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On the dilation and compressibility of water and the displacement of its maximum density by pressure
Dec., i889. ]
Compressibility of IVater, etc.
477
Expansion is here assumed to be approximately hyperbolic, and the terminal pressure to be eight or ten pounds per square inch. General experience to date thus indicates that a triple expansion engine should do best work up to a pressure of about 25o or 3oo pounds, and that the four-cylinder engine should be adopted from that point up to the highest pressures likely to be adopted in the steam-engine, the double expansion compound serving its purpose well below the lowest figures above assigned to the triple engine. Any of the four types of engine may be made to overlap the range assigned its labor by suitably providing against wastes occurring within the engine by increased speed, by superheating, by expedients giving higher effectiveness to the jackets, or other methods of improvement. A n y system which increases the efficiency of the simple engine will improve the efficiency of the compound, and will corresPOndingly increase the range of pressure through which it will give satisfactory gain as compared with the former. (To be conlinued.) ON" THE
DILATATION
AND
COMPRESSIBILITY
OF
W A T E R AND THE D I S P L A C E M E N T OF ITS M A X I M U M D E N S I T Y By P R E S S U R E . ~ By E. H. AMAGAT. Translated by Chief Engineer ISHERWOOD, U.S.N.
I have described in a preceding communication (Comities Rcndus, A u g u s t 23, I886), the method I adopted for the determination of the dilatation and compressibility of liquids under very high pressures, and I gave some of the results obtained, b u t not corrected for the deformation of the piezometers. The ascertainment of this deformation, which I am now engaged on, appears so long and difficult, that I think I should without delay make known the results I have obtained for water, which has a special interest because of its phenomenon of maximum density. Commies Rendus, t887, p. tt59.
478
d m a g a t - [ s h e r w q o d ."
[ J. t~'. I,
Mr. Tait, who, previously to me, i n v e s t i g a t e d w a t e r b e t w e e n wide limits of pressure, has given for t h a t liquid the following f o r m u l a : z , m % = 0"0000489 - - 6"00000026 T J) ~'0
0"0000000067
applicable between 6 ° and I5 °, a n d b e t w e e n I5O and 5oo atmospheres, b u t I believe t h a t no physicist up to the p r e s e n t time has e x a m i n e d the subject relative to the m a x i m u m of density. T h e m e t h o d I e m p l o y gives directly the pressure necessary to m a i n t a i n a c o n s t a n t mass of w a t e r at the s a m e " v o l u m e at all t e m p e r a t u r e s , consequently, if w i t h two different t e m p e r a t u r e s the same pressure is obtained, there m u s t lie b e t w e e n them, as r e g a r d s t h a t pressure, the temp e r a t u r e corresponding to the m a x i m u m of density. T h e use of the same pressure w i t h the different t e m p e r a t u r e s obviates the necessity of correction for the elasticity of the m a t e r i a l of the piezometer, for the calculation of w h i c h the data are still w a n t i n g . T h e correction for difference of temp e r a t u r e relative to the dilatation has been m a d e b y provisionally a d m i t t i n g t h a t the coefficient of d i l a t a t i o n of glass does not v a r y w i t h the pressure, a supposition which cannot cause a n y notable error, i n a s m u c h as in the present case the variation of t e m p e r a t u r e is only of a few degrees. As regards pressure, I have carried nay e x p e r i m e n t s on w a t e r up to 3,-"oo a t m o s p h e r e s ; and as regards t e m p e r a t u r e , I have operated b e t w e e n zero and 5o °, w i t h the following results : A t 2oo atmospheres, in r o u n d numbers, the m a x i m u m d e n s i t y of w a t e r r e t r o g r a d e d towards and n e a r l y r e a c h e d zero. It appeared to be b e t w e e n zero and o'5 ° (half a degree). A t 7oa a t m o s p h e r e s there was no longer a n y m a x i m u m of d e n s i t y above zero, the form of the curves i n d i c a t i n g clearly t h a t it h a d passed below zero; further, the investig a t i o n could be followed to still lower t e m p e r a t u r e s since the freezing point of w a t e r is lowered by increased pressure. To well u n d e r s t a n d the e~zscmbh" of the p h e n o m e n a and
Dec., 1889.]
Compress~bility of Water, etc.
479"
the r e s u l t i n g consequences, curves should be formed b y t a k i n g the pressures as abscissas and the volumes as ordinates, to represent at different t e m p e r a t u r e s the v o l u m e s occupied u n d e r all the pressures by the same mass of water. T h e s e curves intersect each other successively at points w h i c h correspond to the c h a n g e of the sign of dilatation of the water, and fall successively in the order of the temperatures, the pressure increasing. A t 2oo a t m o s p h e r e s t h e y are in t h e n o r m a l order, b e c o m i n g m6re and more closed or s t r a i g h t e n e d as t h e y correspond to lower t e m p e r a t u r e s . T h e pressure c o n s t a n t l y a u g m e n t i n g , t h e y become m o r e a n d more opened in such a m a n n e r t h a t the co-efficient of dilatation increases r a p i d l y at first, and t h e n more slowly w i t h the pressure, which is jizst the c o n t r a r y of w h a t t a k e s place w i t h all the other liquids I have examined. T o w a r d s 3,ooo a t m o s p h e r e s the co-efficient of d i l a t a t i o n ceases to increase, and u n d e r g r e a t e r pressures it probably d i m i n i s h e s as in the case of other liquids ; the effect, too, is m u c h less m a r k e d as the t e m p e r a t u r e , w i t h equal pressure, is h i g h e r . T h e r e results, likewise, from this disposition of the c u r v e s that, b e t w e e n two different pressures, the difference of the ordinates and c o n s e q u e n t l y the co-efficient of c o m p r e s s i b i l i t y d i m i n i s h e s w h e n the t e m p e r a t u r e increases, w h i c h is also c o n t r a r y to w h a t occurs in the case of other liquids, a fact long since shown bv Grassi, a n d a quite n a t u r a l result of t h e disappearance of the m a x i m u m of density. F u r t h e r m o r e , and for the above reasons, this d i m i n u t i o n of the co-efficient of compressibility disappears w h e n the pressure increases, and it also disappears whert the t e m p e r a t u r e increases., c o n f o r m a b l y to the results of Messrs. P a g l i a n i and Vicentini, according to w h o m the compressibility of w a t e r ceases to decrease above 5o °. T h e t e m p e r a t u r e at w h i c h this inversion takes ptace decreases w h e n the pressure increases. Generally, a sufficient increase of pressure or of temperature gives w a t e r a t e n d e n c y to conform to the o r d i n a r y case of l i q u i d s ; and towards 3,ooo a t m o s p h e r e s the last traces have disappeared of the p e r t u r b a t i o n s of the g e n e r a l law w h i c h result from the existence of m a x i m u m density. Such are the general results of the cJtscmb/c of the pile-
Gossart-[sherwood."
480
[J. F. I.,
n o m e n a . I shall c o n t i n u e the s t u d y in detail, a n d investig a t e the s u b j e c t below zero. I can give the definitive :numerical results only after I h a v e finished the work now :in progress on the d e f o r m a t i o n of t h e piezometers. In conclusion, I w o u l d add t h a t none of t h e liquids I h a v e s t u d i e d up to the present time, has s h o w n a m a x i m u m of d e n s i t y u n d e r a n y pressure, w h i c h is c o n t r a r y t o a prevision f o r m u l a t e d r e c e n t l y b y Mr. Grimaldi, based on a s s u m e d cons t a n c y of t h e co-efficient of compressibility w i t h i n wide limits of pressure, an a s s u m p t i o n in complete disaccord w i t h the results I h a v e o b t a i n e d w i t h all the liquids I h a v e investigated. RESEARCHES
ON THE S P H E R O I D A L WATER.*
S T A T E oF
BY MR. GOSSART. Translated by Chief Eagineer [SHERWOOD, U.S.N.
T h e results w h i c h I h a v e the h o n o r of p r e s e n t i n g to the A c a d e m y , are relative to the t e m p e r a t u r e of w a t e r in the state of calefaction u n d e r d e c r e a s i n g pressures comprised b e t w e e n 760 m i l l i m e t r e s and 0"5 millimetre. Recently, Mr. L u v i n i (II Nuovo Cimento, t. xvii) h a s published some researches on the t e m p e r a t u r e of water, of alcohol, and of ether, calefied in a v a c u u m , b u t he could not m a i n t a i n c o n s t a n t the t e m p e r a t u r e of the crucible cont a i n i n g the liquid and m e r e l y r e s t i n g on a brick h e a t e d u n d e r a glass bell. F o r m i n g the v a c u u m rapidly, he followed the s i m u l t a n e o u s c h a n g e of a t h e r m o m e t e r placed in the liquid, and of the pressure. F r o m his o b s e r v a t i o n s he concluded t h a t the temperature o f t/ze liquid spheroid is the same as tke temperature o f ebulh'tion under t/ze pressure in the enclosed space a n d t h a t t h e r e could be t h u s directly caused the freezi n g of water, b u t there c a n n o t be affirmed, p a r t i c u l a r l y as the crucible is not t a k e n o u t and is still very hot, that. t h e l ' q u i d h'as not ceased to be in the spheroidal state. ~ 6~m]5[es R e n d u s , I887, page I27o.
Compressibility of IVater, etc.
477
Expansion is here assumed to be approximately hyperbolic, and the terminal pressure to be eight or ten pounds per square inch. General experience to date thus indicates that a triple expansion engine should do best work up to a pressure of about 25o or 3oo pounds, and that the four-cylinder engine should be adopted from that point up to the highest pressures likely to be adopted in the steam-engine, the double expansion compound serving its purpose well below the lowest figures above assigned to the triple engine. Any of the four types of engine may be made to overlap the range assigned its labor by suitably providing against wastes occurring within the engine by increased speed, by superheating, by expedients giving higher effectiveness to the jackets, or other methods of improvement. A n y system which increases the efficiency of the simple engine will improve the efficiency of the compound, and will corresPOndingly increase the range of pressure through which it will give satisfactory gain as compared with the former. (To be conlinued.) ON" THE
DILATATION
AND
COMPRESSIBILITY
OF
W A T E R AND THE D I S P L A C E M E N T OF ITS M A X I M U M D E N S I T Y By P R E S S U R E . ~ By E. H. AMAGAT. Translated by Chief Engineer ISHERWOOD, U.S.N.
I have described in a preceding communication (Comities Rcndus, A u g u s t 23, I886), the method I adopted for the determination of the dilatation and compressibility of liquids under very high pressures, and I gave some of the results obtained, b u t not corrected for the deformation of the piezometers. The ascertainment of this deformation, which I am now engaged on, appears so long and difficult, that I think I should without delay make known the results I have obtained for water, which has a special interest because of its phenomenon of maximum density. Commies Rendus, t887, p. tt59.
478
d m a g a t - [ s h e r w q o d ."
[ J. t~'. I,
Mr. Tait, who, previously to me, i n v e s t i g a t e d w a t e r b e t w e e n wide limits of pressure, has given for t h a t liquid the following f o r m u l a : z , m % = 0"0000489 - - 6"00000026 T J) ~'0
0"0000000067
applicable between 6 ° and I5 °, a n d b e t w e e n I5O and 5oo atmospheres, b u t I believe t h a t no physicist up to the p r e s e n t time has e x a m i n e d the subject relative to the m a x i m u m of density. T h e m e t h o d I e m p l o y gives directly the pressure necessary to m a i n t a i n a c o n s t a n t mass of w a t e r at the s a m e " v o l u m e at all t e m p e r a t u r e s , consequently, if w i t h two different t e m p e r a t u r e s the same pressure is obtained, there m u s t lie b e t w e e n them, as r e g a r d s t h a t pressure, the temp e r a t u r e corresponding to the m a x i m u m of density. T h e use of the same pressure w i t h the different t e m p e r a t u r e s obviates the necessity of correction for the elasticity of the m a t e r i a l of the piezometer, for the calculation of w h i c h the data are still w a n t i n g . T h e correction for difference of temp e r a t u r e relative to the dilatation has been m a d e b y provisionally a d m i t t i n g t h a t the coefficient of d i l a t a t i o n of glass does not v a r y w i t h the pressure, a supposition which cannot cause a n y notable error, i n a s m u c h as in the present case the variation of t e m p e r a t u r e is only of a few degrees. As regards pressure, I have carried nay e x p e r i m e n t s on w a t e r up to 3,-"oo a t m o s p h e r e s ; and as regards t e m p e r a t u r e , I have operated b e t w e e n zero and 5o °, w i t h the following results : A t 2oo atmospheres, in r o u n d numbers, the m a x i m u m d e n s i t y of w a t e r r e t r o g r a d e d towards and n e a r l y r e a c h e d zero. It appeared to be b e t w e e n zero and o'5 ° (half a degree). A t 7oa a t m o s p h e r e s there was no longer a n y m a x i m u m of d e n s i t y above zero, the form of the curves i n d i c a t i n g clearly t h a t it h a d passed below zero; further, the investig a t i o n could be followed to still lower t e m p e r a t u r e s since the freezing point of w a t e r is lowered by increased pressure. To well u n d e r s t a n d the e~zscmbh" of the p h e n o m e n a and
Dec., 1889.]
Compress~bility of Water, etc.
479"
the r e s u l t i n g consequences, curves should be formed b y t a k i n g the pressures as abscissas and the volumes as ordinates, to represent at different t e m p e r a t u r e s the v o l u m e s occupied u n d e r all the pressures by the same mass of water. T h e s e curves intersect each other successively at points w h i c h correspond to the c h a n g e of the sign of dilatation of the water, and fall successively in the order of the temperatures, the pressure increasing. A t 2oo a t m o s p h e r e s t h e y are in t h e n o r m a l order, b e c o m i n g m6re and more closed or s t r a i g h t e n e d as t h e y correspond to lower t e m p e r a t u r e s . T h e pressure c o n s t a n t l y a u g m e n t i n g , t h e y become m o r e a n d more opened in such a m a n n e r t h a t the co-efficient of dilatation increases r a p i d l y at first, and t h e n more slowly w i t h the pressure, which is jizst the c o n t r a r y of w h a t t a k e s place w i t h all the other liquids I have examined. T o w a r d s 3,ooo a t m o s p h e r e s the co-efficient of d i l a t a t i o n ceases to increase, and u n d e r g r e a t e r pressures it probably d i m i n i s h e s as in the case of other liquids ; the effect, too, is m u c h less m a r k e d as the t e m p e r a t u r e , w i t h equal pressure, is h i g h e r . T h e r e results, likewise, from this disposition of the c u r v e s that, b e t w e e n two different pressures, the difference of the ordinates and c o n s e q u e n t l y the co-efficient of c o m p r e s s i b i l i t y d i m i n i s h e s w h e n the t e m p e r a t u r e increases, w h i c h is also c o n t r a r y to w h a t occurs in the case of other liquids, a fact long since shown bv Grassi, a n d a quite n a t u r a l result of t h e disappearance of the m a x i m u m of density. F u r t h e r m o r e , and for the above reasons, this d i m i n u t i o n of the co-efficient of compressibility disappears w h e n the pressure increases, and it also disappears whert the t e m p e r a t u r e increases., c o n f o r m a b l y to the results of Messrs. P a g l i a n i and Vicentini, according to w h o m the compressibility of w a t e r ceases to decrease above 5o °. T h e t e m p e r a t u r e at w h i c h this inversion takes ptace decreases w h e n the pressure increases. Generally, a sufficient increase of pressure or of temperature gives w a t e r a t e n d e n c y to conform to the o r d i n a r y case of l i q u i d s ; and towards 3,ooo a t m o s p h e r e s the last traces have disappeared of the p e r t u r b a t i o n s of the g e n e r a l law w h i c h result from the existence of m a x i m u m density. Such are the general results of the cJtscmb/c of the pile-
Gossart-[sherwood."
480
[J. F. I.,
n o m e n a . I shall c o n t i n u e the s t u d y in detail, a n d investig a t e the s u b j e c t below zero. I can give the definitive :numerical results only after I h a v e finished the work now :in progress on the d e f o r m a t i o n of t h e piezometers. In conclusion, I w o u l d add t h a t none of t h e liquids I h a v e s t u d i e d up to the present time, has s h o w n a m a x i m u m of d e n s i t y u n d e r a n y pressure, w h i c h is c o n t r a r y t o a prevision f o r m u l a t e d r e c e n t l y b y Mr. Grimaldi, based on a s s u m e d cons t a n c y of t h e co-efficient of compressibility w i t h i n wide limits of pressure, an a s s u m p t i o n in complete disaccord w i t h the results I h a v e o b t a i n e d w i t h all the liquids I h a v e investigated. RESEARCHES
ON THE S P H E R O I D A L WATER.*
S T A T E oF
BY MR. GOSSART. Translated by Chief Eagineer [SHERWOOD, U.S.N.
T h e results w h i c h I h a v e the h o n o r of p r e s e n t i n g to the A c a d e m y , are relative to the t e m p e r a t u r e of w a t e r in the state of calefaction u n d e r d e c r e a s i n g pressures comprised b e t w e e n 760 m i l l i m e t r e s and 0"5 millimetre. Recently, Mr. L u v i n i (II Nuovo Cimento, t. xvii) h a s published some researches on the t e m p e r a t u r e of water, of alcohol, and of ether, calefied in a v a c u u m , b u t he could not m a i n t a i n c o n s t a n t the t e m p e r a t u r e of the crucible cont a i n i n g the liquid and m e r e l y r e s t i n g on a brick h e a t e d u n d e r a glass bell. F o r m i n g the v a c u u m rapidly, he followed the s i m u l t a n e o u s c h a n g e of a t h e r m o m e t e r placed in the liquid, and of the pressure. F r o m his o b s e r v a t i o n s he concluded t h a t the temperature o f t/ze liquid spheroid is the same as tke temperature o f ebulh'tion under t/ze pressure in the enclosed space a n d t h a t t h e r e could be t h u s directly caused the freezi n g of water, b u t there c a n n o t be affirmed, p a r t i c u l a r l y as the crucible is not t a k e n o u t and is still very hot, that. t h e l ' q u i d h'as not ceased to be in the spheroidal state. ~ 6~m]5[es R e n d u s , I887, page I27o.