1899. SUBJECT VIIIC. HEAT. EXAMINERS : PROFESSOR A. W. RÜCKER, M.A., SEC.R.S., PROFESSOR W. GRYLLS ADAMS, M.A., D.Sc., F.R.S., AND PRINCIPAL R. T. GLAZEBROOK, M.A., F.R.S. GENERAL INSTRUCTIONS. If the rules are not attended to, your papers will be cancelled. You may take the Advanced Stage, or Part I. of Honours, or (if eligible) Part II. of Honours, but you must confine yourself to one of them. The marks allotted to each question are given in brackets. You are to confine your answers strictly to the questions proposed. Your name is not given to the Examiners, and you are forbidden to write to them about your answers. The examination in this subject lasts for three hours. Advanced Stage. INSTRUCTIONS. Read the General Instructions above. You are permitted to answer only seven questions. 41. Describe the experiments you would make to prove that for a gas at constant temperature pv is constant, p being the pressure and v the volume of the gas. In a certain gas pv is observed to decrease slightly as the pressure rises. Show that the resistance to compression is less than it would be if Boyle's law held. (28.) 42. A barometer tube is filled with mercury up to within one inch of the top. After inversion the air expands and occupies 12 inches of the tube, and the mercury stands 27 inches in the tube above the level of the mercury in the trough; find the true height of the barometer. (28.) 43. Determine, having given the following data, from what height a lead bullet must be dropped, in order that it may be completely melted by the heat generated by the impact, assuming that four-fifths of the heat generated remains in the bullet. Heat required to raise 1 gramme of lead from the initial temperature of the bullet to the melting point, and to melt it, 15 units. Mechanical equivalent of heat 42 × 106 ergs. Value of 9, 980 cm. per sec. per sec. (28.) 44. Describe an experiment to show that water can be frozen by its own evaporation. Under what circumstances may the freezing point of water and its boiling point coincide? Discuss the consequences of such an arrangement. (28.) 45. Define the critical temperature, pressure, and volume of a vapour, and give some account of the behaviour of a substance near its critical point. (28.) 46. A rod heated at one end has reached a steady state of temperature and the curve of temperature is known. The rate of loss of heat of the surface for different temperatures is also known. Show how to determine the conductivity of the rod from these data. (30.) 47. Explain the method of using Bunsen's ice calorimeter to determine specific heats. (28.) 48. Write a short essay on the methods of maintaining refractory gases in the liquid state for relatively long periods of time, and on the uses to which they may then be put. (28.) 49. Describe fully the arrangements you would make in order to compare the scales of the electrical resistance thermometer and of the air thermometer. (30.) HONOURS-PART I. Read the General Instructions on page 1. You are not permitted to answer more than five questions. 71. A rod heated at one end has reached a steady state of temperature, and the curve of temperature is known. The rate of loss of heat of the surface for different temperatures is also known. Show how to determine the conductivity of the rod. и 8274. H (60.) 72. Write a short essay on the methods of maintaining refractory gases in the liquid state for relatively long periods of time, and the uses to which they may be put. (60.) 73. Describe Regnault's method of determining the specific heat of a gas under constant pressure, and state the general results obtained. (60.) 74. Give an account of experiments on the conduction of heat in crystals and discuss the results obtained. (60.) 75. Prove the law connecting the temperature and volume of a mass of perfect gas undergoing adiabatic compression. How many degrees will dry air at 15° C. and normal pressure rise if it be suddenly compressed to one-fourth its volume? Take the ratio of the specific heats as 1·4. (60.) 76. State and explain on thermodynamic principles the effect of squeezing a mixture of ice and water. (60.) 77. A wire 1 cm. in diameter carrying a current of 10 ampères is found to reach a steady temperature of 100° C. Assuming the specific resistance of the material as 2.1 × 10-4 ohms. per cm. cube and the value of J as 42 × 106 ergs, determine the amount of heat emitted at 100° C. by a square centimetre of the surface. (60.) HONOURS-PART II. PAPER 1. NOTE.-No Candidate is eligible for examination in Part II. of Honours who has not obtained a pass in Honours-Part 1. in 1898, or a 1st or 2nd Class in Honours of the same subject in a previous year. INSTRUCTIONS. Read the General Instructions on page 1. You are not permitted to answer more than five questions. Candidates who do well in Paper I. will be summoned to South Kensington to undergo a further examination, which will consist of (1) another paper, and (2) a practical examination in the laboratory. 101. Show that the equilibrium vapour pressure over a spherical drop of water whose radius is a exceeds the pressure over aqueous vapour, σ that of water, and T the surface tension of the drop. (40.) 102. Show that if the stiffness of a spiral spring decreases as the temperature rises the spring will be cooled by stretching. (40.) 103. Give a critical account of methods which have been devised for the measurement of very high temperatures. (40.) 104. Write a short essay on the characteristic equation of Van der Waals. (40.) (40.) 105. Describe the radiomicrometer of Professor Boys. 106. Investigate the coefficient of thermal conductivity of a gas on the hypothesis of the mechanical theory. (40.) 107. Give an account of and discuss investigations which have been carried out on the variations in the specific heat of water with change of temperature. (40.) HONOURS-PART II. PAPER II. INSTRUCTIONS. You are not permitted to answer more than five questions, of which one must be in Section A. SECTION A. 131. Write an essay on the history of the doctrine of the conser vation of energy. 132. Write an essay on modern thermometry. SECTION B. (40.) (40.) 133. Apply the second law of thermodynamics to show how to determine the absolute zero of temperature from observations on the rise of temperature of a gas when forced through a porous plug. (40.) 134. Give an account of researches made to determine the density of saturated steam. (40.) 135. Obtain on the Kinetic theory of gases an expression for the coefficient of viscosity of a gas. (40.) 136. Describe some accurate method of measuring the thermal emissivity of a wire. (40.) 137. If the relation between the pressure, volume, and temperature of a gas be that given by Van der Waals equation, (p+ (v - B) RT, v2 where R is constant and a B are small constants: show that to the first order of small quantities the velocity of sound U is given by HONOURS (PART II.). PRACTICAL EXAMINATION. 1. Determine the freezing point of the given liquid. 2. Find the specific heat of the given liquid by the method of cooling. 3. Given a Leslie tube and a thermopile, determine the reflecting power, at an angle of incidence of 45°, of the given surface for heat rays. 4. Plot a curve showing the relation between the boiling point of the solution and the percentage of the given salt dissolved in water. 5. Determine the vapour tension of the given liquid at 0° C. |