22. 30 grammes of iron nails at 100° are dropped into 60 grammes of water at 13°.2, and the final temperature is 18°.6. What is the specific heat of the

nails?

23. If you had at your command a supply of boiling water and of tap-water at 10°, what quantities of each would you take in order to prepare a bath containing 20 gallons of water at 35° ?

24. A 7-lb. iron weight was taken out of an oil-bath and immediately immersed in 10 lbs. of water at 8°, whereupon the temperature rose to 20°. If the specific heat of iron is 0.112, what was the temperature of the oil-bath?

This suggests a method of measuring high temperatures, such as those of furnaces: how would you carry it out practically?

25. Equal volumes of turpentine at 70° and of alcohol at 10° are mixed together: find the resulting temperature.

[Sp. gr. of turpentine = 0.87, of alcohol = 0.80. Sp. heat of turpentine = 0.47, of alcohol = 0.62.] Let be the volume taken, and the resulting temperature. The mass of the turpentine is 0.87v, and the amount of heat which it evolves in cooling from 70° to 0° is v x 0.87 × 0.47(70 - 0). This is entirely spent in warming a mass 0.8% of alcohol from 10° to 0°, for which operation vx0.8x0.62 (0-10) heat-units are required. Equating these quantities, we have

Thus

and

0.87 x 0.47(700)=0.8 x 0.62(0-10).

28.623+4.960 × (0·496 +0·4089),

0=33.583/0.9049,

=37°.11.

26. The densities of two substances are as 2 to 3, and their specific heats are 0.12 and 0.09 respectively compare their thermal capacities per unit volume.

27. Assuming that the density of boiling water is 0.96, and that the density of mercury at o° is 13.6, calculate the resulting temperature when equal volumes of boiling water and mercury at o° are mixed.

28. The specific heat of air at constant pressure is 0.237, and a litre of air weighs 1.293 gramme: how much heat is given out by 50 litres of air in cooling from 25° to 5° ?

29. Hot air at 650° is used for superheating steam which is originally at 100°. The air and steam are kept at constant pressure during the operation, under which circumstances their specific heats are 0.237 and 0.48 respectively, and they are introduced into the superheater in the proportion of 2 lbs. of air to 7 lbs. of steam. If the air is allowed to cool to 400°, to what temperature I will the steam be raised?

30. Three liquids, A, B, and C, are at temperatures of 30°, 20°, and 10° respectively. When equal parts (by weight) of A and B are mixed, the temperature of the mixture is 26°; and when equal parts by weight of A and C are mixed, the temperature is 25°. Prove that a mixture of equal parts of B and C will have a temperature of 16°.

Let Sa, Sp, and S, denote the specific heats of the liquids A, B, and C respectively. The equation for the amounts of heat evolved and absorbed when equal parts of A and B are mixed reduces to

If be the temperature of a mixture of equal parts of B

31. 10 grammes of a liquid at 90° were mixed with an unknown quantity of a second liquid of specific heat 0.25 and temperature 16°; the resulting temperature was 43°.75. If the specific heat of the first liquid was 0.45, what was the weight of the second?

32. A liquid of specific heat 0.54 and temperature 29° is mixed with another liquid of specific heat 0.36 and temperature 11°, and the final temperature was 17°. In what proportions were the liquids mixed?

33. Equal weights of three liquids, whose specific

heats are S1, S2, and ავა and temperatures t1°, t2°, and t°

respectively, are thoroughly mixed: find the temperature of the mixture.

34. In order to find the specific heat of absolute alcohol, a quantity of it was boiled in a test-tube, and poured at its boiling - point (78°.5) into a calorimeter containing 74 gm. of turpentine at 10°.6. The calorimeter was weighed before and after the addition; the gain of weight was 14.7 gm., and the final temperature was 25°.2. Find the specific heat of the alcohol, that of the turpentine being 0.466.

What advantage was there in using turpentine in this experiment ?

35. 200 c.c. of water at 55° is poured into a copper calorimeter whose mass is 30 gm. and specific heat 0.095. Assuming that the calorimeter was previously at the temperature of the air, viz. 10°, and that the whole of the heat evolved by the water in cooling is

absorbed by the copper, find the temperature to which the water is cooled.

36. 10 grammes of a metal were taken for a specific heat determination, and by a preliminary experiment it was found that the rise of temperature was insufficient, being only 3°.7. The quantity of water in the calorimeter was reduced by one-third: what weight of the metal should now be taken to produce a rise of 12°, the other conditions remaining the same?

37. 40 gm. of water at 45° were poured into a leaden crucible weighing 300 grammes, which had previously been standing in a room the temperature of which was 16°. The water was cooled to 39°•46: what is the specific heat of lead?

38. In two experiments made to determine the sp. heat of lead shot, the water equivalent of the calorimeter was 1.3, and that of the thermometer was 0.5. You are required to find the mean value from the results given, allowing for the heat absorbed by the calorimeter and thermometer.

39. Describe the method employed by Regnault in determining the specific heats of gases at constant pressure, explaining in detail the construction of the heating apparatus and calorimeter, and the means adopted for obtaining a current of the gas at an uniform pressure.

40. If the quantity of heat required to raise unit mass of a substance from o° to t° be represented by

Qt=at+bt2+ct3,

show that the mean specific heat of the substance between and t° is given by

41. Regnault found that 100.5 units of heat were required to raise the temperature of unit mass of water from o° to 100°, and 203.2 to raise its temperature to 200°; taking the specific heat of water at o° as unity (i.e. putting a 1 in the preceding equations), prove that the true specific heat of water at any temperature t, between o° and 200°, is given by the equation

St=1+0.00004t + 0·000000912.

Show also that the true specific heat of water at 150° is 1.02625.

2. Change of State and Latent Heat.

Note. The latent heat of water is 80, and the latent heat of steam is 536.

42. How would you show that heat is absorbed when common salt is dissolved in water?

Anhydrous calcium chloride eagerly absorbs water, and dissolves in it with evolution of heat; whereas when crystallised chloride of calcium is dissolved in water, the temperature falls. How do you explain these facts?

43. A quantity of common salt is mixed with water, both being at o° C. After solution the temperature is found to be below o°, and if melting ice be employed instead of water, the fall in temperature is still more marked. Explain these results.

44. A glass flask is filled with a mixture of ice and water, and a narrow tube with an india-rubber stopper is fitted into the neck so as to force the water up to a certain height in the tube; the flask is then immersed in lukewarm water. State exactly what will be observed in the tube.