273 degrees Centigrade lower, then the volume of a constant mass of gas will always be proportional to its temperature, provided that the pressure is maintained constant throughout. Hence the connection will be expressed by

m V volume =✪ temperature.

The temperature 273 degrees Centigrade below the freezing point of water is called the absolute zero of temperature. It means the temperature at which the pressure or the volume of a mass of gas would vanish, on the supposition that the same rate of expansion held throughout which holds for the gaseous state.

EXAMPLES.

Ex. 1. 500 cubic centimetres of oxygen gas are measured when the temperature is 20° C., and the temperature is then raised to 40° C., the pressure meanwhile remaining constant. What is the volume of the oxygen at the latter temperature? The coefficient of the expansion of oxygen per degree Centigrade is

Ex. 2. Find the mass of 1,000 cubic centimetres of dry air at 80° C. and the pressure of 25 cm. of mercury. 1,000 cubic centi

metres of dry air at 0° C. and 76 cm. pressure have a mass of

1.293 grammes.

By Art. 134,

=

1.293 gm. per 1000 cc. at 0° 76 cm. pressure,

1. A given mass of air occupies a volume of 600 cubic inches at the temperature of 20° C.; find the volume which the air will occupy at 100° C., supposing the pressure to remain constant.

2. A mass of gas occupying a volume of 273 cubic inches at 0° C. is raised in temperature to 150° C. If it be allowed to expand under constant pressure during the process, what will be its new volume?

3. One hundred cubic centimetres of air at 0° C. are heated to 300° C. under constant pressure. What will be the volume of the air at the higher tem

perature?

4. A thousand cubic inches of air at the temperature of 30° C. are cooled down to zero, and at the same time the external pressure upon the air is doubled. What is its volume reduced to?

5. Find the temperature to which 500 cubic centimetres of air, measured at 15° C. must be raised in order that the volume of the air may become 700 cubic centimetres, no change of pressure taking place meanwhile.

6. Twenty litres of air are taken at 16° C. and 74 cm. pressure; find the volume of the air at 0° C. and 76 cm. pressure.

7. One thousand cubic inches of gas are taken when the barometer stands at 30.5 inches, and the temperature is 16° C. Find the volume of this gas when the pressure is 29.5 inches and the temperature 12°.

8. Find the absolute zero on the Fahrenheit and on the Réaumur scale. 9. A substance, of the approximate specific gravity 3-2, weighs 180 grammes in dry air of 730 reduced mm. pressure and temperature of 16° C. Also the approximate specific gravity of the weights against which it is weighed is 8.5. Find the real weight of the substance, assuming that the weight of one litre of dry air at 0° C. and 760 reduced millimetres pressure is 1.293187 grammes.

SECTION XLV.—THERMAL CONDUCTIVITY.

ART. 200.-Conductivity. By the thermal conductivity of a substance is meant the rate connecting the current of heat with the gradient of temperature, when there is a steady flow of heat through the substance. It is expressed in the form

k H per T per S cross-section = → per L normal.

By "normal" is meant unit of length along the line of flow, and "per L normal" expresses what is called the gradient of temperature, after the analogy of gradient of gravity (Art. 72). The reciprocal idea is thermal resistance; it is expressed by 1/kper L normal = H per T per S cross-section.

When the unit of heat is a dynamical unit, we have conductivity expressed in terms of

For example, by

W per T per

S= per L.

=

erg per sec. per sq. cm. deg. Cent. per cm.; or, which is the same thing, by

erg per sec. per sq. cm. per (deg. Cent. per cm.). When the unit of heat is a thermal unit, we have M of water by → per T per S=→ per L;

for example, gm. of water by deg. Cent. per sec. per sq. cm. = deg. Cent. per cm. A value, expressed in terms of this kind of unit, is independent of the magnitude of ; for enters to the same power in the two members of the equivalence. When the units are allowed to cancel one another as much as possible, there remains M/TL, which expresses the dimensions of the unit.

ART. 201.-Thermometric Conductivity. Suppose that the conductivity of a substance is

k M of water by per T per S = per L,

and that the density of water is

P M =V;

then, by substitution,

k

ρ

V of water by → per T per S=✪ per L.

Suppose further that the specific heat of the substance, referred to volume, is

s V of water = V of substance;

then, by a second substitution,

k

sp

V of substance by → per T per

S=→ per L.

The idea here expressed is called by Clerk-Maxwell the thermometric conductivity of a substance.*

Its dimensions, if a systematic unit, are

L2/T.

THERMAL CONDUCTIVITY.

k (gm. of water by deg. Cent.) per sec. per cm.2 per (deg. Cent. per cm.). Range from 0° C. to 100° C.

ART. 202.-Relative Conductivity and Resistance. Let the conductivity of two substances A and B be

and

Then

and

therefore

Ꮎ

1/k2 S per L of B = H per T per ; k/ka S per L of BS per L of A.

This is the form for expressing the relative resistance in terms of the cross-section and length of the conductor.

The reciprocal is

k/kL per S of B = L per S of A ; and it expresses the relative conductivity.

EXAMPLES.

Ex. 1. How much heat is transmitted per day per square metre of surface, across a slab of rock 10 centimetres thick, whose sides differ in temperature by half a degree Centigrade, supposing the conductivity of the rock to be 004? The centimetre is the unit of length, and the unit of heat is the quantity of heat required to raise the temperature of one gramme of water one degree. ⚫004 gm. of water by deg. Cent. per sec. per sq. cm.

i.e., 1·728 × 105 gm. of water by deg. Cent. per day per sq. metre.