Measurement of Thermal Conductivity of a Solid

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The figure shown above is that of the Searle's apparatus to measure the thermal conductivity of a solid. The solid is taken in the form of a cylindrical rod. One end of the rod goes into a steam chamber. A copper tube is coiled around the other end of the rod. A steady flow of water is maintained in the copper tube. Water enters the tube at the end away from the steam chamber and it leaves at the end nearer to it. Thermometers T₃ and T₄ are provided to measure the temperatures of the outgoing and incoming water. Two holes are drilled in the rod and mercury is filled in these holes to measure the temperature of the rod at these places with the help of thermometers T₁ and T₂. The whole apparatus is covered properly with layers of an insulating material like wool or felt, so as to prevent any loss of heat from the sides.

Steam is passed into the steam chamber and a stream of water is maintained. The temperatures of all the four thermometers rise initially and ultimately become constant when the steady state is reached. The readings q₁, q₂, q₃, and q₄ are noted in steady state.

A beaker is weighed and the water coming out of the copper tube is collected in it for a fixed time t, measured by a stopclock. The beaker is weighed along with the water that has been collected in it. The mass m of the water collected, is then calculated. The area of cross-section of the rod is calculated by measuring its radius with a slide caliper. The distance between the holes in the rod is measured with the help of a divider and a meter scale.

Let the length of the rod between the holes be x and the area of cross-section of the rod be A. If the thermal conductivity of the material of the rod is k, the rate of heat flow (heat current) from the steam chamber to the rod is

In a time t, the chamber supplies a heat

As the mass of the water collected in time t is m, the heat taken by the water is

------(ii)

where s is the specific heat capacity of water.

As the entire rod is covered with an insulating material and the temperature of the rod does not change with time at any point, any heat given by the steam chamber must go into the flowing water. Hence, the same Q is used in (i) and (ii). Thus,

Black body radiation

Consider two bodies of equal surface areas suspended in a room. One of the bodies has a polished surface and the other is painted black. After sufficient time, the temperature of both the bodies are equal to the room temperature. As the surface areas of the bodies are the same, equal amount of radiation falls on the two surfaces. The polished surface reflects a large part of it and absorbs very little, while the black surface reflects very little and absorbs a large part of it. As the temperature of each body remains constant, we conclude that the polished surface radiates at a slower rate and the black surface radiates at a faster rate. Therefore, good absorbers of radiation are also good emitters.

A body that absorbs all the radiation falling on it is called a black body. The radiation inside an enclosure with its inner walls maintained at a constant temperature has the same properties as the black body radiation. A black body is also called an ideal radiator. A perfect black body, absorbing 100% of the radiation falling on it, is only an ideal concept. Among the materials, lampblack is almost a black body. It reflects only about 1% of the radiation falling on it. If an enclosure is painted black from inside and a small hole is made in the wall (as in the figure below) the hole acts as a very good black body.

Any radiation that falls on the hole goes inside. This radiation has little chance to come out of the hole again and gets absorbed after multiple reflections. The cone directly opposite to the hole ensures that the incoming radiation is not directly reflected back to the hole.