“Determination of the Specific Heat Capacity of Graphite Using Absolute and Differential Methods”

Susanne Picard David Burns Philippe RogerBIPM

Absorbed Dose and Air Kerma Dosimetry Workshop - Paris 9-11 May 2007

Outline

Why ?

How ?

First, direct method to measure specific heat capacity

Second, differential method ….

Test of method on sapphire

Conclusion

Outline

Why ?

How ?

First, direct, method to measure specific heat capacity

Second, differential, method ….

Test of method on sapphire

Conclusion

• Desired quantity isabsorbed dose to water, Dw

• Two techniques in use:• ionometry (BIPM primary standard)• calorimetry (NMIs)

• calorimetry• ionometryWATER GRAPHITE

• calorimetry

+

• ionometryWATER GRAPHITE

Long term stabilitySensitivityPrecision

Need for…cavity theory orinteraction coefficients-

• calorimetry

+

• ionometryWATER GRAPHITE

Long term stabilitySensitivityPrecision -

Need for…cavity theory orinteraction coefficients- + +/-

+/-

• calorimetry

+

• ionometryWATER GRAPHITE

WHY graphite calorimetry ?

Long term stabilitySensitivityPrecision

Need for…cavity theory orinteraction coefficients- + +/-

- +/-

• calorimetry

+

• ionometryWATER GRAPHITE

WHY graphite calorimetry ?

Long term stabilitySensitivityPrecision

Need for…cavity theory orinteraction coefficients- + +/-

- +Heat defectHeating of probesCompactness and simplicity

- +/-

- +/-

• calorimetry

+

• ionometry

WHY graphite calorimetry ?

Long term stabilitySensitivityPrecision

Need for…cavity theory orinteraction coefficients- + +/-

- +Heat defectHeating of probesCompactness and simplicity

WATER GRAPHITE

HOW ?

HOW ?

opted to separate electrical calibration fromradiation measurements to optimize the conditionsfor each, i.e...

HOW ?

opted to separate electrical calibration fromradiation measurements to optimize the conditionsfor each, i.e...

need to determine the temperature response fora known quantity of injected energy

HOW ?

opted to separate electrical calibration fromradiation measurements to optimize the conditionsfor each, i.e...

need to determine the temperature response fora known quantity of injected energy

= Specific heat capacity

TmcE pΔ=

Precautions to reduce heat loss due to…

Conduction Q = -A ⋅k ⋅dT/dx

Convection Q = A⋅h⋅(T1 - Tsur)

Radiation heat transfer Q = A⋅ε⋅σ⋅F⋅(T14 - T2

4)

Precautions to reduce heat loss due to…

Conduction Q = -A ⋅k ⋅dT/dx

Convection Q = A⋅h⋅(T1 - Tsur) VACUUM

Radiation heat transfer Q = A⋅ε⋅σ⋅F⋅(T14 - T2

4)

TmcE pΔ=

Determination of Mass :- test mass in Dural® for control of stability- air buouyancy correction- relative uncertainty 2 parts in 105

Determination of Mass :- test mass in Dural® for control of stability- air buouyancy correction- relative uncertainty 2 parts in 105

Determination of Energy :- thermistor as heating element- use DAQ card

- high sampling rate of I and U- 2 parts in 105 resolution

- integration over time of I x U- transform electric energy into thermal energy- minimize thermal losses

nV

UI

Determination of Mass :- test mass in Dural® for control of stability- air buouyancy correction- relative uncertainty 2 parts in 105

Determination of Energy :- thermistor as heating element- use DAQ card

- high sampling rate of I and U- 2 parts in 105 resolution

- integration over time of I x U- transform electric energy into thermal energy- minimize thermal losses

nV

UI

t

TIDEAL DISTRIBUTION

T

Determination of Temperature

nV

UI

t

TIDEAL DISTRIBUTION

REAL DISTRIBUTION

T

Determination of Temperature

nV

UI

t

TIDEAL DISTRIBUTION

REAL DISTRIBUTION

T

Determination of Temperature

nV

UI

t

TIDEAL DISTRIBUTION

REAL DISTRIBUTION

T

Determination of Temperature

nV

UI

24.503

24.504

24.505

24.506

24.507

24.508

24.509

24.51

24.511

24.512

24.513

24.514

0 50 100 150 200 250 300

(T-2

73.1

5) /

K

t / s

24.503

24.504

24.505

24.506

24.507

24.508

24.509

24.51

24.511

24.512

24.513

24.514

0 50 100 150 200 250 300

24.503

24.504

24.505

24.506

24.507

24.508

24.509

24.51

24.511

24.512

24.513

24.514

0 50 100 150 200 250 300

24.503

24.504

24.505

24.506

24.507

24.508

24.509

24.51

24.511

24.512

24.513

24.514

0 50 100 150 200 250 300

Transfer coefficient

24.503

24.504

24.505

24.506

24.507

24.508

24.509

24.51

24.511

24.512

24.513

24.514

0 50 100 150 200 250 300

Ambient temperature…

…and initial temperature

• transfer coefficient

24.503

24.504

24.505

24.506

24.507

24.508

24.509

24.51

24.511

24.512

24.513

24.514

0 50 100 150 200 250 300

Losses

• transfer coefficient• ambient temperature• initial temperature

24.503

24.504

24.505

24.506

24.507

24.508

24.509

24.51

24.511

24.512

24.513

24.514

0 50 100 150 200 250 300

Heat input

• transfer coefficient• ambient temperature• initial temperature• losses

24.503

24.504

24.505

24.506

24.507

24.508

24.509

24.51

24.511

24.512

24.513

0 50 100 150 200 250 300

• transfer coefficient• ambient temperature• initial temperature• losses• heat input

24.503

24.504

24.505

24.506

24.507

24.508

24.509

24.51

24.511

24.512

24.513

0 50 100 150 200 250 300

-100-80-60-40-20

020406080

100

0 50 100 150 200 250 300

RESIDUALS

But how do we deal with the losses by radiation transfer ?

« High » reflectivity of innersurface

But how do we deal with the losses by radiation transfer ?

« High » reflectivity of innersurface

Most emitted radiation from the black sample is re-absorbed

But how do we deal with the losses by radiation transfer ?

« High » reflectivity of innersurface

Most emitted radiation from the black sample is re-absorbed

The shiny surrouning emits onlya small quantity

But how do we deal with the losses by radiation transfer ?

)( 42

41 TT −

« High » reflectivity of innersurface

Most emitted radiation from the black sample is re-absorbed

The shiny surrouning emits onlya small quantity

But how do we deal with the losses by radiation transfer ?

))()(()( 21212

22

14

24

1 TTTTTTTT −++=−

« High » reflectivity of innersurface

Most emitted radiation from the black sample is re-absorbed

The shiny surrouning emits onlya small quantity

But how do we deal with the losses by radiation transfer ?

))()(()( 21212

22

14

24

1 TTTTTTTT −++=−

change by 5 parts in 105 when heating by 10 mK

« High » reflectivity of innersurface

Most emitted radiation from the black sample is re-absorbed

The shiny surrouning emits onlya small quantity

But how do we deal with the losses by radiation transfer ?

700

705

710

715

720

725

19 21 23 25(T- 273.15) / K

c p /

[J k

g-1K

-1]

cp of a graphite sample using 10 windings to avoid injected energy losses,correcting for added impurities

?

?

I II u(y)/y u(y)/y statistical uncertainties 2 ×10–4 6 ×10–4

energy determination (including calibration of heating circuit resistance and DAQ, integration method, influence of resolution and sample speed)

2 ×10–4 ⎯

mass 1 ×10–4 1 ×10–4

added impurity correction 2 ×10–4 0 absolute temperature calibration 1 ×10–4 ⎯ relative temperature calibration 5 ×10–4 5 ×10–4

simulation of temperature curve 4 ×10–4 4 ×10–4

long term stability of power supply 1 ×10–4 ⎯ voltmeter calibration, time stability <1 ×10–4 <1 ×10–4

uc(y)/y 7.5×10–4 8.8×10–4

Uncertainty budget

700

705

710

715

720

725

730

735

740

19 20 21 22 23 24 25

(T - 273.15) / K

cg

/ [Jk

g-1K

-1]

Different number of windings….

700

705

710

715

720

725

730

735

740

19 20 21 22 23 24 25

(T - 273.15) / K

cg

/ [Jk

g-1K

-1]

705

710

715

720

725

730

735

740

2 4 6 8 10number of windings

c p /

[Jkg

-1K-1

]

cp measured for sample H for n windings arrangementcorrected for added impurities

705

710

715

720

725

730

735

740

2 4 6 8 10number of windings

c p /

[Jkg

-1K-1

]

cp measured for sample H for n windings arrangementcorrected for added impurities

705

710

715

720

725

730

735

740

2 4 6 8 10number of windings

c p /

[Jkg

-1K-1

]

cp measured for sample H for n windings arrangementcorrected for added impurities

705

710

715

720

725

730

735

740

2 4 6 8 10number of windings

c p /

[Jkg

-1K-1

]

cp measured for sample H for n windings arrangementcorrected for added impurities

705

710

715

720

725

730

735

740

2 4 6 8 10number of windings

c p /

[Jkg

-1K-1

]

cp measured for sample H for n windings arrangementcorrected for added impurities

705

710

715

720

725

730

735

740

2 4 6 8 10number of windings

c p /

[Jkg

-1K-1

]

cp measured for sample H for n windings arrangementcorrected for added impurities

705

710

715

720

725

730

735

740

2 4 6 8 10number of windings

c p /

[Jkg

-1K-1

]

cp measured for sample H for n windings arrangementcorrected for added impurities

707.8(5) J kg-1K-1

?

?

I II u(y)/y u(y)/y statistical uncertainties 2 ×10–4 6 ×10–4

energy determination (including calibration of heating circuit resistance and DAQ, integration method, influence of resolution and sample speed)

2 ×10–4 ⎯

mass 1 ×10–4 1 ×10–4

added impurity correction 2 ×10–4 0 absolute temperature calibration 1 ×10–4 ⎯ relative temperature calibration 5 ×10–4 5 ×10–4

simulation of temperature curve 4 ×10–4 4 ×10–4

long term stability of power supply 1 ×10–4 ⎯ voltmeter calibration, time stability <1 ×10–4 <1 ×10–4

uc(y)/y 7.5×10–4 8.8×10–4

Uncertainty budget

?

?

I II u(y)/y u(y)/y statistical uncertainties 2 ×10–4 6 ×10–4

energy determination (including calibration of heating circuit resistance and DAQ, integration method, influence of resolution and sample speed)

2 ×10–4 ⎯

mass 1 ×10–4 1 ×10–4

added impurity correction 2 ×10–4 0 absolute temperature calibration 1 ×10–4 ⎯ relative temperature calibration 5 ×10–4 5 ×10–4

simulation of temperature curve 4 ×10–4 4 ×10–4

long term stability of power supply 1 ×10–4 ⎯ voltmeter calibration, time stability <1 ×10–4 <1 ×10–4

uc(y)/y 7.5×10–4 8.8×10–4

Uncertainty budget

Contribution fro

mloss

via wire

s At 10: 4 x 1

0-3

I II u(y)/y u(y)/y statistical uncertainties 2 ×10–4 6 ×10–4

energy determination (including calibration of heating circuit resistance and DAQ, integration method, influence of resolution and sample speed)

2 ×10–4 ⎯

mass 1 ×10–4 1 ×10–4

added impurity correction 2 ×10–4 0 absolute temperature calibration 1 ×10–4 ⎯ relative temperature calibration 5 ×10–4 5 ×10–4

simulation of temperature curve 4 ×10–4 4 ×10–4

long term stability of power supply 1 ×10–4 ⎯ voltmeter calibration, time stability <1 ×10–4 <1 ×10–4

losses from heat source <1 ×10–3 ⎯

uc(y)/y <1.3×10–3 8.8×10–4

?

?

I: DIRECT MEASUREMENT

I II u(y)/y u(y)/y statistical uncertainties 2 ×10–4 6 ×10–4

energy determination (including calibration of heating circuit resistance and DAQ, integration method, influence of resolution and sample speed)

2 ×10–4 ⎯

mass 1 ×10–4 1 ×10–4

added impurity correction 2 ×10–4 0 absolute temperature calibration 1 ×10–4 ⎯ relative temperature calibration 5 ×10–4 5 ×10–4

simulation of temperature curve 4 ×10–4 4 ×10–4

long term stability of power supply 1 ×10–4 ⎯ voltmeter calibration, time stability <1 ×10–4 <1 ×10–4

losses from heat source <1 ×10–3 ⎯

uc(y)/y <1.3×10–3 8.8×10–4

?

?

I: DIRECT MEASUREMENT

II: DIFFERENTIAL MEASUREMENT

ab

lossab

iiigab

ab

ab

TEmccm

TE

Δ++=

Δ ∑ma mb

Principle of differential measurement…

ab

lossab

iiigab

ab

ab

TEmccm

TE

Δ++=

Δ ∑

a

lossa

iiiga

a

a

TEmccm

TE

Δ++=

Δ ∑

ma mb

ma

Principle of differential measurement…

ab

lossab

iiigab

ab

ab

TEmccm

TE

Δ++=

Δ ∑

a

lossa

iiiga

a

a

TEmccm

TE

Δ++=

Δ ∑

ma mb

ma

y = b m + a

Principle of differential measurement…

X

lossX

iiigX

X

X

TEmccm

TE

Δ++=

Δ ∑

T

E/ΔT

y = b m + a

T = 22 °C

X

lossX

iiigX

X

X

TEmccm

TE

Δ++=

Δ ∑

T

E/ΔT

y = b m + a

T = 22 °C

X

lossX

iiigX

X

X

TEmccm

TE

Δ++=

Δ ∑

T

E/ΔT

y = b m + a

T = 22 °C

X

lossX

iiigX

X

X

TEmccm

TE

Δ++=

Δ ∑

T

E/ΔT

y = b m + a

T = 22 °C

X

lossX

iiigX

X

X

TEmccm

TE

Δ++=

Δ ∑

T

E/ΔT

y = b m + a

T = 22 °C

X

lossX

iiigX

X

X

TEmccm

TE

Δ++=

Δ ∑

T

E/ΔT

y = b m + a

T = 22 °C

9.011.013.015.017.019.021.023.0

0.013 0.018 0.023 0.028m g / kg

l / [

JK-1

]RESULTS

9.011.013.015.017.019.021.023.0

0.013 0.018 0.023 0.028m g / kg

l / [

JK-1

]RESULTS

706.9(6) J kg-1K-1

DIFFERENTIAL:

9.011.013.015.017.019.021.023.0

0.013 0.018 0.023 0.028m g / kg

l / [

JK-1

]RESULTS

707.8(9) J kg-1K-1

706.9(6) J kg-1K-1

706.0

706.5

707.0

707.5

708.0

708.5

cg /

J k

g-1 K

-1

H R

DIFFERENTIAL:

DIRECT:

I II u(y)/y u(y)/y statistical uncertainties 2 ×10–4 6 ×10–4

energy determination (including calibration of heating circuit resistance and DAQ, integration method, influence of resolution and sample speed)

2 ×10–4 ⎯

mass 1 ×10–4 1 ×10–4

added impurity correction 2 ×10–4 0 absolute temperature calibration 1 ×10–4 ⎯ relative temperature calibration 5 ×10–4 5 ×10–4

simulation of temperature curve 4 ×10–4 4 ×10–4

long term stability of power supply 1 ×10–4 ⎯ voltmeter calibration, time stability <1 ×10–4 <1 ×10–4

losses from heat source <1 ×10–3 ⎯

uc(y)/y <1.3×10–3 8.8×10–4

?

?

I: DIRECT MEASUREMENT

II: DIFFERENTIAL MEASUREMENT

I II u(y)/y u(y)/y statistical uncertainties 2 ×10–4 6 ×10–4

energy determination (including calibration of heating circuit resistance and DAQ, integration method, influence of resolution and sample speed)

2 ×10–4 ⎯

mass 1 ×10–4 1 ×10–4

added impurity correction 2 ×10–4 0 absolute temperature calibration 1 ×10–4 ⎯ relative temperature calibration 5 ×10–4 5 ×10–4

simulation of temperature curve 4 ×10–4 4 ×10–4

long term stability of power supply 1 ×10–4 ⎯ voltmeter calibration, time stability <1 ×10–4 <1 ×10–4

losses from heat source <1 ×10–3 ⎯

uc(y)/y <1.3×10–3 8.8×10–4

I: DIRECT MEASUREMENT

II: DIFFERENTIAL MEASUREMENT

Test of the experimental method and analysis…

Al2O3

…using a sapphire sample

767.5

768.0

768.5

769.0

769.5

770.0

770.5

c p /

[Jkg

-1K

-1]

[4] [12]this work

Agreement and relative uncertainty of 7 parts in 104

Grønvold et al

Compilation by Archer

BIPM value

Results at 22 °C

1 part in 103

Conclusion

Specific heat capacity determined for a sampleto 9 parts in 104;

Method tested on sapphire, result agree withother groups better than 7 parts in 104;

This uncertainty is not the limiting factorin the determination of absorbed dose to water.

Susa

nne

Pica

rd D

avid B

urns

Philip

pe R

oger

BIP

M

Graphite sample in a copper recepient, inside the vacuum container

Susa

nne

Pica

rd D

avid B

urns

Philip

pe R

oger

BIP

M

Temperature stabilized cabinhousing the vacuum chamber