grammes. What will be the temperature of the mixture, supposing that there is no exchange of heat except among the substances mentioned? What is the water-equivalent of the calorimeter employed?

13. The mechanical equivalent of heat is 1,390 foot-pounds = pound of water by deg. Cent.; if the standard substance were iron instead of water, what would be the value of the equivalent?

14. How much will a mass of copper be raised in temperature by striking a hard non-conducting surface after a fall of 368 feet?

15. A bullet moving at 1,605 feet per second strikes an iron target; how much is its temperature raised?

16. With what velocity must a mass of iron strike a hard non-conducting substance to have its temperature raised by one degree Centigrade?

SECTION XLII.-LATENT HEAT.

ART. 185.-Latent Heat. The latent heat of a substance is the quantity of heat which must be communicated to unit mass of the substance in a given state in order to convert it into another state without any change of temperature. It is expressed in the form absorbed = M changed. given out

ΖΗ

When the unit of heat is defined as in Art. 177, the above rate becomes

7 M of water by → = M of substance.

As the unit of mass appears in the same mode on either side of the equivalence, the value of 7 is independent of the unit of mass, depending only on the unit of temperature.

ART. 186.-Changes of State. There are two changes of state of the kind referred to, and each has a different name according to the direction of the change. A substance may change from the solid to the liquid state, or oppositely, from the liquid to the solid; and it may change from the liquid to the gaseous state, or oppositely, from the gaseous to the liquid. These changes are

denominated respectively, liquefaction or fusion, solidification, vaporization, condensation.

As pressure has only a slight effect on the change from liquid to solid, the latent heat of liquefaction or solidification is constant. But as pressure has a great effect on the change from liquid to gas, the latent heat of vaporization or condensation depends on the pressure at which the change takes place. If heat is absorbed in one change it is given out in the opposite change and according to the same rate.

ART. 187.-Total Heat. By total heat is meant the number of units of heat required to change unit of mass of a substance from one temperature to another temperature, the interval including a change of state. Thus for changing water-substance from water at 0° C. to steam at 100° C., and under a pressure of 760 mm., 636 lb. of water by deg. Cent. lb. of water changed.

=

LATENT HEAT OF FUSION, AND OF VAPORIZATION AT THE PRESSURE OF ONE ATMOSPHERE.

7 M of water by deg. Cent. per M of substance changed.

EXAMPLES.

Ex. 1. The latent heat of fusion of ice is 79-25 in terms of the degree Centigrade. Express this constant in terms of the degree Fahrenheit.

..

79.25 M of water by deg. Cent. = M melted,

deg. Fahr. deg. Cent.;

=

79.25M of water by deg. Fahr. = M melted,

i.e., 142.65 M of water by deg. Fahr. M melted.

=

Ex. 2. One pound of boiling water is poured over two pounds of powdered ice; what will be the temperature, and what the physical condition of the result?

Since the latent heat of water is

79 lb. of water by deg. Cent. = lb. of ice melted,

it will require 158 of these units of heat to melt the 2 pounds of powdered ice. But the reduction of the one pound of boiling water to the temperature of 0° C. can give only 100 units of heat; hence a portion only of the ice will be melted. Suppose x lbs.; then

*x × 79=100,
x = 1.27.

Hence the resulting temperature will be that of melting ice, and 1.27 lbs. of the ice will be melted.

Ex. 3. Assuming the latent heat of melting ice to be 142, that of steam at 212° to be 966, and the specific heat of ice to be 0·5; find the temperature of a solid weighing 40 lbs., and having a constant specific heat 01, which on being plunged into 1 lb. of snow at temperature zero would just convert it into steam at 212°, supposing that no heat is received from or imparted to any other bodies by the ice and the solid.

The total heat of the lb. of snow is

32 × 5 + 142 + 180 + 966 lb. of water by deg. Fahr.

Suppose that the temperature of the solid is t° F., then the heat it

loses is

Hence

40 x 1(212) lb. of water by deg. Fahr.

4 (t-212)=1,304,

.'. t = 538. Answer-538° Fahr.

Ec. 4. The latent heat of fusion of ice is 79.5, and its specific gravity is 917. Ten grammes of metal at 100° C. are immersed in a mixture of ice and water, and the volume of the mixture is found to be reduced by 125 cubic millimetres without change of temperature. Find the specific heat of the metal.

and, by equating the two quantities of heat,

EXERCISE XLII.

1. 16 lb. of ice at 0° C. mixed with 9 lb. of water at 20°, yielded 10'6 lb. of water at 5o; find the latent heat of water.

2. If a lb. of ice at 0° C. be dropped into 2 lbs. of water at 26°5 C., how much of the ice will be melted?

3. How much ice at 0° C. can be converted into water at 0° C. by an ounce of steam at 100° C., if we assume heat to be transmitted from the steam only to the ice?

4. How much steam at 100° C. is required to raise the temperature of 54 ounces of water from 0° C. to 100° C. ?

5. How many pounds of steam at 100° C. will just melt 20 pounds of ice at 0° C. ?

6. It is found that a kilogramme of water at 100° C., mixed with a kilogramme of melting snow without loss of heat, gives two kilogrammes of water at the temperature of 10° 36; find the latent heat of water.

7. One lb. of steam at 100° C. is passed into a vessel containing 5 lbs. of water at the temperature of 20o C., and then condensed. What will be the temperature of the mixed steam and water?

8. Half a pound of powdered ice is mixed with 4 pounds of water at 8° C.; what is the result, and what the final temperature of the mixture?

9. It is found as the result of experiment that 25 grammes of copper at the temperature of 100° C. are just sufficient to melt 2.875 grammes of ice at 0°, so that water and copper are finally at 0°. Find from these data the specific heat of copper?

10. If a pound of steam at 100° C. be injected into a gallon of water at 15o C., calculate the temperature to which the water will be raised.

11. Into a mass of water at 0° C., 100 grammes of ice at -12° are introduced; 7.2 grammes of the water freeze about the lump immersed, while its temperature rises to zero. What is the specific heat of the ice?

12. By proper arrangement a vessel, whose capacity for heat is to be neglected, containing 10 grammes of water, is reduced in temperature 15 degrees Cent. below the freezing point of water. A small spicule of ice is then dropped in; calculate the quantity of ice formed.

13. Two kilogrammes of steam at 100° are conducted into a copper vessel weighing kilogramme, and containing 30 kilogrammes of water at the temperature of 10°; find the temperature of the resulting mass after condensation, supposing no heat to be lost by radiation.

14. The heat produced by the complete combustion of one gramme of carbon in a calorimeter can convert 100 grammes of ice at 0° C. into water at 0° C. How many grammes of water could be raised by the same amount of heat from 0° C. to 1o C.?