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ture is 32.765° C.: find the latent heat of steam at 160° C. Matric. 1883.

117. The specific heat of mercury is .03. A pound of steam at 100° C. is made to pass into a vessel containing 300 lbs. of mercury initially at o° C., the capacity for heat of the vessel being equal to 10 lbs. of water : what will be the temperature of the vessel and contents at the end of the experiment? Matric. 1884. 118. Distinguish between calorimetry and thermometry.

20 grammes of steam at 100° C. are condensed in a metal worm surrounded by 200 grammes of water at 10° C. If the water equivalent of the worm be 10 grammes, and the latent heat of steam be 536, determine the temperature to which the water is raised.

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Matric. 1886.

in a closed It is found,

119. I lb. of ice at 10° C. is placed vessel, and steam at 100° C. passed into it. after making the necessary corrections, that when the ice is just melted the resulting water weighs 1.134 lbs.; and that when the temperature has risen to 100° C., it weighs 1.345 lbs. The specific heat of ice is 5 find the latent heats of water and steam. Camb. B.A. 1878.

CHAPTER V

CONDUCTIVITY AND THERMODYNAMICS.

Conductivity.

The thermal conductivity (or coeffi cient of conductivity) of a substance is measured by the number of units of heat which pass in unit time across unit area of a plate whose thickness is unity, when its opposite faces are kept at temperatures differing by one degree. In the statement of this definition it is supposed that the flow of heat has become steady, and that the lines of flow of heat are perpendicular to the surfaces of the plate.

The thermal conductivity of a substance, in the C.G.S. system, is measured by the quantity of heat which flows per second, under these circumstances, across one square centimetre of a plate one centimetre in thickness, the opposite faces of the plate being kept at temperatures differing by 1° C.

The quantity of heat (H) which flows in a given time across a plate of given dimensions is inversely proportional to the thickness (d) of the plate, and is directly proportional to the area of its surface (s), to the difference of temperature (0) between its opposite faces, and to the time t. If the thermal conductivity of the substance be denoted by k,

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1. A large tank is covered with a layer of ice 6 cm. thick and 24 square metres in area: assuming that the

coefficient of conduction of ice in C.G.S. units is 0.0057, determine the amount of heat transmitted per hour from the water up through the ice, the upper surface of which is at the temperature of the air, viz. — 10° C.

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In order that the answer may be given in gramme-degrees of heat, we must express all quantities in terms of the corresponding C.G.S. units. Thus s = 24 sq. metres = 240,000 sq. cm., and t=60 minutes = 3600 seconds. Substituting these values in equation (1), we have

H=0.0057 × 240,000 × 10 × 3600/6

= 8,208,000 units.

2. The top of a steam chamber is formed of a stone slab 6 decimetres long, 5 decimetres broad, and I decimetre thick. Ice is piled upon the slab, and it is found that 5 kilogrammes of ice are melted in half an hour: what is the thermal conductivity of the stone?

Since the latent heat of fusion of ice is 80, the amount of heat required to melt 5 kilogrammes of ice is

H = 5 x 1000 x 80 = 400,000 heat-units.

This amount of heat is transmitted in 1800 seconds through a slab of 60 × 50 = 3000 sq. cm. area and 10 cm. thickness, its opposite faces being kept at 0° and 100° degrees respectively. Thus

and

400,000 = k × 3000 × 100 × 1800/10,
k=4/540=0.00741.

3. The coefficient of conduction of copper is 0.96: how many heat-units will pass per minute across a plate of copper 1 metre long, I metre broad, and 1 cm. thick, when its opposite faces are kept at temperatures differing by 10°?

4. The wall of a cottage is 2 decimetres thick, and is built of stone whose thermal conductivity is 0.008; the temperature inside the cottage is 18°, while the outside temperature is 2°: how much heat is lost by transmission per hour across each square metre of the wall?

5. It is found that 1.44 × 107 heat-units are transmitted per hour across an iron plate 2 cm. thick and 500 sq. cm. in area, when its opposite sides are kept at o° and 100° respectively: what is its coefficient of conductivity?

6. An iron boiler is made of plate o.8 cm. thick, and its total surface is 8 square metres: the water inside is at a temperature of 120°, and the external surface of the boiler is at 95°. Assuming that the thermal conductivity of the iron is o.164, find how much heat is lost by conduction per hour.

7. A metal plate, I sq. decimetre in area and 0.5 cm. thick, has the whole of one face covered with melting ice, while the other face is in contact with boiling water. The coefficient of conductivity of the metal is 0.14: how many kilogrammes of ice will be melted in an hour?

8. "In a solid, heat may be transmitted from point to point in two ways, and in a fluid in three ways." Discuss this statement, and comment upon the following facts: When a sheet of glass is held in front of a hot stove it appears to cut off the heat given out by the stove; but when the sun shines upon the glass windows of a greenhouse the heat passes readily through without producing any considerable change in the temperature of the glass itself. Explain carefully how it is that the air inside the greenhouse may in this way become hotter than the outside air.

9. An iron vessel containing a kilogramme of ice is partially immersed in a tank of water at 15°, so that the total area of the immersed surface is 400 sq. cm. The mean thickness of the wall of the vessel is 0.8 cm., and exactly one minute after immersion all the ice is found to have melted. Calculate from this the thermal conductivity of iron, and discuss the validity of any assumptions made in your solution.

10. Péclet states that the quantity of heat which passes in an hour through a plate of lead 1 square metre

in area and 1 metre thick, with a difference of 1o between the temperatures of its surfaces, is 13.83 kilogrammedegrees what value does this give for the C.G.S. coefficient of conductivity for lead?

11. Point out the experimental difficulties which would be met if you attempted to carry out practically the idea contained in the definition of conductivity given on p. 137. Describe the principle and the general results of Forbes's experiments, indicating how the calculations were made; and find the value of the multiplier for reducing to the C.G.S. system coefficients of conductivity expressed in kilogramme-degrees per square metre, per millimetre, per second.

Mechanical Equivalent of Heat. -The amount of work which is equivalent to one heat-unit is called the mechanical equivalent of heat. Its value was determined by Joule (whence it is sometimes called "Joule's equivalent "), and is denoted by the letter J.

=

Joule found that 772 foot-pounds of work were required to raise the temperature of a pound of water through one degree Fahrenheit; the corresponding number in terms of the degree Centigrade is 772 x 9/5, or 1389.6. Since I foot 30.48 cm., the mechanical equivalent is 1389.6 × 30.48 = 42355 gramme-centimetres per gramme-degree, or about 424 kilogramme-metres per kilogramme-degree of heat.1 To convert this into absolute measure we have to multiply by g (=981), which gives 42355 × 981, or 4.155 × 107 ergs per grammedegree.

More recent experiments have shown that the number

1 Observe that the value of J is not affected by a change in the unit of mass employed, for it is a ratio between an amount of work and a corresponding amount of heat, and the unit of mass is involved in the same degree (i.e. to the first power) in the units of work and heat. On this account the usual statement that the mechanical equivalent of heat is 1390 foot-pounds" is somewhat misleading.

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