THE CLERMONT AND THE LEVIATHAN This page shows the relative sizes of Robert Fulton's Clermont, the first successful steamboat, and the Leviathan, the largest strides have been made toward it. Forty years ago the lowest temperature which had ever been measured was - 110° C., the temperature attained by Faraday in 1845 by causing a mixture of ether and solid carbon dioxide to evaporate in a vacuum. But in 1880 air was first liquefied and found, by means of a gas thermometer, to have a temperature of - 190° C. When liquid air evaporates into a space which is kept exhausted by means of an air pump, its temperature falls to about 220° C. Recently hydrogen has been liquefied and found to have a temperature at atmospheric pressure of 243° C. All of these temperatures have been measured by means of hydrogen thermometers. By allowing liquid hydrogen to evaporate into a space kept exhausted by an air pump, Dewar in 1900 attained a temperature of - 260°. In 1911 Kamerlingh Onnes liquefied helium and attained a temperature of 271.3° C., only 1.7° above absolute zero (see § 217). QUESTIONS AND PROBLEMS 1. Define 0° C. and 100° C. What is 1° C.? 1° F.? 2. From a study of the behavior of gases we conclude that there is a temperature at which the molecules are at rest and at which bodies therefore contain no heat. Give the reasoning that leads to this conclusion. 3. Normal room temperature is 68° F. What is it centigrade? 4. The normal temperature of the human body is 98.6° F. What is it centigrade? 5. What temperature centigrade corresponds to 0° F.? 6. Mercury freezes at about 40° F. What is this centigrade? 7. The temperature of liquid air is 190°C. What is it Fahrenheit? 8. The lowest temperature attainable by evaporating liquid helium is 271.3° C. What is it Fahrenheit? 9. What is the absolute zero of temperature on the Fahrenheit scale? 10. Why is a fever thermometer made with a very long cylindrical bulb instead of a spherical one? 11. When the bulb of a thermometer is placed in hot water, it at first falls a trifle and then rises. Why? 12. How does the distance between the 0° mark and the 100° mark vary with the size of the bore, the size of the bulb remaining the same? 13. What is meant by the absolute zero of temperature? 14. Why is the temperature of liquid air lowered if it is placed under the receiver of an air pump and the air exhausted? 15. Two thermometers have bulbs of equal size. The bore of one has a diameter twice that of the other. What are the relative lengths of the stems between 0° and 100°? EXPANSION COEFFICIENTS 163. The laws of Charles and Gay-Lussac. When, as in the experiment described in § 159, we keep the volume of a gas constant and observe the rate at which the pressure increases with the rise in temperature, we obtain the pressure coefficient of expansion, which is defined as the ratio between the increase in pressure per degree and the value of the pressure at 0° C. This was first done for different gases by a Frenchman, Charles, in 1787, who found that the pressure coefficients of expansion of all gases are the same. This is known as the law of Charles. When we arrange the experiment so that the gas can expand as the temperature rises, the pressure remaining constant, we obtain the volume coefficient of expansion, which is defined as the ratio between the increase in volume per degree and the total volume of the gas at 0°C. This was first done for different gases in 1802 by another Frenchman, Gay-Lussac, who found that all gases have the same volume coefficient of expansion, this coefficient being the same as the pressure coefficient, namely, 1/273. This is known as the law of Gay-Lussac. From the definition of absolute temperature and from Charles's law we learn that, for all gases at constant volume, pressure is proportional to absolute temperature; that is, Also, from Gay-Lussac's law we learn that, for all gases at constant pressure, volume is proportional to absolute temperature; V T (3) If pressure, temperature, and volume all vary,* we have Any one of these six quantities may be found if the other five are known. 1 If the volume remains constant, that is, if V, V, equation (4) reduces to (2), that is, to Charles's law. If the pressure remains constant, P, = P, and equation (4) reduces to (3), that is, to Gay-Lussac's law. If the temperature does not change, T and equation (4) reduces to P1V1 = PV2, that is, to Boyle's law. If the ratio of densities instead of volumes is T、 V 1 2 D sought, it is only necessary to replace in (3) and (4) by 2. 2 QUESTIONS AND PROBLEMS D1 1 1. Why is it unsafe to let a pneumatic inkstand like that of Fig. 30, p. 33, remain in the sun? 2. To what temperature must a cubic foot of gas initially at 0° C. be raised in order to double its volume, the pressure remaining constant? 3. If the volume of a quantity of air at 30° C. is 200 cc., at what temperature will its volume be 300 cc., the pressure remaining the same? 4. If the air within a bicycle tire is under a pressure of 2 atmospheres, that is, 152 cm. of mercury, when the temperature is 10° C., what pressure will exist within the tube when the temperature changes to 35° C.? 5. If the pressure to which 15 cc. of air is subjected changes from 76 cm. to 40 cm., the temperature remaining constant, what does its volume become? (See Boyle's law, p. 36.) If, then, the temperature of the same gas changes from 15° C. to 100° C., the pressure remaining constant, what will be the final volume? 6. The air within a half-inflated balloon occupies a volume of 100,000 1. The temperature is 15° C. and the barometric height 75 cm. What will be its volume after the balloon has risen to the height of Mt. Blanc, where the pressure is 37 cm. and the temperature 10° C.? * If this is not clear to the student, let him recall that if the speeds of two runners are the same, then their distances are proportional to their times, that is, D1/D2 = t1/t; but if their times are the same and the speeds different, D1/D2 81/82. If now one runs both twice as fast and twice as long, he evidently goes 4 times as far; that is, if time and speed both vary, D1/D2 = t11/t282 = 14. Why is the te the receiver of an ai 15. Two thermon has a diameter twice of the stems between Ε 163. The laws of experiment described constant and observe with the rise in temper expansion, which is de pressure per degree and was first done for diff in 1787, who found the all gases are the same. When we arrange the as the temperature rises obtain the volume coefficie ratio between the increase ume of the gas at 0°C. Thi 1802 by another Frenchm gases have the same volume being the same as the press is known as the law of Ga From the definition of Charles's law we learn that, pressure is proportional to abe rates: for - 10 C. is *f mercury, -folents at dif is regular. erveen 0 and - instead Also, from Gay-Lussac's la constant pressure, volume is pre that is, Τ. paraAs |