## Sentence Examples

**Thomson**(**Lord****Kelvin**)**from****Regnault'****s****tables****of****the****properties****of****steam**,**assuming****the****gaseous****laws**,**did****not****vary****exactly****as****J**/**T**.**If****we****also****assume****that****they****are****constant****with****respect****to****temperature**(**which****does****not****necessarily****follow****from****the****characteristic****equation**,**but****is****generally****assumed**,**and****appears****from****Regnault'****s****experiments****to****be****approximately****the****case****for****simple****gases**),**the****expressions****for****the****change****of****energy****or****total****heat****from**00**to**0**may****be****written****E**-**Eo**=(0 - 0 0),**s****F**-**Fo**=(0**S****-**00).**Soc**.**Ed**., 1854)**to****represent****Regnault'****s****experiments****on****the****deviations****of****CO**2**from**.**The****method****differed****from****Regnault'****s****inasmuch****as****the****flask****was****exhausted****to****an****almost****complete****vacuum**,**a****performance****rendered****possible****by****the****high****efficiency****of****the****modern****air-pump**.**The****actual****experiment****necessitates****the****most****elaborate****precautions**,**for****which****reference****must****be****made****to****Morley'****s****original****papers****in****the****Smithsonian****Contributions****to****Knowledge**(1895),**or****to****M**.**Soc**. 43,**p**. 361)**an****important****correction****which****had****been****overlooked****by****previous****experimenters****with****Regnault'****s****method**,**viz**.**Mag**., 1868, 35,**p**. 161,**and****the****full****account**,**which****serves****as****an****excellent****example****of****the****extraordinary****care****and****ingenuity****of****Regnault'****s****work**,**is****given****in****the****Memoires****de****l'academie****des****sciences**, 1868,**xxxvii**.**In****diameter**,**and**,**using****Regnault'****s****apparatus**,**found**,**that****the****velocity****could****be****represented****by**33 3(1 +**C**/**P**),**where****P****is****the****mean****excess****of****pressure****above****the****normal**.**Bosscha****From****An****Independent****Reduction****Of****Regnault'****S****Experiments****Is****Probably****Within****The****Limits****Of****Accuracy****Between****Ioo**°**And****Zoo**°**C**.,**So****Far****As****The****Mean****Rate****Of****Variation****Is****Concerned**,**But****The****Absolute****Values****Require****Reduction**.**These****Experiments**,**Which****Have****Been****Extended****By****Barnes****Over****The****Whole****Range****O**°**To**100°,**Agree****Very****Well****With****Rowland****And****Griffiths****In****The****Rate****Of****Variation****At**20°**C**.,**But****Show****A****Rather****Flat****Minimum****Of****Specific****Heat****In****The****Neighbourhood****Of**38°**To**40°**C**.**At****Higher****Points****The****Rate****Of****Variation****Is****Very****Similar****To****That****Of****Regnault'****S****Curve**,**But****Taking****The****Specific****Heat****At**20°**As****The****Standard****Of****Reference**,**The****Actual****Values****Are****Nearly**0.56%**Less****Than****Regnault'**.**S****Above**60°**C**.**Regnault'****S****Formula****Is****Adopted**,**The****Absolute****Values****Being****Simply****Diminished****By****A****Constant****Quantity****O**O056**To****Allow****For****The****Probable****Errors****Of****His****Thermometry**.**Many****Authors**,**Adopting****Regnault'****S****Formula**,**Have****Selected****O**°**C**.**As****The****Standard****Temperature**,**But****This****Cannot****Be****Practically****Realized****In****The****Case****Of****Water**,**And****His****Formula****Is****Certainly****Erroneous****At****Low****Temperatures**.- 1.40,
**Rankine****found**= .385,**S****a****value****which****he****used**,**in****default****of****a****better**,**in****calculating****some****of****the****properties****of****steam**,**although****he****observed****that****it****was****much****larger****than****the****coefficient**.305**in****Regnault'****s****formula****for****the****variation****of****the****total****heat**. = 475,**S****greatly****increased****the****apparent****discrepancy****between****Regnault'****s****and****Rankine'****s****formulae****for****the****total****heat**.**Assuming****an****equation****of****the****form****log**(**p**/760) =**a****log**(0/373),**their****results****give****a**=/**S****R**=4.305,**or**=0.474,**S****which****agrees****very****perfectly****with****Regnault'****s****value**.- 1889),
**who****has****devoted****minute****attention****to****the****reduction****of****Regnault'****s****observations**,**assuming**/**S**=1.400**s****as****the****theoretical****ratio****of****specific****heats****of****all****vapours****on****his**"**aether-pressure****theory**,"**has****calculated****the****properties****of****steam****on****the****assumption**=0.384.**S** **He****endeavours****to****support****this****value****by****reference****to****sixteen****of****Regnault'****s****observations****on****the****total****heat****of****steam****at****atmospheric****pressure****with****only**19°**to**28°**of****superheat**.**A****similar****objection****applies**,**though****with****less****force**,**to****Regnault'****s****main****experiments****between**125°**and**225°**C**.,**giving****the****value**=0.475,**S****in****which****the****superheat**(**on****which****the****value****of****S****depends**)**is****only****one-sixteenth****of****the****total****heat****measured**.**Perry**(**Steam****Engine**,**p**. 580),**assuming****a****characteristic****equation****similar****to****Zeuner'**(**s****which****makes****v****a****linear****function****of****the****temperature****at****constant****pressure**,**and****S****independent****of****the****pressure**),**calculates****S****as****a****function****of****the****temperature****to****satisfy****Regnault'****s****formula**(10)**for****the****total****heat**.**This****method****is****logically****consistent**,**and****gives****values****ranging****from**0.305**at****o**°**to**0.345**at****Ioo**°**C**.**and**0.464**at**210°**C**.,**but****the****difference****from****Regnault'****s**= 0.475**S****cannot****easily****be****explained**.**If****the****steam****at****A****were****dry****and****saturated**,**we****should****have**,**assuming****Regnault'****s****formula**(**to**),**H****A**-**H****D**= 305 (0**'-O**),**whence**,**if**= .475,**S****we****have****zL**= .3 0 5 (0 '- 0)-.**It****is****evident****that****this****is****a****very****delicate****method****of****determining****the****wetness****z**,**but**,**since****with****dry****saturated****steam****at****low****pressures****this****formula****always****gives****negative****values****of****the****wetness**,**it****is****clear****that****Regnault'****s****numerical****coefficients****must****be****wrong**.**If****we****assume****Regnault'****s****formula**(10)**for****the****total****heat**,**we****have****evidently****the****simple****relation**=0.305(0**S****'-**0)/(0"-**o**),**supposing****the****initial****steam****to****be****dry**,**or****at****least****of****the****same****quality****as****that****employed****by****Regnault**.**Whatever****may****be****the****objections****to****Regnault'****s****method****of****measuring****the****specific****heat****of****a****vapour**,**it****seems****impossible****to****reconcile****so****wide****a****range****of****variation****of****S****with****his****value**5=0.475**between**125°**and**225°**C**.**It****is****also****extremely****unlikely****that****a****vapour****which****is****so****stable****a****chemical****compound****as****steam****should****show****so****wide****a****range****of****variation****of****specific****heat**.**The****method****of****deducing****the****specific****heat****from****Regnault'****s****formula****for****the****variation****of****the****total****heat****is****evidently****liable****in****a****greater****degree****to****the****objections****which****have****been****urged****against****his****method****of****determining****the****specific****heat**,**since****it****makes****the****value****of****the****specific****heat****depend****on****small****differences****of****total****heat****observed****under****conditions****of****greater****difficulty****at****various****pressures**.**Between**103°**C**.**and**113 °**C**.**This****is****about**4%**larger****than****Regnault'****s****value**,**but****is****not****really****inconsistent****with****it**,**if****we****suppose****that****the****specific****heat****at****any****given****pressure****diminishes****slightly****with****rise****of****temperature**,**as****indicated****in****formula**(16)**below**.**Admitting****the****value**=0.497**S****for****the****specific****heat****at**108°**C**.,**it****is****clear****that****the****form****of****Regnault'****s****equation**(**io**)**must****be****wrong**,**although****the****numerical****value****of****the****coefficient**0.305**may****approximately****represent****the****average****rate****of****variation****over****the****range**(**loo**°**to**190°**C**.)**of****the****experiments****on****which****it****chiefly****depends**.**Regnault'****s****experiments****at****lower****temperatures****were****extremely****discordant**,**and****have****been****shown****by****the****work****of****E**.**The****introduction****of****this****correction****into****the****calculations****would****slightly****improve****the****agreement****with****Regnault'****s****values****of****the****specific****heat****and****total****heat****between**100°**and**200°**C**.,**where****they****are****most****trustworthy**,**but****would****not****materially****affect****the****general****nature****of****the****results**.**The****values****of****H****at****o**°**and**40°**agree****fairly****with****those****found****by****Dieterici**(596.7)**and****Griffiths**(613.2)**respectively**,**but****differ****considerably****from****Regnault'****s****values**606.5**and**618.7.**The****rate****of****increase****of****the****total****heat**,**instead****of****being****constant****for****saturated****steam****as****in****Regnault'****s****formula**,**is****given****by****the****equation****dH**/d0 =(1 -**S****Qdp**/d0).**The****mean****value**, 0.313**of****dH**/d0,**between****loo**°**and**200°**agrees****fairly****well****with****Regnault'****s****coefficient**0.305,**but****it****is****clear****that****considerable****errors****in****calculating****the****wetness****of****steam****or****the****amount****of****cylinder****condensation****would****result****from****assuming****this****important****coefficient****to****be****constant**.**Regnault'****s****formula****for****the****total****heat****is****here****again****seen****to****be****inadmissible**,**as****it****would****make****the****latent****heat****of****steam****vanish****at****about**870°**C**.**instead****of****at**365°**C**.**It****should****be****observed**,**however**,**that****the****assumptions****made****in****deducing****the****above****formulae****apply****only****for****moderate****pressures**,**and****that****the****formulae****cannot****be****employed****up****to****the****critical****point****owing****to****the****uncertainty****of****the****variation****of****the****specific****heats****and****the****cooling****effect****Q****at****high****pressures****beyond****the****experimental****range**.**Since****it****is****much****easier****to****measure****p****than****either****L****or****v**,**the****relation****has****generally****been****employed****for****deducing****either****L****or****v****from****observations****of****p**.**For****instance**,**it****is****usual****to****calculate****the****specific****volumes****of****saturated****steam****by****assuming****Regnault'****s****formulae****for****p****and****L**.- 103,
**p**. 185, 1858)**to****represent****the****vapour-pressure****of****a****solution**,**and****was****verified****by****Regnault'****s****experiments****on****solutions****of****H**2**SO**4**in****water**,**in****which****case****a****constant**,**the****heat****of****dilution**,**is****added****to****the****latent****heat**. **A****formula****of****the****same****type****was****given****by****Athenase****Dupre**(**Theorie****de****chaleur**,**p**. 96,**Paris**, 1869),**on****the****assumption****that****the****latent****heat****was****a****linear****function****of****the****temperature**,**taking****the****instance****of****Regnault'****s****formula**(**io**)**for****steam**.**The****justification****of****this****assumption****lies****in****the****fact****that****the****values****of****c****found****in****this****manner**,**when****substituted****in****equation**(25)**for****the****saturation-pressure**,**give****correct****results****for****p****within****the****probable****limits****of****error****of****Regnault'****s****experiments**.**The****values****of****the****saturation-pressure****given****in****the****last****column****are****calculated****by****formula**(25),**which****agrees****with****Regnault'****s****observations****better****than****his****own****empirical****formulae**.