National Bureau of Standards Ubrar Admin. Bldg.

PEC 8 J366

NBS

Reference book not to be

1 library,

TECHNICAL NOTE

299

Calculation of the Heating Value

of a Sample of High Purity Methane

for Use as a Reference Material

George T. Armstrong

4

Q

Z

/

«*** "' °°.

o

1*

\ T

Q

US DEPARTMENT OF COMMERCE

National Bureau of Standards
THE NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards1 provides measurement and technical information services

essential to the efficiency and effectiveness of the work of the Nation's scientists and engineers. The

Bureau serves also as a focal point in the Federal Government for assuring maximum application of the physical and engineering sciences to the advancement of technology in industry and commerce. To

accomplish this mission, the Bureau is organized into three institutes covering broad program areas of research and services: THE INSTITUTE FOR BASIC STANDARDS . . . provides the central basis within the United

States for a complete and consistent system of physical measurements, coordinates that system with the measurement systems of other nations, and furnishes essential services leading to accurate and uniform

physical measurements throughout the Nation's scientific community, industry, and commerce. This

Institute comprises a series of divisions, each serving a classical subject matter area: —Applied Mathematics—Electricity—Metrology—Mechanics —Heat—Atomic Physics—Physical

Chemistry—Radiation Physics—Laboratory Astrophysics2 —Radio Standards Laboratory,2 which

includes Radio Standards Physics and Radio Standards Engineering—Office of Standard Refer- ence Data. THE INSTITUTE FOR MATERIALS RESEARCH . . . conducts materials research and provides

associated materials services including mainly reference materials and data on the properties of materials. Beyond its direct interest to the Nation's scientists and engineers, this Institute yields services which are essential to the advancement of technology in industry and commerce. This Institute is or- ganized primarily by technical fields: —Analytical Chemistry—Metallurgy—Reactor Radiations—Polymers—Inorganic Materials—Cryogenics2—Materials Evaluation Laboratory—Office of Standard Reference Materials. THE INSTITUTE FOR APPLIED TECHNOLOGY . . . provides technical services to promote the use of available technology and to facilitate technological innovation in industry and government. The

principal elements of this Institute are: —Building Research—Electronic Instrumentation—Textile and Apparel Technology Center

Technical Analysis—Center for Computer Sciences and Technology—Office of Weights and Measures—Office of Engineering Standards Services—Office of Invention and Innovation—Clearinghouse for Federal Scientific and Technical Information.3

1 Headquarters and Laboratories at Gaithersburg, Maryland, unless otherwise noted; mailing address Washington, D. C,

20234.

2 Located at Boulder, Colorado, 80302.

3 Located at 5285 Port Royal Road, Springfield, Virginia, 22151.
UNITED STATES DEPARTMENT OF COMMERCE • John T. Connor, Secretary

NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

NBS TECHNICAL NOTE 299

ISSUED DECEMBER 15, 1966

Calculation of the Heating Value

of a Sample of High Purity Methane

for Use as a Reference Material

George T. Armstrong

Heat Division

Institute for Basic Standards

National Bureau of Standards

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, Government Printing Office Washington, D.C.. 20402 - Price 25 cents

Contents

Page

Abstract 1

1. Introduction 1

2. ASTM Definition of Terms

3. Defined Quantities and Exact Equivalent Quantities . U

k' Accepted Physical Quantities k

5. Total Moles of Ideal Gas in a Cubic Foot at

Standard Temperature and Standard Pressure .... 5

6. Moles of H-0 and CH in a Cubic Foot of Ideal Gas

(Saturated Basis)

7. Gas Imperfections of CH . 6

8. Moles of Methane jji a Standard Cubic Foot of Real Gas

(Saturated Basis) and a Cubic Foot of Dry Gas ... 7

9. Heating Value of Pure Methane 8

10. Adjustment of Heat of Combustion to 60°F 10

11. Value of the British Thermal Unit (Btu) 11

12 . Heat of Combustion of CH in Btu per Cubic Foot ... 12

13. Analysis of Two Special Methane Samples for

Certification 13

IJ4. Heat of Combustion of the Two Special Samples lit

15. Certificate Values for Heat of Combustion of

Special Samples of Methane 15

16. References 16

Appendix I. Report of Analysis of Two Cylinders

of Methane 18

III

Calculation of the Heating Value of a Sample

of High Purity Methane for Use as a Reference Material

George T. Armstrong

Abstract

The heat of combustion of CH^ has been recalculated in kj (mol) , Btu (mol) -1

, Btu (cu ft)-1 (dry basis) and Btu (std. cu ft) -1 (saturated

basis), using the best available experimental determinations of the

heat of combustion and other measured quantities and the most recent

generally accepted physical constants and defined physical units. The

calculations are outlined in detail. The resulting quantities are applied to calculation of the heat of combustion of a reference sample

of CHj. submitted for analysis of composition and certification of

heating value by the Institute of Gas Technology.

1. Introduction

A former activity of the National Bureau of Standards (NBS) was to supply to industry reference samples of fuel gas, certified with

respect to heat of combustion, for calibrating gas combustion

calorimeters. In 1962, following a reorganization of the NBS chemistry

divisions, this activity was transferred to the Institute of Gas

Technology (IGT) (Illinois Institute of Technology, Chicago. Illinois),

with the understanding that the NBS would periodically certify samples

for use as the IGT primary laboratory reference materials.

Samples issued by the IGT are supplied with a secondary certification of the Gross- or Total-Heating Value, which is determined in

their laboratory by calorimetric comparison with their primary

laboratory reference material. The uncertainty limits stated by the

IGT in their secondary certification are ±0.9 Btu (standard cu ft) .

The heat of combustion of a sample of methane containing only

small amounts of impurities can be calculated from the composition

and known heats of combustion of CHk and the impurities, together

with certain physical properties and conversion factors.
The most precise determination of the heat of combustion of

CH^ is based on the mass rather than the volume burned because of

the greater accuracy with which mass can be measured. However,

the users require the heat of combustion on a volume basis . In

making a conversion from the precise experimental determination of

the heat of combustion of pure CH4 to the heat of combustion of the

sample required by the users, the following factors must be taken

into account:

(1) The energy unit in which the determination was made and

the unit to which it must be convert ed.

(2) The mass unit in which the determination was made and

the current accepted value of the mass unit.

(3) The temperature dependence of the heat of combustion.

CO The current best value for the ideal molar volume of a gas.

(5) The current best value for the vapor pressure of water.

(6) The current best coefficients for the real gas behavior

of methane and its mixtures with small quantities of

H_0 and other impurities.

(7) The analysis of the gas.

This report outlines in detail how these factors are taken

into account The results are then applied to two samples submitted

by the Institute of Gas Technology and their heating values are calculated on a dry basis and on a saturated basis in Btu (cu ft)"-'-

at 60°F. The calculations are shown in elaborate detail because It

has been our experience that annoying small discrepancies in calculations by different people can occur because of differences either

in source data or in method of rounding figures Q In these calculations an excessive number of figures is carried, in many instances

well beyond the level of significance, in order to prevent any

errors of rounding. In general each physical quantity used

is treated as exact for the purpose of calculation, and rounding to

a significant figure is only done at the end of the calculations.

The procedure as outlined in sections 2-12 is valid as a calculation of the heat of combustion of pure methane on a weight basis

and on a volume basis, both dry and water- saturated. Because the

best available value from NBS for the heat of combustion of CH4 and

of other measured physical quantities, and the values of general

physical constants and defined units accepted by NBS have been used,

the calculation of the heat of combustion may be taken as our best

estimate of this quantity on the basis of current information.
The American Society for Testing and Materials (ASTM) definitions for standard cubic foot, heating value, and related quantities

have been used (except where distinctions are noted) because the

principal use of the gas described is as a reference gas for calibrating calorimeters following ASTM procedures [l],

2. ASTM Definitions of Terms [l],

(1) Total Calorific Value: The total calorific value (Total or Gross Heating Value) of a gas is the number of British

thermal units evolved by the complete combustion, at

constant pressure, of one standard cubic foot of gas with

air, the temperature of the gas, air and products of

combustion being 60 F, and all the water formed by the

combustion reaction being condensed to the liquid state

„

(2) Net Calorific Value : The net calorific value of a gas is

the number of British thermal units evolved by the complete

combustion, at constant pressure, of one standard cubic

foot of gas with air, the temperature of the gas, air, and

products of combustion being 60 F, and all of the water

formed by the combustion reaction remaining in the vapor

state.

(3) British Thermal Unit 3

: A British thermal unit, or Btu,

is the quantity of heat that must be added to one avoirdupois pound of pure water to raise its temperature from

58 „ 5 F to 59.5 F under standard pressure a

(4.) Standard Cubic Foot of Gas : A standard cubic foot of gas

is the quantity of any gas that at standard temperature

and under standard pressure will fill a space of one

cu. ft. when in equilibrium with liquid water.

(•5) Standard Temperature : The standard temperature is 60 F,

based on the International Temperature Scale.

(6) Standard Pressure : The standard pressure is the absolute

pressure of a column of pure mercury 30 in. in height at

32 F and under standard gravity (32. 174- ft sec~2) (See

footnote (a), Section 3o0 o )

(7) Saturated Basis: The expressed total calorific value of

a gas when it is saturated with water at standard temperature and pressure; 1 cu. ft. of this gas is equivalent in

dry gas content to 0.9826 cu. ft. of dry gas at the

temperature and pressure. (See footnote (a) , Section 6.0.)

Note that the Btu as used in ASTM methods for gaseous fuels is

different from that used in ASTM methods for liquid petroleum fuels

and ASTM methods for coal and related solid fuels.

We interpret this as the International Practical Te^erature Scale

of 191+8, Text Revision of I960.
3. Defined Quantities and Exact Equivalent Quantities

The quantities listed in Table 1 are the definitions and exact

equivalents used in this report. Where inconsistencies exist between

definitions of Table 1 and ASTM definitions, the definitions in

Table 1 are used. Such inconsistencies are explained in footnotes

to Table 1.

Table 1

1 inch = 2.%k cm (exactly) [2]

1 cubic foot = (2.5H x 12

)

3

= 28316. 8U6592 cm

3

-2 a Standard gravitational acceleration = 980.665 cm s [2

]

_2b

1 standard atm. pressure =* 1,013,250 dyn cm [2]

1.8 deg F = 1 deg C [2]

32 °F O 'CO 273-15 °K [2]

1 int. J (NBS) = 1.000165 J [3,H]

1 lb. = U53. 59237 g [2]

1 cal = J4.I8UO J [2]

U. Accepted Physical Quantities

In Table 2 are listed values for the derived physical quantities

whose values are not defined but are dependent upon the properties

of some material.

Table 2

R (gas constant) = 8.31U3 ±0.0008c J (deg K)"

1

mol'

1

[2]

V (ideal gas) = (2.21036 ±0.00010)

c x 10^ cm

3 mol

-1

[2]

On the basis of this definition the acceleration in ft s"^ is

32.17UOU855, which differs from the value listed in definition (6)

Section 2.0 by 1.5 parts in 1CP.

b

We take 13.595080 g cm"3

[20] for the density of mercury at 0°C and

one atm pressure, which we adjust to 13. 595052 g cm~3 at 0°C under an average pressure of 1/2 atm as is appropriate for the density of a column of mercury supported by one atm of gas pressure. The

height of a column of mercury of this density supported by one atm

pressure under standard gravitational acceleration is 76.000257 cm.

Uncertainties in R and V are interdependent. The uncertainties

given are 2o.
In Table 3 are listed values for thermodynamic properties of

materials that were accepted for use as data in making the calculations

of this Technical Note.

Table 3

C° (CH.) at 25°C = 8.439* cal deg"

1 mol"1

[19]

P 4

C° (02

) at 25°C = 7.016

3

cal deg

-1

mol"

1

[19]

C° (CO ) at 25°C = 8.87

a cal deg"1

mol"

1

[19]

p <. C° (HO) at 15°C = 4.1858 Jg"

1

(deg C)"1 [ul

P ^ H°

Q

-H°

5 (H2

0) = 20.8949 Jg"

1

[U]

H

25°C"

H

15.555°C (H

2

0) = 39.4962 Jg"

1

[U]

P(H

2

0) at 15°G = 0.017429 atm [5,6]

AH°[CH. (g)] at 25°C = 212.790

3

kcal mol"1 [Section 9]

C 4

5 • Total Moles of Heal Gas in a Cubic Foot at

Standard Temperature and Standard Pressure

In the calculation below, t is the temperature in degrees above the

ice point, T is the temperature in degrees K, P is the absolute pressure,

R is the gas constant, V is the volume, and N is the number of moles in a cubic foot at standard temperature and standard pressure. All values are taken from Table 1 or Table 2

.

t - 6o°f - 15 . 55555 °c

T = 273-15 + ^S.SS^S - 288.70555°K

P - 30 in. Hg - 762 mm Hg - 1.002628185 atm

- 1,015,913-01 dyn cm"

2

N

PV „ 1,015,913.01 x 28316.8U6592 x lo"7 RT * (8.3m3 ±.0008) x 288.70555

1.198U52 ± .000115 mol ft"3

The uncertainty in the number of moles per cubic foot is almost

solely due to the uncertainty of the gas constant R.

See footnote Section 12
6. Moles of HO and CH in a Cubic Foot of Ideal Gas

(Saturated Basis)

Osborne and Meyers [5] report the vapor pressure of water to be

0.25592 lb (in.)" 2 at 60 F which we adjust upward by 0.00022 lb (in.) -2

to 0.25614 lb (in.) -2

on the basis of the difference at 15 °C between

the values given by Osborne and Meyers and the later revision by

Osborne, Stimson and Ginnings [6], Using the same conversion factor,

14.6960 lb (in.) -2 = 1 atm, as was used by Osborne and Meyers, we find

for the partial pressure of H2O vapor 0.0174.29 atm. or 17659.93 dyne cm

-2

.

The residual pressure of gas is 1,015,913.01 - 17,659.93 or 998, 25 3o 08 dyne cm~2

. a The water present is o 0208330 moles and the

other gas present is 1.177619 moles ±0.000114 moles. The uncertainty

in the number of moles is based primarily on the uncertainty in R.

7. Gas Imperfection of CH.

4

In calculating the heating value of methane, real gas, for

NBS Circular 464. [7], Jessup used a value of 0.99800 ±0.00005 for the

quantity PV/RT [8], at one atm pressure and 60 °F, which he obtained from

unpublished calculations of C. S. Cragoe. Since then Dous±in [9] has measured the P-V-T relations of methane. For the Beattie-Bridgman equation (l)

P = [RT (l-e)/V2 ][V+B] - A/V2

(l)

A = A (l-a/v) = 2.2152 (1-0.02174-/V)

o B = B (l-b/v) = 0.05159 (1+0.02198/V)

o

e = C/T3V = 15 x 1oVt3V

We assume that for a mixture of CH/ with a small amount of H2O

P (total) is appropriate for P in calculating PV/RT. We calculate

V roughly from the ideal gas equation.

V = RT/P = (8.3143 x 288o 705 55 )/l, 015, 916. U5 = 23, 627 o 776 cm3

Next we calculate the constants A, B and £.

A = 2o2152 (0o99908) = 2.21316

B = 0.05159 (1.000930) = 0.051638

£ = 15 x 10V( 288 o 7055

)

3 x 23.627 = 15 x I0V56 x 107 = 0.26 x 10~3

3 The residual pressure leads to a factor of 0.9826167 for the ratio of

moles of CH^ in a cubic foot of saturated gas to moles of CH4 in a cubic foot of dry gas. This differs by 17 »0 parts in 106 from the

factor 0.9826 given in definition (7) Section 2.0.

he lists
The Beattie-Bridgman equation can be rearranged to give equation (2).

PV/RT = [(l-e)[V+B]/V] + A/VRT (2)

We are now prepared to calculate the factors and terms of

equation (2 )

.

(1 - e) - (1 - 0.00026) = 0.9997U

(V + B)/V = (23-627 + 0. 051638 )/23- 627 = 1.002186

(1 - e)(V + B)/V = 1.00192U

A/VRT = 2. 21316/2 3- 62 7 x .08205U x 288.7055 - 0.00395U

PV/RT = 1.00192U - 0.00395U = 0.997970

This value for PV/RT is within the limits 0.99800 ±0.00005 suggested

by Jessup and so we retain the same uncertainty, but use our calculated

value of PV/RT for PV/RT (real, saturated) and also for PV/RT (real, dry).

8 . Moles of Methane in a Standard Cubic Foot of Real Gas

(Saturated Basis) and a Cubic Foot of Dry Gas

Using symbols as defined in Section 5, but allowing N (real, saturated)

now to be the number of moles of real gas in a standard cubic foot, we calculate as follows . For the saturated gas

N(real, saturated) x (PV/RT) (real, saturated) = N( ideal saturated)

1-177619 to.oooiiU

N(real, saturated) .99797 ±0.00005

= 1.18001U ±(o.ooonU) ±(0.000059)

= 1.18001U ±.000128 moles CH /Standard

cubic foot real gas) (saturated basis).

For the dry gas we simil arly calculate

N(real, dry) x (PV/RT ) (real, dry) = N( ideal, dry)

»/ i j \ 1-198U52 N(real, dry) = 0>99797

= 1.200890 moles CHjAcubic foot real

gas) (dry basis).
9. Heating Value of Pure Methane

Prosen and Rossini reported the heat of combustion of CHh at 25°C

to be -212.798 ±0.072 kcal mol-1 [10]. This was derived from the measure'

ments of Rossini [11], and is consistent with the values -212.80, and

-212.798 kcal mol~l reported by Rossini and co-workers [Jj. , 13 ] in their

compilations for the American Petroleum Institute. Rossini's determination is used in this work as the best value for the heat of combustion

of methane. A detailed description of adjustment of the heating value

to correspond to currently accepted physical units and standard

conditions is given below.

(a) Citation of original data. The value originally reported by

Rossini [11, a] at 30°C and one atm pressure of real gas, for a mole

corresponding to 36.0312 grams of H2O formed was AHj, = -889. 700

±0.218 int. kJ (NBS) mol-1

. This was modified by Rossini [11, b] to

correct for an error in reducing his conditions to one atm pressure

to AHc = -889.720 ±0.230 int. kJ (NBS) mol-1

.

(b) Adjustment to standard states. We assume that in the combustion

as carried out by Rossini, oxygen and methane entered the calorimeter in

the pure state at one atm pressure and the exit gases consisted of H2O at

its vapor pressure and CO2 at a sufficient pressure to make up one atm.

The enthalpy correction for non-ideality, H°-H, is shown for these

gases in Table k and in Figure 1 for convenience in interpolation. The

data for CO2 and O2 are taken from Hilsenrath, et al. [17], and the data

for CH^ are taken from Tester [18], The mixture of CO2 with a small

amount of H2O is presumed to have the same P-V-T properties as pure CO2

at one atm pressure

.

The enthalpy change in the ideal gas state at one atm pressure is

the same as the enthalpy change of the real gases at zero pressure . The

correction reactions are shown below as reactions 1-5

.

CH^(g,p=l atm) + 20

2 (g,p= 1 atm) = 2^0(4) + C0

2 (g,p-1 atm)AH

30

=-889.720 (l)

CI^(g,p=0) = CH

i| (g,p = 1 atm) at 30°C, AH - (H -H )^) - - .0162 (2)

20

2 (g,p=0) = 202 (g,p = 1 atm) at 30°C, AH - (K -H°)(20

2

) - - ..0l£6 (3)

C0

2 (g,p=l atm) = C02 (g,p=0) at 30#C, AH = (H°-H )(C0

2

) - + .01*18 (U)

CI^(g,P=0) + 20

2 (g,p=0) = 2^0(4) + C0

2 (g,p=0) AH°

30

= -839-710 (5)

AH for reaction (5) is the standard heat of reaction at 30°C in int.

kj(NBS) mol"1 for a mole equivalent to 36.0312 g K^O.

8
(c) Adjustment to absolute Joule (abbreviation. J). As one int. J(NBS) is 1.000165 J, the value listed in eq (5) is equal to

AH^ = -889.8568 kJ mol"1 for a mole equivalent to 36.0312 g HgO.

(d) Adjustment of atomic weights. At the time of publication

of Prosen and Rossini [10] the atomic weight scale of l°hl was in use and the molecular weight of water was taken to be 18.016 j the mole

of methane thus corresponding then to 36.032 g H2O. Converting we

find AH° = -889.8766 kJ mol"1 (19U1) for a mole equivalent to

36.032 g H20. At the time of the present report the atomic weight

scale of 1961 [16] is in use, and the molecular weight of water is

18. 0153^. Converting by this number we find

AH? = -889.8UUO kJ mol"

1

(1961)

for a mole of CE corresponding to 36.03068 g JL0.

(e) Adjustment to 25°C. From Table 3 we find

(H25

_H30

)(2H

2 0) = -36 ' 03068 x 20 - 8^9 " -752.857U J mol"1

(H25"H

30

)(C0

2

) "

"5 X U * 18U X 8 ' 87 - -185.560U

(H°-^)(CH

1; ) = +5 x U.18U x 8.U39 - +176.5U39

(H^ -H^)(20

2

) - +5 x U.18U x 2x7.0]£ - +293.5U9U

(H°

5

-H° ) (Reaction (5)) = -U68.32U5 J mol"

1

Adjusting the heat of reaction we find AH° at 25 °C = -890.3U5 kJ mol"

(19U1) = -212.798 kcal mol-1 (l°Ul) based on a mole equivalent to

36.016 g BjO. The latter value is the value reported by Prosen and

Rossini [10], who assigned an uncertainty (twice the estimated

standard deviation of the mean) of 0.072 kcal mol -^-.

On the basis of a mole equivalent to 36.03068 g H2O. we find

AH° at 25°C = -890.312 ±0.300 kJ mol

-1

(1961

)

= -212.790 ±0.072 kcal mol"1 (1961

)
Table U. Values of Enthalpy Functions

at One Atmosphere Pressure

2 [17] C02 [17] CH

U

[18]

(H°-E°)/RT

o (H-E°)/RT

Q (H°-E°)/RT

o (H-E°)/RTq H°-H° H-H°

°K RT = 2271 J mol

o -1

RT 2271 J mol" cal mol cal mol

280 3.5875 3.5835

290 3.7166 3-7129

300 3-8U59 3.81+21+

310 3-975U 3.9721

320

3.8300

3.9908

U.1537

U.3186

3. 808

3.970

U.135

U.301

22U3.U 2238.7

2U12.7 2I4O8.7

2585-5 2582.1

10. Adjustment of Heat of Combustion to 60°F

The reaction involved in the combustion is reaction (1)

CH

u

(g) + 20

2 (g) = C0

2 (g) + 2^0(4) (1)

For this reaction

AH^ = AH

25 o G

+ (H

T

-H

25

)[C0

2

] + (l^-H^) [2BfeO(i )]

- (H^H^MCHjJ - (H

T

-H

2 ^)[202

]

For C02 (g), CH^(g), and 2 (g) we take Hj-H^ to be (T-25) x Cp at 25 °C and

calculate Ht-H2£ for H2O from enthalpy tables. Values for Cp at 25°C are selected from Wagman, et al. [19], as listed in Table 2. For water

we find enthalpy data by Osborne, Stimson, and Ginnings [lUl at one atmosphere pressure, which has the values 10l4*899H J g at 25 °C

and 67.2632 >. J g"1 at 16 *C. Using an interpolated value of

Cp » U.l85lJg" deg"1 for the heat capacity of water at 15.7777°C, we calculate for the enthalpy difference Hi£°c " %5.5555°C = 1.86QO

J g

-1

. The enthalpy difference H25°c-Kl5.^555°C = 39.U962 J g"

(that is 10U.899U - 67.2632 + 1+.1851 x .UUiUUl ) • This is equal to

711.5375 J (mol)-1 .

10
We tabulate below the heat capacity contributions.

H

l5.5555~H

25

J

C0

2 - 350.66

2^0(4) -1U23.09

20

2 + 55U.U8

CH, + 333-U7

Reaction (l) - 885-79

Estimated uncertainty ± 8.8

From above we have -0.886 ±0.0088 kJ mol for the adjustment to

60°F (15.55555°F). The standard heat of combustion at 60°F is therefore

AH60F

= _891 - 196 jK mol"

ia

(1961 basis)

with an uncertainty of 0.300 kJ mol01 .

We now make the adjustment to real gases at 60°F. The reactions

given below indicate the changes required to reduce the combustion energy

from that of the ideal gas reaction to that of the real gas reaction at

60°F. The data for reactions (2'), (3 ' ) and (k ' ) are taken from Figure 1.

AH° at 60°F

CI^(g,p=0) + 20

2 (g,p=0) = 2^000 + C02 (g,p=0) -891.196 kJ mol"1

(1 '

)

CH^(g,p=l atm) = C^(g,p=0) (H°-H)(CI^) = .OI83 (2')

20

2 (g,p=l atm) = 20

2 (g,p=0) (H°-H)(202

) = .0172 (3')

C0

2 (g,p=0) = C0

2 (g,p=l atm) (H-H°)(C0

2

) = .0U70 (U '

)

CH

i+ (g,p=l atm) + 20

2 (g,p=l atm) -891.2075 (5')

= 2^0(4) + C0

2 (g,p=l atm)

11. Value of the British Thermal Unit (Btu

)

From definition (3), the specific heat of water from Osborne,

Stlmson, and Ginnings [lU], and constants from Table 1, we calculate

1 Btu to be 105U.803 ±0.08 J (lb) -1 (deg F) _1 in the following way.

The heat capacity Cpof water at 59°F (l5°C) is H.1858 J g"1(deg C)"1

and between lU°C and 16 °C deviates from this in an approximately linear

way, so that the average heat capacity from 58.5°F to 59-5°F can be

taken as the heat capacity at 59°F.

aSee footnote Section 12

.

11
The value of the Btu is , therefore

:

1 Btu = [1+.1858 x U53- 59237/1- 8] - 10£H.80U J

±0.08 J

An uncertainty of 0.0003 J g (deg C) is assigned to the

heat capacity of water at this temperature on the basis that W. J. de Haas

selected H.1855 J g

- ^ (deg C)-1 for the best value of the heat capacity

of water (see Stimson [15]). This is equivalent to an uncertainty of

0.08 J in the Btu as defined in Section 2. Note that

this uncertainty applies only to the British thermal unit as defined

above. Other definitions of the Btu may lead to values differing by

larger amounts.

12 . Heat of Combustion of CH in Btu per cubic foot

Using figures previously calculated, we evaluate the heat of combustion of CH as listed below.

The heat of combustion in Btu (mol) is

Al£60F (CH, ) = -891.2075/105U.80U = -8UU.903U Btu (mol)"1

with an uncertainty of (0.286 + .OO8I4 + 0.071 Btu mol" ) « 0.295 Btu mol" '

The heat of combustion in Btu per cubic foot is

AH°

60F

(CH, ) (dry basis) = 1.200890 x 8J4J4.903U » IOII4.636 Btu (cu ft)"1

AH°6Q (CH ) (saturated basis) = l.l800lU x 8J4I4-.903U = 996.998

a Btu (std cu ft)"

1

The fractional uncertainty in the heat of combustion of pure methane

is

,-8

^mB)2 + ( I3Hom)

2 =/(o.ooo35o)2 + (0.000108 f =/i3 .U x io"

= 3.65 x 10"^ = .0365 percent or O.36O Btu (std cu ft)"

1

9. The value listed here differs slightly but not significantly from a value informally reported previously. The difference is due to (a) a slight change in heat capacities accepted for the reaction components,

and (b) a slight difference in the corrections to the molar heat of

reaction for non-ideality of gases at 30°C and at 15'5555°C.

12
13. Analysis of Two Special Methane Samples for Certification

Cylinder No. 58156 and No. 20608T of methane supplied by the

Matheson Company, were submitted by the Institute of Gas Technology

for analysis for certification. The analyses were performed by

E. E- Hughes of the Analysis and Purification Section, of the NBS Analytical

Chemistry Division. The report of analysis forms Appendix I. The two

cylinders of gas were of the same composition so far as could be

determined, and therefore only one analysis was submitted. The analysis

indicates that the samples were as pure as or purer than that used by

Rossini [11] in his experimental determination of the heat of combustion

of Ctt •

In Table 5 we give the analysis used in the calculation together

with the uncertainty in the mole fraction of each component and the

heat of combustion of each component.

Table 5

Composition of Gas Samples Submitted for Certification

Component Mole Fraction Uncertainty

Btu

AH

c (std cu ft)

CH^ 0.999521 0.000201 997.001

C

2 H

6

.oooUoo .000200 1758.

N

2

. 000017 .oooool* 0.0

°2 .000002 .000002 0.0

C0o .000060 .000020 0.0

-1

[7]

13
14.„ Heat of Combustion of the Two Special Samples

Only one heat of combustion was calculated for the two samples,,

It was calculated from equation (2), in which

AH (CH, samde) = AH (CH. ) x n(CH, ) + AH (C„H, ) x n(C„H,)

c 4 c 4 4 c 2 6

K 2 6

+ AH ( Inert s) x n(inerts) (2)

Each term is the contribution of a component to the heating value,

and is obtained as the product of the heating value of the component

times its mole fraction. Oxygen, nitrogen and carbon dioxide are treated as inert, having zero heat of combust ion

The heat of combustion of the samples is therefore:

(0.999521) (10U.636) + (0.000400) (l789 o 0) = 1014.150 + 0.716 = IOI4.866

Btu (cu ft)" 1 (dry basis).

(0.999521) (996.998) + (0.000400) (1758.0) = 996.520 + 0.703 = 997.223

Btu (standard cu ft) (saturated basis).

The uncertainty in the heat of combustion of the sample is based

on the uncertainty in the heat of combustion of pure CH^, and on the

uncertainties in the amounts of CH/ and 02^. The uncertainty in the

heat of combustion of pure C2H6 does not make a significant contribution to the uncertainty of the heat of combustion of the sample,

because of the small amount of C2H6 present. The uncertainty in the

heat of combustion of the sample due to the uncertainty in its

composition is

A(U ) (sample) = AH (CH.) x An(CH.) + AH (C H,) x An(C_HA ) c c4 4 c <: o do

We take the uncertainty in the mole fraction of CH^, Aa(CH4), to be

the square root of the sum of the squares of the uncertainties in

the mole fractions of all the impurities. Since the major contribution to the uncertainty in CH4 is due to the uncertainty in C2H6,

An(C2H6) will be of opposite sign from An(CH4).

The uncertainty in the heat of combustion of the sample due to

uncertainty in composition is therefore:

-996-. 998 x 0.000201 + 1758 x 0.000200

= ±(-.200 + 0.352) = ±0.152 Btu (std cu ft)

-1

14
The combined uncertainty in heat of combustion of the sample

due to uncertainty in composition and uncertainty in heat of

combustion of methane is ^ (o. 3 6o)2 + (0.152)2

= ^„153 = 0.391 Btu (std cu ft)" 1

We have attempted to estimate errors in such a way that the

true heat of combustion of the sample will fall within the bounds

set by the error limits with a 95 percent probability.

15 « Certificate Values for Heat of Combustion

of Special Samples of Methane

In the foregoing calculations an excessive number of figures

has been carried in order to avoid rounding errors. Rounding to

the nearest 0.1 Btu (cu ft)

- ^- we therefore report for the heats

of combustion of the samples submitted:

Dry Basis: 1014.9 Btu (cu ft)

-1

Saturated Basis: 997.2 Btu (standard cu ft)"

with an uncertainty (95$ confidence limits) of 0.4- Btu (cu ft) „

15
16„ References

[l] "ASTM Standards on Gaseous Fuels", Second Ed. (American Society

for Testing and Materials, Philadelphia, Pa., 1962).

a. ASTM Designation D900-55.

b, ASTM Designation D1826-61T.

[2] "Values for the Physical Constants Recommended by the NAS-NRC",

Natl. Bur. Standards Tech. Nevs Bull., October 1963.

[3] F. B. Silsbee, "Establishment and Maintenance of the Electrical

Units", NBS Circular 4-75 (U. S. Government Printing Office,

Washington, D. C., 194-9), p. 22.

[4.] F. D Rossini, K. S. Pitzer, R. L. Arnett, R. M. Braun, and

G. C. Pimental, "Selected Values of Physical and Thermodynamic

Properties of Hydrocarbons and Related Compounds", (Carnegie

Press, Pittsburgh, 1953).

[5] N. S. Osborne and C. H. Meyers, A Formula and Tables for the

Pressure of Saturated Water Vapor in the Range to 374-°C,

J. Research N.B S. 22, 1-20 (1934-).

[6] N. S. Osborne, H. F Stimson, and D. C a Ginnings, J» Research

Natl. Bur. Standards 23, 261-270 (1939).

[7] R. S. Jessup and E. R. Weaver, "Gas Calorimeter Tables",

Natl. Bur. Standards Circular 4-64- (U. S. Government Printing

Office, Washington, D C. 194-8) p. 37.

[8] R. S. Jessup, Unpublished data.

[9] D. R. Douslin, J. Chem. Eng. Data 2, 358-63 (1964-).

[10] E. J, Prosen and F. D. Rossini, J. Research Natl. Bur. Standards 24,

263-269 (1945).

[11] Fo Do Rossini, (a) J. Research Natl. Bur B Standards _6, 37-4-9 (1931).

(b) ibid. %, 329-30 (1931).

[12] F D Rossini, D. D. Wagman, W. H. Evans, S. Levine, and I. Jaffe,

Selected Values of Chemical Thermodynamic Properties,

NBS Circular 500, (U. S. Government Printing Office,

Washington, D. C, 1952).

16
[13] F. D. Rossini, K. S. Pitzer, W. J. Taylor, J P. Ebert,

J, E Kilpatrick, C, W. Beckett, M. G. Williams, and H. G. Werner,

"Selected Values of Properties of Hydrocarbons", Natl© Bur

Standards Circular 4-61% (U. S. Government Printing Office,

Washington, D. C. 194-7; •

[14] N. S. Osborne, H B FB Stimson, and D. C. Ginnings, J. Research

Natl. Bur. Standards £3_, 197-260 (1939).

[15] H. F. Stimson, Am. J. Phys. 21> 6U (1955).

[16] A. E. Cameron and E. Wichers, J. Am. Chem. Soc, 84, 4-175-97 (1962).

[17] J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge,

J. F Masi, R. L. Nuttall, I. S. Touloukian, and H„ W. Woolley,

"Tables of Thermal Properties of Gases", Natl. Bur. Standards

Circular 564. (U. S. Government Printing Office, Washington, D.C.,

1955).

[18] H. -E. Tester, pp. 1-71 in "Thermodynamic Functions of Gases",

Vol. 3, F„ Din, editor (Butterworbhs, London, 196l)

.

[19] D. D. Wagman, W. H. Evans, I. Halow, V. B. Parker, S. M. Bailey,

and R» H Schumm, "Selected Values of Chemical Thermodynamic

Properties, Part 1. Tables for the First Twenty-Three Elements

in the Standard Order of Arrangement", NBS Tech. Note 270-1,

(U S. Government Printing Office, Washington, D„ C., 1965).

[20] A. H. Cook, Phil. Trans. Roy. Soc. (London) 25U, 125-15U (1961-2).

17
FG , M NM-M*

(4-6-84)

June 18, 1965

APPENDIX Io

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

WASHINGTON, D.C. 20234

NATIONAL BUREAU OF STANDARDS

REPORT OF ANALYSIS

of

Two Cylinders of Methane*

Submitted by G. T. Armstrong, 221.02

Proj. 2210627, Div. Req. 221-2330

Ref: Institute of Gas Technology

Test No. 185179

The contents of each cylinder were examined both by mass spectrometric

and gas chromatographic techniques. Only those substances listed below

were detected and the remainder of each sample is considered to be

methane. The composition of each sample was identical within the stated

limits and the composition given below can be considered that of either

cylinder.

Mole Percent

Ethane 0.04 ±0.02

Nitrogen 0.0017 ± 0.0004

Oxygen 0.0002 ± 0.0002

Carbon dioxide 0.006 ± 0.002

The limit shown is a conservative intuitive guess as to the certainty

of the value of the concentration. It is based on uncertainty in the

measurement of chromatographic peak areas, ion currents, conversion

factors, and general experience with the two methods of analysis.

zE. s

E. Hughes,

^

Chemist

y

(ohn K. Taylor, Chief

Analysis and Purification

Analytical Chemistry Division

65-423

*Cvlinder Nos. 58156 and 20608T
50-

40-

iH

I i-lI

O

30-

20-

10-

f )

•o

NO -

-II - O

1

o

•o

o

uA

"

i

i-

-\ O^ 1

r\ YGnZ

^ J

-f * t s

-* x9"

280 290 300 310 320

T° K

Figure 1„ H°-H for combustion gases at p = one atmosphere pressure

Sources of Data

2

and C0

2

: NBS Circ. 564 [17]

CH . : 4H. E» Tester [18]

»|U.S. GOVERNMENT PRINTING OFFICE: 1966 —251 -021/^5 19


U.S. DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20230

POSTAGE AND FEES PAID

U.S. DEPARTMENT OF COMM

OFFICIAL BUSINESS