。° C. If at 30° the mark is 0.0255 cm. from the end of the iron rod, what is the coefficient of expansion of copper, that of iron being 0.000012?

Univ. Coll. Lond. 1886.

103. Distinguish between the absolute and the apparent expansion of mercury contained in a thermometer.

The coefficient of absolute (cubic) expansion of mercury is .00018, the coefficient of linear expansion of glass is 000008. Mercury is placed in a graduated glass tube, and occupies 100 divisions of the tube. Through how many degrees must the temperature be raised to cause the mercury to occupy 101 divisions?

Matric. 1883.

104. How is the apparent related to the absolute expansion of a liquid?

A glass bottle holds 1359.6 grammes of mercury at the temperature of melting ice. If the temperature be raised to that of boiling water, how much mercury will be expelled from the bottle, the coefficient of apparent expansion of mercury in the glass being 0.000154 ?

Matric. 1886.

105. A glass bottle holds at o° C. 10169.3 grains of mercury, while at 100° C. it only holds 10011.4 grains. Assuming that the dilatation of mercury between oo and 100° is .018153, find the coefficient of cubical expansion of the glass bottle.

Owens Coll. 1886.

106. Describe some method by which the expansion of water has been studied.

If 8 be the expansion of water between 4° and o° C., and ▲ its expansion between 4° and ť°, show what is the density of water at t° referred to water at o°•

Int. Sc. 1884.

It should be noticed that the change of volume is positive on either side of 4°, because water expands on cooling from 4° downwards. Thus if unit volume of water be taken at 4°, its volume at o° will be (1 + d), and at t° will be (1 + ▲). Let do and de represent the densities of water at o° and t°

respectively. Since the mass of water remains the same, the product of the volume into the density remains constant.

107. Given the absolute expansion of mercury between two fixed temperatures, show how to determine the absolute expansion of a liquid between these temperatures by means of a weight thermometer about which nothing is previously known.

Thermometers constructed with liquids A, B agree with a mercurial thermometer at temperatures O° T°, 0° T'° respectively. Find at what temperature on the mercurial thermometer they give the same reading, having given Apparent expansion of A= a1t+at2,

B=b1t+b2t2,

where t is measured on the mercurial thermometer.

Oxford 1885.

108. A solid weighs 320 grammes in vacuo, 240 grammes in distilled water at 4° C, and 242 grammes in water at 100° C., of which the density is 0.959. Find the volume of the solid at these two temperatures, and deduce therefrom its mean coefficent of cubical expansion for 1° C. Int. Sc. 1876.

109. Describe carefully some method of measuring the coefficient of expansion by heat of a solid substance.

The apparent mass of a piece of glass weighed in water at 4° is 25 grammes, its real mass being 37.5 grammes; its apparent mass when weighed in water at 100° is 25.486 grammes. The coefficient of cubical expansion of glass per 1° C. is .000026. Show that the volume of 1 gramme of water at 100° C. is 1.043 cubic centimetres.

Ind. C. S. 1886.

110. Iron is 7.8 times as dense as water when they are compared at 4° C. What are their relative densities at 100° C.? The coefficient of linear expansion of iron

is 0.000012, and the expansion of water between 4° and 100° is 0.043 of the volume at 4°.

Prel. Sc. 1886.

111. The weight of a body in air is 10k, in water at 4° is 9.49998k, and in water at 10° is 9.50007k: find the coefficient of expansion of the body and its density, given that I c.c. of water at 4° becomes 1·00025 c.c.

at 10°.

Balliol Coll. 1881.

112. A solid is weighed in a liquid at o° C. and 100° C. The volume of the solid at o° C. is unity and at 100° C. 1.006. Also the loss of weight by weighing in the liquid is, at o° C., 1800 grains, and at 100° C., 1750 grains. Find the coefficient of dilatation of the liquid. Int. Sc. Honours 1877.

113. Suppose that the proportional cubical internal expansion of a glass sp. gr. bottle between o° and 100° C. is .00235, while the similar expansion of mercury is 018153. Suppose also that, when the bottle contains a piece of iron weighing 2000 grains, the remainder of it will contain 6707.8 grains of mercury at o° C., while at 100° C., under these circumstances, it will only contain 6599.4 grs. Finally, assume that the sp. gravities of mercury and iron at 100° C. are 13.2 and 7.8 respectively. Determine the cubical dilatation of iron between 0° and 100° C. B. Sc. 1877.

114. Experiments on the expansion of benzene gave the following results :

Show that the coefficient of expansion can be represented by the formula a+bt, and determine the values of the constants a and b. B. Sc. 1884. 115. Determine the height of the barometer when a milligramme of air at 27° C. occupies a volume of 20

cub. cm. in a tube over mercury, the mercury standing 73 cm. higher inside the tube than outside. (I gramme of air at o° C. under a pressure of 76 cm. of mercury measures 773.4 cub. cm.) Int. Sc. 1885.

Let / denote the height of the barometer, then the pressure of the air in the tube over mercury is h-73. At this pressure, and at 27°, a milligramme of air measures 20 c.c., whereas at o° and 76 cm. pressure it measures 0.7734 c. c. By equation (9), p. 102, we have

...h−73=76× 0.7734 × 300/20 x 273 = 3.23,

and the required barometric height is 76.23 cm.

116. How may the relation between the pressure and temperature of a given mass of air at constant volume be determined?

at o° C. and

What will be

A quantity of air occupies 10 cubic feet under a pressure of 20 inches of mercury. its volume at 30° C. and under a pressure of 1200 inches of mercury?

Matric. 1884.

117. Explain accurately what is meant by the statement that the coefficient of expansion of air is 1/273. The volume of a certain quantity of air at 50° C. is 500 cubic inches. Assuming no change of pressure to take place, determine its volumes at 50° C. and at 100° C. respectively. Matric. 1887.

118. What is meant by saying that the absolute temperature of a gas is 300° C.? If the absolute temperature be 260° C., what is the temperature in the Centigrade scale ?

One

Two condensers contain equal quantities of air. of them at temperature 47° C. is 30 in. long, 20 in. broad, and 10 in. high; and the other at 57° C. is 30 in. long, 25 in. broad, and 81 in. high. pressure of the air is the same in both.

Show that the

Camb. B.A. 1883.

119. A vessel contains air at o° C. and at atmospheric

pressure.

It is heated to 100° C., and during the process one ounce of air escapes. How many ounces of air were there originally in the vessel, the expansion of the vessel itself being neglected? The coefficient of expansion of air at constant volume is 1/273.

Matric. 1886.

120. A given quantity of a gas is made continually to occupy the same space. Explain what changes will take place in its pressure when changes take place in its temperature.

A straight vertical tube, the section of whose bore is one inch, is closed at its lower end, and contains a quantity of air which supports an air-tight piston whose weight is 1 lb. The position of the piston is observed when the temperature of the air is 31° C., and the weight of the piston is then increased by 1 lb. Find what increase of temperature will be required to bring back the piston to its former position, the atmospheric pressure being 15 lbs. per square inch, and the absolute zero of the air thermometer being - 273° C.. Camb. B.A. 1884.