Physics Part 28

The formulas for the laws of Boyle and Charles are sometimes combined into one expression as follows:

_PV/T = P'V'/T'_

or the product of the volume and pressure of a constant ma.s.s of gas is proportional to its absolute temperature.

Important Topics

1. Heat units; calorie, British thermal unit.

2. Three thermometer scales, fixed points on each.

3. Absolute zero, how determined. Its value on each scale.

4. Law of Charles, its meaning. Combination of laws of Boyle and Charles.

Exercises

1. Does ice melt at the same temperature at which water freezes? Express the temperature of freezing water on the three thermometer scales.

2. A comfortable room temperature is 68F. What is this temperature on the centigrade and absolute scales?

3. Change a temperature of 15C. to F.; 15F. to C.; -4C. to F.; -20F.

to C.

4. The temperature of the human body is 98.6F. What is this temperature on the absolute and centigrade scales?

5. The temperature of liquid air is -180C. What is it on the Fahrenheit scale?

6. Mercury is a solid at -40F. What is this on the centigrade scale?

7. How much heat will be required to raise the temperature of 8 lbs. of water 32F.; 5 lbs. 10F.?

[Ill.u.s.tration: FIG. 125.--A clinical thermometer used to take the temperature of the body.]

8. How much heat will be required to raise the temperature of 30 g. of water 43C.; 20 g., 50C.?

9. Compute the temperature of absolute zero on the Fahrenheit scale.

10. Take three basins of water, one hot, one cold, and one lukewarm. If one hand be placed in the hot water while the other is placed in the cold and after a few minutes both are placed in the lukewarm water, this water will feel cool to one hand and warm to the other. Explain.

11. If 200 ccm. of air at 200 absolute is heated to 300A. under constant pressure, what volume will the air occupy at the latter temperature?

12. How does one change a reading on the centigrade scale to a corresponding reading on the absolute scale?

(3) EXPANSION OF LIQUIDS AND SOLIDS

=146. Expansion of Gases.=--The law of Charles is found to apply to all gases. That is, all gases change in volume in proportion to the change of temperature provided the pressure remains constant. It is for this reason that we have the _gas thermometer_ (see Fig. 126) which gives in skillful hands more accurate temperature readings than the best mercurial thermometer. Galileo devised and used the first _air thermometer_ which consisted of a hollow bulb blown on a gla.s.s tube and inverted in a dish of water. (See Fig. 1.) The _water thermometer_ consists of a gla.s.s bulb filled with water which rises into a tube attached to the bulb. One disadvantage of the water thermometer is its limited range since it cannot be used below 0 or above 100. Why?

=147. Expansion of Liquids.=--The expansion of liquids differs from that of gases in several important respects:

(a) Liquids have a smaller rate of expansion than gases. The _rate_ of expansion per degree is called the _Coefficient of Expansion_. For example, the coefficient of expansion of a gas under constant pressure at 0C. is {1/273} of its volume per degree centigrade.

(b) Different liquids expand at wholly different rates, that is, their coefficients of expansion differ widely. For example, the coefficient of expansion of mercury is 0.00018 per degree centigrade, of glycerine 0.0005 per degree centigrade, of petroleum 0.0009 per degree centigrade.

[Ill.u.s.tration: FIG. 126.--Gas thermometer.]

(c) The same liquid often has different coefficients of expansion at different temperatures. Water between 5C. and 6C. has a coefficient expansion of 0.00002 per degree centigrade, between 8 and 50 of 0.0006, between 99 and 100 of 0.00076. The coefficient of expansion of mercury, however, is constant for a wide range of temperature and, therefore, it is well adapted for use in thermometers.

=148. Peculiarity in the Expansion of Water.=--Water has a peculiar rate of expansion. This is ill.u.s.trated by the following experiment:

A test-tube filled with cold water is closed by a stopper containing a small gla.s.s tube, the water extending up into the small tube. (See Fig. 127.) The test-tube is placed in a freezing mixture of salt and ice contained in a tumbler. As the water cools, the level of the water in the small tube at first _sinks_. But before the water freezes it _rises_ again, showing that after the water cools to a certain temperature that _expansion of the water occurs with further cooling_.

Careful tests show that the water on cooling contracts until it reaches 4C. On cooling below this temperature it expands. For this reason, when the water of a lake or river freezes, the coldest water is at the surface. On account of this the ice forms at the top instead of at the bottom. If water contracted as it cooled to the freezing temperature the coldest water would be at the bottom. Freezing would begin at the bottom instead of at the surface. Lakes and rivers would freeze solid. In the summer only in shallow waters would all the ice melt. The result would be that fish and other aquatic life would be killed. Climate would be so changed that the earth might become uninhabitable. Since water is densest at 4C. all the water in a lake or river, when it is covered with ice, is at 4C. except that near the surface.

[Ill.u.s.tration: FIG. 127.--Apparatus used in testing the expansion of water.]

=149. The Expansion Of Solids.=--Most solids when heated expand less than liquids and gases. Careful experiments show that expansion is:

(a) Proportional to the change in temperature.

(b) Different in different solids.

Here are a few coefficients of linear (length) expansion.

Bra.s.s 0.000018 per degree C.

Gla.s.s 0.000009 per degree C.

Ice 0.000052 per degree C.

Iron 0.000012 per degree C.

Platinum 0.000009 per degree C.

Zinc 0.000027 per degree C.

_The coefficient of linear expansion is the fraction of its length that a body expands when heated one degree._

_The coefficient of cubical expansion is the fraction of its volume that a body expands when heated one degree._

The expansion of solids is used or allowed for in many cases:

a. Joints between the rails on a railroad allow for the expansion of the rails in summer.

b. One end of a steel truss bridge is usually supported on rollers so that it can expand and contract with changing temperatures. (See Fig.

128.)

[Ill.u.s.tration: FIG. 128.--Truss bridge showing roller support at one end.]

c. Suspension bridges have expansion joints where the ends of the iron girders can move in or out of an expansion joint thus making the bridge longer or shorter according to the temperature.