb which will weigh, with the water value of the apparatus, an even number of grams. In the case above, 2622.28 grams of water placed in the cylinder will make a water value of 3,000 grams, which is one quite convenient for calculation.

=565. Computing the Calories of Combustion.=—In the preceding paragraph has been given a brief account of the construction of the calorimeter and of the methods of standardizing it and securing the necessary corrections in the data directly obtained in its use. An illustration of the details of computing the calories of combustion taken from the paper of Stohmann, Kleber and Langbein, will be a sufficient guide for the analyst in conducting the combustion and in the use of the data obtained.

Weight of substance burned, 1.07 grams.

Water value of system (water + apparatus), 2,500 grams.

Preliminary thermometric readings, t₁ = 26.8; t₂ = 27.2; t₃ = 27.7; t₄ = 28.1; t₅ = 28.5; tₙ₁ = 28.9.

Thermometric reading after combustion, Θ₁ = 28.9; Θ₂ = 202; Θ₃ = 213; Θ₄ = 214.2; Θₙ = 214.0.

Final thermometric readings, tʹ₁ = 214.0; tʹ₂ = 213.8; tʹ₃ = 213.6; tʹ₄ = 213.5; tʹ₅ = 213.3; tʹ₆ = 213.1; tʹ₇ = 212.9; tʹ₈ = 212.7; tʹ₉ = 212.6; tʹ₁₀ = 212.4; tʹₙ₂ = 212.2.

From the formulas given above the following numerical values are computed:

v = 0.42. vʹ = -0.18. t = 27.9. tʹ = 213.1. n = 5.

ⁿ⁻¹ Θ₂ - Θ₁ ∑ Θr = Θ₁ + Θ₂ + Θ₃ + Θ₄ + ------- = 667. ₁ 9

Substituting these values in the formula of Regnault-Pfaundler, the value of the correction for the influence of the external air is

0.42 - (-0.18) 214 + 29 ∑ Δt = [--------------- (677 + --------- - (5 × 27.9)) 213.1 - 27.9 2

- (4 × 0.42)] = 0.45,

which is to be added to the end temperature (Θₙ = 214.0).

The computation is then made from the following data:

Corrected end temperature (Θₙ + 0.45) 214.45 = 15°.3699 Beginning temperature (Θ₁) 28.90 = 12°.8406 Increase in temperature 185.55 = 2°.5293 Total calories 2.5293 × 25000 = 6323.3 Of which there were due to iron burned 9.1 ” ” ” ” nitric acid dissolved 8.2 Total calories due to one gram of substance 5893.5

The thermometric readings are given in the divisions of the thermometer which in this case are so adjusted as to have the number 28.90 correspond to 12°.8406, and each division is nearly equivalent to 0°.014 thermometric degree.

The number of calories above given is the proper one when the computation is made to refer to constant volume. By reason of the consumption of oxygen and the change of temperature, although mutually compensatory, the pressure may be changed at the end of the operation. The conversion of the data obtained at constant volume referred to constant pressure may be made by the following formula, in which [Q] represents the calories from constant volume and Q the desired data for constant pressure, O the number of oxygen atoms, H the number of hydrogen atoms in a molecule of the substance, and 0.291 a constant for a temperature of about 18°, at which the observations should be made.

H Q = [Q] + (--- - O) 0.291. 2

=566. Calorimetric Equivalents.=—By the term calorie is understood the quantity of heat required to raise one gram of water, at an initial temperature of about 18°, one degree. The term ‘Calorie’ denotes the quantity of heat, in like conditions, required to raise one kilogram of water one degree.