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XXVI. On the Determination of Thermal Conductivity and Emissivity. By N. EUMORFOPOULOS, B.Sc., Demonstrator in Physics, University College, London*.
F a long metallic bar of uniform cross-section be heated at one end, and be left long enough to acquire a steady state, the distribution of temperature along it is usually expressed by
ux = uje
where u, is the excess of temperature over surroundings of a point on the bar at a distance from the point whose excess of temperature is uo, a being measured positively along the direction of decreasing temperatures;
hand k are the emissivity and conductivity respectively;
is the periphery of the bar, and s the cross-section.
If the bar be of circular cross-section and r its radius, the above expression reduces to
that is, if two bars have at one point of each the same temperature uo, they will also have the same temperature u, at distances a and a respectively, measured from these points, and such that
If the bars are of different radii, but of the same material, and we accordingly write h1=h, and k1=k2, we get
Some time ago Prof. G. C. Foster suggested to me, as a laboratory exercise, to undertake the verification of this relation.
The method adopted was to heat the ends of two such rods in steam until they had acquired the steady state, and then by means of two thermoelectric joints (one on each rod) to find a series of isothermal points.
With two brass rods of radii r1=34 and r2=2.6 mm. respectively, the distances at which equal temperatures were * Communicated by the Physical Society: read January 11, 1895.
Similar experiments with copper rods gave:
r1=3·35 mm., r2=2.45 mm.
Another set of experiments with the same rods gave :—
To ascertain whether the copper rods really consisted of the same metal, their specific electrical resistances were compared. The result was
Assuming that the ratio of thermal conductivities was the same as that of electrical conductivities, this gives
as the calculated ratio of the distances at which equal temperatures should be found, instead of 60 and 55, the mean ratios actually found in the two sets of experiments already mentioned.
In order to test the trustworthiness of the method employed, one of the above rods was heated in the middle under the same conditions as before, and isothermal points found on each side of the heated portion. The results were satisfactory, as the following numbers show :
At this point the experiments were abandoned for a time. They were subsequently resumed, when a Bunsen burner was used as the source of heat, in order to have a greater range of temperature. In the experiments mentioned before, and also in these, no screens were employed, a sheltered part of the laboratory being used. The following are some of the results obtained :
mean of five
Making =10·3 cm., 1= 11·95 cm. as a
mean of a large number of experiments, making x=10·0 cm., x1 was found to be 11.68 cm., or
The arrangements were then slightly changed, so as to experiment on a hotter part of the rod, with the following result as a mean of a series of experiments :
x=100 cm., x1=11·86 cm. ; or
The ratio of specific electrical resistances for these rods was
found to be 95; assuming this as the ratio of ką to k1,
the mean result found by experiment being 0.85.
It is to be noted that there is not so much difference between the radii of the two rods as there was in the other
Brass Rods, being the rods previously experimented on. x1=65 mm.;
x=47.3 mm. (mean of three determinations).
x=33 mm. (mean of three determinations).
Brass Rods. These are two new rods, which were used in experiments to be described later.
1=3.21 mm., 72=1·69 mm.,
As a mean result of a series of experiments, for a1⁄2=5 cm., a was found to be 7.96 cm. ; or
It must be pointed out, however, that with the Bunsen burner the parts of the rod nearest the flame become visibly oxidized, this being especially noticeable in the case of the thicker rod-so much so that the increased emissivity so obtained can apparently overcome the greater transmission of heat of the thicker rod. Thus, with the above brass rods, 5 cm. on the thinner rod were found equivalent in this region to 5.2 cm. on the thicker; and after the heating had continued for some time 37 cm. on the thicker rod balanced 5 cm. on the thinner one. The ratio given above, 63, is for parts of the rods that were not oxidized, and did not become so after several days' heating.
It will be seen that in every case the rate of fall of temperature along the thinner of the various pairs of rods compared is more rapid than would be inferred according to the usual formula from the distribution of temperature observed along the thicker rod. Consequently this formula cannot be legitimately used for the comparison of conductivities, unless the radii of the rods compared are equal and their surfaces in the same condition.
The only way of escaping from this conclusion is by supposing that the thermal conductivity of the smaller of each pair of rods was less than that of the thicker one. Although it seemed very unlikely that this should be so in the case of every pair, it could not be regarded as impossible. To settle the matter, it was decided to determine the absolute conductivity of at least one pair of rods.
For this purpose Angström's method was adopted, in which one end of the rod is alternately heated and cooled, and the alternations of temperature observed at two points along the rod. Fig. 1 is a diagram of the apparatus used. CD is the rod, passing into a glass tube E, through which cold water or steam can be passed as desired. E is held up by a clamp, and F is a clamp supporting the rod at the other end, no other clamps being used for the rod. S1, S2, S3, S are brown-paper screens, about 2 ft. high, resting on the table and open at the top; S, is about 14 ft. wide. A and B are the two points whose temperatures have to be measured. This was done by fine iron wires passing over the rod at the required point, and held down by suitable weights. The wires pass to a key K, through the galvanometer G, to a vessel H containing cold water. H contains the other junction, and a thermometer T. A brass wire connects D to H. T2 is a thermometer reading the temperature of the air. Both thermometers were divided into fifths and read by a telescope.
As it was not possible to keep the temperature of the air constant, allowance had to be made for the change. As the