CondiPer Sand tion of I,ead cent. Per cent. cupel. Gins 10 80 20 coarse soft 80 20 coarse hard 10 10 80 20 fine soft hard 10 80 20 fine 10 S5 15 coarse soft 10 S5 15 coarse hard MgO.
85 85
15 fine 15 fine
soft hard
10
Silver
h'gs 35-45 35-45 35-45 35-45 3545 35-45 35-45 35-45
10
Silver loss Per cent. Surface. slightly cracked 2 5 2 6 siightly cracked deer, cracks 2.3 2.5 deep cracks badly pitted 3.2 2.2 badly pitted cracked 3.3 slightly cracked 2.5 badly cracked
and
None of the magnesium oxide cupels have properties either as t o loss of silver or as t o hardness after cupellation, which warrant the substitution of t h a t substance fclr other cupel material. SUMMARY.
Under similar conditions, with about I O grams of lead and 40 mgs. of silver, the average percentage losses in different cupels were as follows: Silver loss. Per cent. Morganite.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Casseite., . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rron-nlte.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bone ash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cement. . . . . . . . . . . . ? . . . . . . . . . . . . . . . . . . . . . 1:quaI parts cement and bone a s h . . . . . . . . . . .
1 99 3.09 2.89 2.36 3.38 2.95
I t was furthermore determined t h a t cupels made of different grades and sizes of bone ash give the same percentage loss of silver within the limits of experimental error. UNIVERSITY O F ARIZOA-A,
'rucs,JK
Heat of conduction flows through solids, its rate of transit depending on the heat-transferring properties of the solid, its density, its specific heat, and its thermometric conductivity. Heat of radiation passes through space between surfaces, its rate of transit depending on the nature and disposition of the surfaces between which it passes and not on the space itself, t h a t is, not on the nature of the gas or vapor filling t h a t space. This is not absolutely correct, as there is no gas which is completely diathermanous, t h a t is, which does not absorb radiant h e a t ; but for air, products of combustion, and most gases of common occurrence, the absorption of radiant heat is negligible over short distances. The fourth-power law of heat radiation was first advanced b y Stefan' who found it t o accord with the results of experimental researches of Dulong anrl Petit, de la Provostaye and Desains, and Draper and Tyndall. Boltzmann later demonstrated math,.matically from thermodynamic principles t h a t sut 11 a law should hold. A surface of A square feet a t a temperatur:. af Q1 degrees absolute (equals 0, degrees Fahrenheit plus 460.7) radiates R heat units2 t o another surface whose absolute temperature is @,, in a length of time T hours. The mean solid engle subtended b y the latter surface with respect t o the surtace in question is o hemispheres. The net coefficient of emission and absorption between two surfaces is E. According t o the Stefan-Boltzmann radiation law, the following relation exists:
HEAT RADIATION. nv HAROLDP GURNEY Received Aun 9. 1911
Heat transmission b y radiation is utilized in the abstraction of heat from the zone of combustion in furnaces, and it is the principal restrictive factor in the maintenance of high temperature. Chemical and metallurgical industries abound with instances where application of the well established laws of heat radiation and conduction would reveal important information with regard t o economy of operation or design. Although heat radiation is rarely unaccompanied b y conduction and convection of heat, i t may well be treated separately, a t first, as i t is subject t o different laws. The laws of heat radiation differ in very essential respects from the laws of heat conduction. Heat always flows from high t o low tem'perature, b u t the rate of flow of radiant heat is not proportional t o the temperature difference. When heat IS transmitted b y conduction, the thermal pressure causing the flow of heat may be considered as proportional t o the absolute temperature, consequently the rate of flow per unit of temperature drop IS a constant, because the differential of the thermal pressure with respect t o the temperature is a constant. The pressure of radiant heat is proportional t o the fourth power of the absolute temperature, consequently the rate of flow per unit of temperature drop a t a n y tempetature is proportional t o the cube of the absolute temperature
R
=
---4 ----41 o.16TAyE [o.oI@, -- o.o~@,,J
The constant in the above expression has been variously assigned t o values ranging from 0.136 t o 0.190.3 I t was originally given as o . r g z , b u t late work4 b y Bauer and Moulin places i t a t 0.160, and it has ordinarily been quoted a t 0.I 60. The coefficient of absorption of a surface is the ratio of the amount of radiant heat absorbed t o the amount of heat incident on the surface. Lampblack absorbs practically all heat rays impinging on its surface and reflects none; its coefficient of absorption, then, is unity. The coefficient of emission is the ratio of the heat actually radiated t o the heat an ideal black body would radiate, and i t is the same in value as the coefficient of absorption. The net coefficient between two surfaces is very nearly the product of the coefficients of both surfaces, as the heat transmitted will be diminished both in emission and in absorption. y is the mean of the solid angles subtended b y one surface with respect t o each elementary area of the other surface. A unit solid angle is bounded by a hemisphere and this is the most usual technical case. Rules cannot be given for evaluating y under all circumstances; but as this matter is seldom given b u t scant consideration, it will here be taken u p more in detail. 1 2
3 4
Wiener, B c r . , 1872. British thermal unit. C. Fer,., Compf. r e n d . . 1909. E. Bauer and A f . Moulin, Jouvnnl Physique, 1910.
d
T H E J O U R N A L OF I N D U S T R I A L A N D EAJGINEERIXG C H E X I S T R Y .
808
By definition, the mean solid angle q , is
VALUESOF E. Lampblack.. . . . . . . . . . . . . . 1 .OO Interior of furnaces. 0.90-0.95
Sheet l e a d . . . . . . Polished s t e e l . . Polished sheet i r o n . .
......
...........
................... 0 . 8 0
Polished t i n . .
Glass. Ordinary sheet iron
.......
0.18
0.17 0.12
....
..
...........
Polished silver.. Mica. . . . . . . . . . . . Graphite. . . . . . . . . Tarnished l e a d . . . . . . . . . . . . 0 . 4 5 Mercury.. . . . . . . . . . . . . . . . . 0 . 2 0 Polished l e a d . . . . . . . . . . . . . . 0.19 Polished i r o n . , . . . . . . . . . . . . 0 . 1 2
0.98
. . . . . . . . . . . 0.96 Sealing w a x . . . . . . . . . . . . . . 0 . 9 5 Crown glass. . . . . . . . . . . . . .0.90
Building s t o n e . . . . . . . . . . . . . 0.90 Sawdust.. . . . . . . . . . . . . . . . . 0 . 8 8 Powdered charcoal.. . . . . . . . 0.85 Powdered chalk. . . . . . . . . . . 0 . 8 3 . . . . . . . . . . . . 0.73 Zinc. . . . . . . . . . . . . . . Tin ...................... 0.05
.
Fine s a n d . . Wood.... 0.90 Plaster. . . . . . . . . . . . . . . . . . 0 . 9 0
...............
Polished silver.
......
As far as radiation is concerned, a perfectly plane or even surface will radiate just as much heat as a rough, corrugated, or irregular surface of the same extent as far as boundaries are concerned. For a rough surface, the true value of 'p would be less, and the true value of A greater than for a smooth surface of the same extent. With heat radiation, then, all surfaces may be treated as though they were smooth, an assumption which would be impermissible with heat conduction and convection. I n Fig. I , the plane A,, subtends a mean solid angle of q, hemispheres with respect to A, a n d ' i t is desirable to express q, in terms of quantities which may be more easily estimated than solid angles.
- - - - 9- -
I
I
sin a is the mean of all values of --
a
-YT)
between could be practice, mation,
rz
m
dA, and dA,,. For regular surfaces this obtained exactly b y calculus, but in general it will be close enough t o obtain it by estior by averaging a representative series of
sin a
values of
between evenly distributed
on the two surfaces. When the surfaces are planes and parallel, then h sin a = - where h is the perpendicular distance beY
tween the planes.
Then, q , = - -hA11 .
1
rm3
2ii
r, is the mean distance from any point in plane A, t o any point in A,, and may generally be taken as the mean between the maximum and minimum distances between the surfaces. Also, 311
hA,
-
=
.
1 .-7
2n
rm3
hence, G,
A,,
711
A,
- = _
or
A131 = AI,%,. The fundamental law of heat conduction is expressed in the following relation, where Q is the heat units transmitted in T hours through a wall whose conductance is G units and under aetemperature drop of a degrees:
- - AG Q-
T
a temperature drop 3. degrees from or t o a surface whose radiant conductance is C, R = AC. T H is the total heat transmitted where radiation and conduction occur simultaneously: H=Q R = AT(C G)
/
+
+
And just as the conductivity g Fig. 1
Both A, and A,, may be divided into elementary areas dA, and dA,, whose distances apart are 7 , and where the lines r connecting these make angles a with the surface of A,, a t dA,,. Then, if p is the solid angle subtended by dA,, with respect t o dA,, its value is dAl,sin a
q 1 2
points
r2
A similar though arbitrary relation will be assumed to hold for the heat units R radiated in T hours under
I
r
(sin
Here
-0
--I----
\
N o v , 1911
=
7
-
Leslie. Watts' "Dictionary of Chemistry." Ser. Physique industrielle.
e
=
G
- where A
A is
the area of the wall or surface in square feet, so the C radiant conductivity c = -. A
In referring to actual experiments, it is convenient t o refer to a value K
k
I
0.3. Since greatly from I/&( I
+ + +
a=-
O.OI@,,
a n approximate expression for c is
0 OIO,
__2 c
=
-4H = T'
+a+
---I
0.006qE0.01~,0.01@,,.
The usual case of combined heat radiation a n d conduction is where heat passes from a surface a t temperature I O 1 through a space of approximately the same temperature, a conducting wall of thickness
AA
e,,
I
rl + cl + 6 P +
Very commonly, the quantities 6p and neglected in comparison with and
e,,
may be
-2.-
71 + Cl
H
+
= AA(7, cl). T Since the temperature drops are proportional t o the included resistivities, then,
-
10,
-
'el1
-
xoll
- IIe,
-
Generally 6 p may be neglected especially for metallic walls, but if dlIo, representing the thickness of material like boiler scale multiplied into its internal resistivity, it cannot be neglected: lie,
Iell
Fig. 2
'el1 and and into a fluid of temperature x1611. The internal resistivity of the wall is p . At I O l 1 the conductivity is y, a n d the radiant conductivity is c,, a n d a t 110, the boundary resistivity is til. Both IO^, I X O l 1 , and A = I O 1 - 1 ~ 6 ,are ~ known, but 1011
6 inches whose outside temperatures are I1O1,
-110,~ -1
x 0 ~
=
~
=
8pxrl
1
1
~
+ cl) (
~
1
+ cl)
A few samples will demonstrate the practical application of these formulae. In a steam boiler the temperature of the steam is z 50' [ = 7 IO' absolute], the temperature of the grate is IZOO' [ = 1660' absolute], a n d the thickness of the boiler plate is I/, inch. I t is now desired to find the temperature difference between the water side amd the fire side of the plates exposed t o direct radiation, where the value of p = 0.003, y1 = 3 and 0 = 0.70: o.oI@,, = 7.1 O.OI@, = 16.6
-_ c,
=
0.006 X 0.70 X 16.6 X
7.1 = 8.2
T H E JOI/'RLY\;ALOF I - / - D C S T R I A L A N D EiVGI.VEERI.VG
810
+
6, y1 = 1 1 . 2 950 x 1/4 x 0.003 x 1 1 . 2 = 8' If instead, copper plate had been used of I / ~ inch thickness and 0.003 internal resistivity, then, IOl1 - " 8 , = 950 X 1 / 2 X 0.0003 X 1 1 . 2 = 1.6' IOl1
- 118,
Nov
1911
A
H
=
I t is here assumed t h a t the copper plate has been sooted over, and E is around 0.95 instead of 0.05 were t h e copper polished. These temperature drops of I per cent. and per cent. of the total tkmperature drop are absolutely negligible in comparison with the inaccuracy of data @ and assumptions. Blechyndenl in experiments on the heat transmission of iron a n d copper plates exposed to combustion found no appreciable difference. With boiler scale, it is quite different. Under the same conditions as before, it will be assumed t h a t the heating surface is coated with a boiler scale of I/* inch thickness and of internal resistivity 0.07, a fair value. I/. X 0 . 0 7 X 11.2 = 270°, qll- I r e , = 950 x I I / Z X 0 . 0 7 X 11.2 I O l l = 5 2 0 '[ = 980 O absolute]. If the temperature of the boiler plate exposed t o the fire of absolute temperature 1660' is 980' absolute instead of IO', a new value for c should be solved, for
+
*
&_
2
c = 0.006 X 0.70 X 16.6 X 9 . 8 = 11.4
7
r = 3
+
C
14.4
r e l 1 = 570'. As the decrease in heat transmission is proportional t o the ratio of the resistance of the boiler scale t o the total resistance, this means a decrease of 33 per cent. on the heat transmitted were no new scale present. Under the same conditions the temperature drop 1 1 0 , - 11011 from the water side of the plate to the mean temperature of the water may well be investigated. Here Lll ranges from 0.001 t o 0.01, b u t in common practice with good circulation, Lll would not much exceed 0 . 0 0 2 . This would mean a temperature drop of z o o in 950' of total temperature drop, t h a t is, only 2 per cent. Had a sluggish liquid like sulphuric acid been evaporating in a platinum or cast iron still, the value of would probably exceed 0.01 and 0 . 0 2 and would impose a large temperature drop on the boundary between the metal and the liquid. The common problem of determining the loss of heat from steam pipe may readily be handled by this method of analysis. A steam pipe of 80 feet length a n d 3 inches diameter is covered with a I inch packing of asbestos. The temperature of the steam is 2 7 5 O , and of the outside air a n d surroundings 80' [ = 540" absolute] ; and it is desired t o find the hourly condensation of steam in the pipe. Other d a t a to be given is p1 = 1.1 for asbestos, = 0.0004 from steam t o metal, a very low value, = 0.45 from the surface of t h e asbestos t o air, $ = I , a n d o.oo64E = 0.Ooj:
I,,
r,,
E n g z i i i c r , 1896
CHEMISTRY.
r
8 o X 3 X z
=
~~
All
=
A
63
=
8 0 _~X 4-X n
I2
=
84
I2
-3 y1+c1=I.25 A = I95 The value of c1 here is incorrect. On this assumption, the total resistance is 0.0206 while the outside surface resistance is 0.0076 which means a ' temperature drop of 7 2 ' , an outside surface temperature of
6,p,=1.1 c 1 = o . o o 5 X j . 4 = o . 8
Ij
z
and
O
which is 613 O absolute. 1/4(1
+ c1
a
+
+
a2
as)
Hence a
=
S4I 613
=
0.88
0.84.
-3 X 6.13 X 0.84
= 0.00j
=
=
0.97
H I95 - _ 9900 B . t . U . T 0.000006 0.013 b.0067 = 10.8 pounds of steam condensed per hour. A simple practical application of the combined conduction a n d radiation of heat is the investigation of the resistivities of air spaces of ,furnace walls a t high and low temperature, and the resistivities of t h e same thicknesses of fire-brick. I n a furnace wall where the mean temperature is IOOOO, a n air space of 2 inches is left open t o act a s a non-conductor of heat. The value of o.oo64E will be assumed a t 0.004 and the value of 7 for either surface a t o 4 , consequently the resultant conductivity of both surfaces in series with respect t o the flow of heat is r / z r = 0 . 2 :
+
+
____ 3
c = 0.004 X
IO
+
+ 4.6
= 12.5
c r / z r = 12.7 AAT I - _ --_ _ - - 0.08 H 12.7 Had the air space been filled In with fire brick with ,Q = 0.14, then, AAT __ = 6 ,=~ 2 x 0.14 = 0.28.
Q
This shows t h a t it would be better t o have the space filled in with fire brick, as i t would offer greater resistance t o the flow of heat. Had the space been AAT inch in thickness, = 0 . 0 8 as before, but H -AAT _ - 0.04, in which instance, the air space would ~
Q
offer the greater resistance. Had the mean temperature of the space been 100' instead of IOOO', then, _-- 3 c = 0.004 X I 4.6 = 0.7 c 1/2r = 0 . 9 AAT I _~ -. - 1 . 1 H 0.9 and ' AAT
+
~~
Q
+
= 0.28.
Ti ov., 1911
T H E J O U R i Y i l L OF IA’DL-STRIAL A,VD EAYGI.YEERI.\-G
I n this case the air space would offer more resistance. This has been well brought out both b y experiment a n d b y calculation b y Ray and ICreisingerI in “The Flow of Heat through Furnace Walls.” Hence a practical criterion for air spaces for insulating purposes is
0”
