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. 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 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 × 1000 × 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 x 100 x 1800/10, 3. The coefficient of conduction of copper is 0.96: how many heat-units will pass per minute across a plate of copper I 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 0° 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, 1 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 o.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 I metre thick, with a difference of 1° 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 × 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. which we have given is somewhat too low. As the third significant figure of this important constant has not been determined with any accuracy, we shall adopt in our calculations the approximate value J = 4.2 × 107. [It should be noticed that all the above numbers-772, 424, etc. —with the exception of the last, give the value of J in gravitation measure, and care should be taken to make the required conversion into absolute measure (or vice versa) where it is necessary. In working problems relating to potential energy, or the energy of bodies falling from a height, it is convenient to use gravitation measure; but it is preferable to work in absolute measure throughout.] The energy of a body of mass m moving with velocity v is mv2/2 in dynamical measure (pp. 35-38). The thermal equivalent of this is mv2/2J. Suppose the body to meet an obstacle and to fall dead. Also let s denote its specific heat, and let us assume that all the heat developed by its impact goes to raise its temperature through (say) 0°. The amount of heat required to produce this rise of temperature is ms0. Thus Similarly, if the body be raised to a height h above the ground, its potential energy is mgh ergs, and the thermal equivalent of this is mgh/J. If the body falls to the ground, and if we suppose that all the heat produced by the arrest of its motion is spent in warming it, the rise of temperature produced will be 0=gh/Js. In both cases the elevation of temperature is independent of the mass of the body. 12. A leaden bullet of specific heat 0.032 strikes against an iron target with a velocity of 400 metres per second. If the bullet falls dead, and the heat produced is equally divided between it and the target, find its temperature, supposing it originally at 10°. If the mass of the bullet be m, its kinetic energy is (40,000)2 xm/2, and the equivalent of this in heat-units is (40,000)2 × m/2 × 4.2 × 107 = 80m/4·2. Half of this goes to heat the bullet. temperature produced is 0°, then and 40m/4.2= = m × 0.0320, 0=40/4.2 x 0.032 = 298. Suppose the rise of Since the bullet was originally at 10°, its temperature after striking the target is 308°. 13. In obtaining work from an engine at the rate of 20 H.P., 56 lbs. of coal are consumed per hour: find the efficiency of the engine, assuming that the heat produced by the combustion of 1 lb. of coal is sufficient to convert 15 lbs. of water at 100° into steam at the same temperature. The efficiency of a steam engine is the ratio between the useful work performed and the work represented by the heat of combustion of the fuel. The work done per minute by the engine is 20 × 33,000 = 660,000 ft. -lbs. The combustion of 1 lb. of coal produces 15 × 536=8040 thermal units. Since 56 lbs. of coal are consumed per hour, the amount of ' heat evolved per minute is 56 × 8040/60=7504, which is equivalent to 7504 × 1390=10,430,560 ft. lbs. E=66000/10430560=0.06328 14. How much heat is set free when a body of mass |