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125. Þ:p=g/3: 93. 126. 71.93 cm. 127. 360 lbs. per sq. in.; 3.6 in.

128. As 1:1.306. 129. 1.395 gm.

130. Pressure = 2 atmospheres. 131. 96.6 cm. 132. It will descend 1.2 in. 133. :$' =r:r. 135. 54:1 cm. 136. The tube should have been raised until a length of 80 cm. stood out of the mercury. 138. 68.85 cm.

139. About 18 cm. 140. f cub. in. 142. (1) 34.2 C.c.; (2) 87 c.c. 144. 4:34 ft. 145. 4:49 ft. 146. It must be lowered until its top is 66 ft. below the surface. 148. 164:3 cub. ft. ; 80.3 in. 149. 0.876 in. 150. The jar must be sunk until its mouth is 33.64 ft. below the surface. 152. Dn= (3/4)10D=0.05631D. 154. 0.4363 gm.

155. 0.741 gm.

158. 260 kgm.

EXAMINATION QUESTIONS

159. See Ch. VII, p. 172. 164. See p. 58 ; pres

166. Whole pressure sure = 2379.3 gm. per sq. cm. = 3750 lbs.; resultant pressure = 625 lbs. 167. A force equal to the weight of 320 lbs. 172-175. See pp. 62, 63, and Ex. 171. 189. See Ex. 137.

CHAPTER III-HEAT

1. Expansion of Solids.

4 2.0068 metres ; 150° 5. 153.86 cm. 6. 0.0432 in. 7. 263.16 cm. 8. 87.2464 cm. 9. 1.00095 yard. 10. 22.128 cm. 11. Coefficient of expansion = 0.00008 ; temperature = 260°. 12. 100 cm. 13. 0.02864 in.

14. 0.0144 sq. ft. 15. 0.01764 ft. 17. 300.912 sq. cm. 18. 1.00649 metre. 19. 36 cm. 20. When the pendulum keeps correct time (i.e. at 5°), it swings 86,400 times per day (supposing it to be a seconds pendulum ; see p. 30). At 30° its length is increased in the ratio of 1.0003 : 1, and it now swings 86,400 V 1/1.0003 times per day. Referring to p. 19, it will be seen that VI/1.003 = 1/1.000 15 = 1 – 0.00015 approximately. Therefore the clock loses 86,400 x 0.00015 12.96 secs. per day. 21. It will gain 20:52 secs. per day. 23. The required temperature is 196°:4, and the common length at this temperature is 251.424 cm. 24. 12°. See § it for this and the next example, 25. Increase in volume= 2.592 cub, in. 27. 10:22. 28. 48.373 c.c.

2. Expansion of Liquids. - 29. 0.00002797. 33. 0.000302. 34. 0.000301. 37. 0.0001817. 38. 103°.8. 45. 0.0001 558. 46. The coefficient of

apparent expansion of the mercury is 0.000 1546, and this gives 0.0000274 as the coefficient of expansion of the glass. 47. 1.57 C.C.

48. 132°:3 49. 1099.65. 50. 9.517 gm.

54. The volume of the solid is 12.9752 c.c. at 10°, and 12.9914 c.c. at 95°; .. its coefficient of expansion is o.o000 1468.

3. Expansion of Gases.—58. 3.187 litres ; 54°:6. 59. (1) 11.16 litres; (2) 12:38 litres. 60. 221.978 c.c. 61. 0.10231 gm.

62. 333°. 63. 69.63 cm. at oo; 95.12 cm. at 100°.

64. 2190.1 C.C. 65. 0.00367. 66. 77o.6. 69. 18°.74. 70. The temperature must rise from 10° to 57°.16. 71. 322.6 c.c.

77. As 1:0.9269. 78. 998.9 c.c. 79. 10:47 atmospheres. 80. As I:0.7808. 81. As 1 : 2.256. 82. The temperature must fall to – 2°}. 84. 0.599 gm.

85. 924.9 kgm. 86. 11.66 litres. gm. 88. 0.3743 gm.

90. 1991 C.C.

91. 37.98 in.; at 459o.5. 92. As I : 1:02. 93. The temperature must rise to 7o.18. 94. (1):(2)=1:0:891. 95. 299o. 96. 91°.8. 99. 139.65.

87. 11.97

EXAMINATION QUESTIONS 100. The lengths must be inversely proportional to the coefficients of expansion. 101. Observe that the

coefficient of superficial expansion is approximately double the coefficient of linear expansion ; see Introduction, $11. 103-105. See footnote, p. 92. 108-113. See Exs. 51 and 53. 117. For “50° C.” in the last line read “ – 50° C.”

CHAPTER IV-SPECIFIC AND LATENT HEAT

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1. Specific Heat.-5. 76,800 heat units.

7. 1995 units. 8. 4,804,800 units.

9. 11.875. 11. 0.208. 12. Temperature = 17°:14. 13. 88°.

14. As 1:0.453. 15. 22,666. 17. 0.0313. 18. 0.0962. 19. o.615. 20. 9°:49. 21. 0.0556. 22. 0.1327. 23. 55 gals. of boiling water, and 14 gals, of tap-water. 24. 173°.1. 26. As 8:9. 27. 68o. 28. 306.4 units. 29. 135°:3. 31. 30 gm.

32. In the proportion of 1 to 3. 33. (siti +592 +5g63)/(sı + sz+sz). 34. 0:6426. 35. 54°:37. 36. 21.6 gm.

37. 0.0315.

38. Exp. I., sp. ht. = 0.03097; Exp. II., sp. ht. = 0.03185; mean value=0.03141. 40. Express Qt and Qt' in terms of a, b, and c: the difference between these (Qt' – Qt) is equal to the mean sp. ht. (S') multiplied by the difference of temperature (ť t). Again, let this interval become indefinitely small; in the limit coincides with t, and the mean sp. ht. between t° and to becomes the true sp. ht. at t° (St).

2. Latent Heat.–48. 6.25 gm. 49. 1of lbs. 51. 176.5 gm. 52. 8o. 53. 54 lbs.

54. 1•125 gm. 55. 79.5.

56. 0.0941. 57. 0.1148. 59. 15,544.8 pound-degree units. 60. 11,312 of the same units; 5966.2 lbs. 63. 1.5 lb. 64. 0.5625 lb. of ice will be melted, and the result will be a mixture of ice (0.4375 lb.) and water (1.5625 lb.) at oo. 65. The temperature will be lowered by 17°.5 (i.e. to 7°:5). 66. 10 lbs. of water at 18° 67. The snow will be

melted and raised to 10°. 69. 3.26 gm. 70. 3/16 of the water will be frozen. 73. Contraction = 0.17 c.c. 74. 888.8 units. 75. Contraction=0.102 I C.C. 76. Contraction

0.0214 C.C. 77. Sp. heat 0.07655. 78. Sp. gr. of ice = 11 =0.916. 79. Ice melted=0.0873 gm. ; sp. heat of substance = 0.0814.

87. Vapour-pressure 6.55 mm.; relative humidity =0.55 (or 55 per cent).

90. 31,200.

91. 21,480 units. 92. 6.29 lbs. 93. 536.3 94. 37:31. gm. 95. As 1 : 5.

97. 541.

98. 25.04.

EXAMINATION QUESTIONS

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100. The amount of heat required to raise a volume v of mercury through to is Q= =V x 13.6 x 0.033t. To raise an equal volume of alcohol through to would require an amount Q' = =V x 0.85 st. Thus

Q' 0.855

Q 13.6 x 0.0330.528' and ... Q'>= <Q according as s> = <0.528.

102. The heat will be divided in the ratio of 1 : 12.5, and the rise of temperature will be 1°.85. 104. Notice that the thermal capacity (8) of the copper vessel must be added to that of the cold body (the milk). heat of the milk is 0.934. 110-112. See pp. 127, 128. 113. See Deschanel, Natural Philosophy, Part ii. S 435.

The sp.

CHAPTER V-CONDUCTIVITY AND THERMODYNAMICS

1. Conductivity. — 3. 5,760,000. 4. 230,400 units. 5. 0:16. 6. 1.476 x 1010 units. 7. 126 kgm. 9. 0.019. 10. 0.0384. 11. The multiplier for reducing to the C.G.S. system is o.01.

2. Thermodynamics. — 14. 7.44 gramme-degrees. 15. 1390 ft. 16. 1.905 x 1010 ergs. 17. 678 metres. 18. 0°:7155 warmer. 19. 4480 gramme-degrees; 194 metres per sec. 20. 2010:16 watts.

21. 85,714 gm. 22. Work done = 3,68 3,500 ft.-Ibs.; rate of working 24,557 ft.-lbs.

per min. 24. 6.77 x 109 ergs. 25. 362.46 metres per sec. 26. The engine is of 67 H.P., and its efficiency is 0.106 (or 10.6 per cent). 29. 24,396 units. 33. 2.87 x 108 ergs. 34. The work done is 2124 ft.-Ibs., and the heat - equivalent of this would suffice to raise 1.528 lb. of water through 1° C. 36. J= 4.2 x 107

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EXAMINATION QUESTIONS

38. Taking as units the pound, the inch, and the second, the absolute conductivity is 0.00002893 41. Efficiency 3.37 % ; heat wasted 96.63 % 42. See Ex. 13. 44. 1258.7 lbs. 45. Work done = 1.25 X 107

ergs.

47. Work done = 2.85 x 107 ergs.

CHAPTER VI-LIGHT

3. 4:41 candle-power. 4. As 16:1.

5. (1) i ft. from candle, between this and the lamp ; (2) 2 ft. on other side of candle. 8. 5 images. 13. 45°. (Notice that the successive angles of incidence diminish by 15o.) 21. p=90 in.; image is 5 in. long. 23. f= + 15 cm. (concave). 24. 8 in. 25. 30 in. behind the mirror; magnification=6. 26. fri ft. i in.; mirror must be placed i ft. from object. 27. (1) Image is virtual and inverted, 4 in. behind mirror, fin. in length; (2) image 8 in. behind mirror, } in. in length. 28. p=18 in., Þ' = 36 in.; image would be half size of object. 30. The image is real and twice the size of the object; the magnification is the same when p=f/2, but in this

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