SPECIFIC AND LATENT HEAT 1. Specific Heat. 1. A COIL of copper wire weighing 45.1 gm. was dropped into a calorimeter containing 52.5 gm. of water at 10°. The copper before immersion was at 99°.6, and the common temperature of copper and water after immersion was 16°.8. Find the specific heat of the copper wire. The quantity of heat (Q) given out by a body of mass m and specific heat s in cooling through an interval of temperature 0 is Q = ms0. Thus if s denote the specific heat of the copper, the amount of heat evolved by it in cooling from 99°.6 to 16°.8 is 45.1 × s × (99.6 – 16.8). Since the specific heat of the water is unity, the amount of heat required to raise its temperature from 10° to 16°.8 is 5.2.5 × 1 × (16.8 – 10), and as no heat is supposed to be gained or lost these two quantities are equal. and ... 45.1 × s× 82.8 = 52.5 × 6.8, 2. What is the temperature of an iron ball weighing 5 lbs., which, when immersed in 8 lbs. of water at 13o, raises the temperature to 48°? The specific heat of iron is 0.112. If the temperature of the ball before immersion was t°, the number of heat-units 1 which it gives out, in cooling to the final temperature of 48°, is 5 × 0.112 × (t − 48). 1 Since specific heat is merely a number, or a numerical ratio between quantities of heat, it is independent of the unit of I Assuming that no heat is gained or lost during the experiment, this must be equal to the number of heat-units absorbed by the cold water, i.e. to 8 × (48 - 13). Equating these two quantities, we have 5 × 0.112 × (t −48) = 8 × (48 − 13), ... 0.56t=8 × 35 + (0.56 × 48), and = 280+26.88=306.88, t=548°. 3. In order to determine the specific heat of silver, a piece of the metal weighing 10.205 gm. was heated to 101°.9 and dropped into a calorimeter containing 81.34 gm. of water, the temperature of which was raised from 11°.09 to 11°.71. The water equivalent of the calorimeter, agitator, and thermometer employed was 2.91 gm.: find the specific heat of the silver. The heat evolved by the hot body is 10.205 × SX (101.9 11.71), where s is the sp. heat of the silver. The heat is partly absorbed by the water and partly by the calorimeter, etc., and these are together equivalent to (81.34 +2.91) gm. 84.25 gm. Since these are raised from 11°.09 to 11.71, the heat absorbed is 84.25 (11.71 - 11.09). Equating these quantities, we have and mass (or weight) employed; and this is also true for latent heat. In the statement or solution of a problem it is a matter of indifference whether we take as our unit of mass the pound, the kilogramme, or the gramme, provided that we use this unit consistently, the corresponding units of heat in the three cases being the pound-degree (or amount of heat required to raise one pound of water through 1o C.), the kilogramme-degree, and the gramme-degree. The last, which is the C. G. S. unit, is sometimes called a "calorie," and Berthelot distinguishes the kilogramme-degree from this by calling it a "Calorie" (1 Calorie = 1000 calories). 4. The same piece of silver was heated to 102°.2 and immersed in 75.3 gm. of turpentine at 10°.98: the experiment was performed with the same apparatus as in Ex. 3, and the final temperature was 12°.47. Calculate the specific heat of the turpentine. Taking the sp. heat of the silver as 0.05677, the amount of heat which it gives out is 10.205 × 0.05677 × (102.2 – 12.47) = 51.97. Of this, 75.3 × × (12.47 - 10.98) is absorbed by the turpentine, s being its sp. heat; and the calorimeter absorbs 2.91 × (12.47 – 10.98) = 4.336. Equating the amounts of heat absorbed and emitted, 51.97 = (75.3 × 5 × 1·49) + 4·336, 5. A certain vessel holds 800 c.c. of water at its temperature of maximum density (4°). How much heat must be imparted to the water before it begins to boil? 6. Define specific heat. A body of mass M and specific heat S at a temperature T° is dropped into a mass m of a liquid of specific heat s at t°: prove that the final temperature is 7. How many units of heat are required to raise the temperature of 150 grammes of copper (of specific heat 0.095) from 10° to 150°? 8. What amount of heat must be given to an iron armour-plate 2 metres long, I metre broad, and 20 cm. in thickness, in order to heat it from 10° to 140°? [Sp. gr. of iron, 7.7; sp. heat, o.112.] 9. The thermal capacity (or water equivalent) of a body being defined as the product of its mass into its specific heat, calculate the capacity for heat of a copper calorimeter of 125 grammes. What special name is given to the thermal capacity of unit mass of a substance? 10. A body of mass M at a temperature T° is dropped into a mass m of a liquid of specific heat s contained in a calorimeter of mass m' made of a substance of specific heat s', both the calorimeter and the liquid being at ť°: if the final temperature is 0, prove that the specific heat of the solid is [Expressions such as those developed in Examples 6 and 10 are convenient when a number of similar problems have to be solved, or in calculating the results of actual laboratory examples where corrections have to be applied; but the student will find that in general it is best to work out problems in specific and latent heat directly by equating the quantities of heat evolved by the hot body and absorbed by the cold body, as in the solved examples 1-4.] 11. Find the specific heat of a substance 100 grammes of which at 90°, when immersed in 250 grammes of water at 12°, gave a resulting temperature of 18°. 12. What is meant by the statement that the specific heat of water is thirty times the specific heat of mercury? If a kilogramme of mercury at 120° is poured into a vessel containing 200 gm. of ice-cold water, what will be the temperature after the whole is mixed? How would the weight and material of the vessel affect the result? Note.-In Examples 13-16 the specific heat of mercury is to be taken as 1/30. 13. Two pounds of boiling water are poured upon ten pounds of mercury at 16°: what will be the common temperature after mixing? 14. Compare the thermal capacities of equal volumes of water and mercury, the density of mercury being 13.6. 15. A flask containing half a litre of mercury at o° is immersed in boiling water, and allowed to remain there until the mercury has attained the temperature of the water: how many heat - units does it gain from the water? 16. Equal masses of boiling water and of mercury at - 5° are mixed together: prove that the resulting temperature is 96°.65. 17. A kilogramme of mercury contained in a glass flask is heated by immersing the flask in a beaker of boiling water; it is then poured into a large flask containing 500 c.c. of water at 10°, and after shaking thoroughly the temperature is found to be 15°.3: find the specific heat of mercury. What errors would probably occur in carrying out these operations, and how would they influence the result? 18. 35 grammes of copper are heated to 98°.5 and mixed with 30 grammes of water at 10°.3. The temperature of the mixture is found to be 19°.2: what is the specific heat of copper? 19. 61 ounces of water are mixed with 100 ounces of alcohol, and the final temperature is found to be midway between the two initial temperatures: what is the specific heat of alcohol? 20. A pound of boiling water is allowed to cool down to 10° if all the heat given out were employed in warming 40 pounds of air, initially at o°, to what temperature would it be raised? [Sp. heat of air =0.237.] 21. Calculate the specific heat of silver from the following data : |