“determination of the specific heat capacity of … c - graphite...“determination of the...
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![Page 1: “Determination of the Specific Heat Capacity of … C - Graphite...“Determination of the Specific Heat Capacity of Graphite Using Absolute and Differential Methods” Susanne Picard](https://reader031.vdocuments.mx/reader031/viewer/2022022004/5aa781cc7f8b9a424f8c659d/html5/thumbnails/1.jpg)
“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
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Outline
Why ?
How ?
First, direct method to measure specific heat capacity
Second, differential method ….
Test of method on sapphire
Conclusion
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Outline
Why ?
How ?
First, direct, method to measure specific heat capacity
Second, differential, method ….
Test of method on sapphire
Conclusion
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• Desired quantity isabsorbed dose to water, Dw
• Two techniques in use:• ionometry (BIPM primary standard)• calorimetry (NMIs)
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• calorimetry• ionometryWATER GRAPHITE
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• calorimetry
+
• ionometryWATER GRAPHITE
Long term stabilitySensitivityPrecision
Need for…cavity theory orinteraction coefficients-
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• calorimetry
+
• ionometryWATER GRAPHITE
Long term stabilitySensitivityPrecision -
Need for…cavity theory orinteraction coefficients- + +/-
+/-
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• calorimetry
+
• ionometryWATER GRAPHITE
WHY graphite calorimetry ?
Long term stabilitySensitivityPrecision
Need for…cavity theory orinteraction coefficients- + +/-
- +/-
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• calorimetry
+
• ionometryWATER GRAPHITE
WHY graphite calorimetry ?
Long term stabilitySensitivityPrecision
Need for…cavity theory orinteraction coefficients- + +/-
- +Heat defectHeating of probesCompactness and simplicity
- +/-
![Page 10: “Determination of the Specific Heat Capacity of … C - Graphite...“Determination of the Specific Heat Capacity of Graphite Using Absolute and Differential Methods” Susanne Picard](https://reader031.vdocuments.mx/reader031/viewer/2022022004/5aa781cc7f8b9a424f8c659d/html5/thumbnails/10.jpg)
- +/-
• calorimetry
+
• ionometry
WHY graphite calorimetry ?
Long term stabilitySensitivityPrecision
Need for…cavity theory orinteraction coefficients- + +/-
- +Heat defectHeating of probesCompactness and simplicity
WATER GRAPHITE
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HOW ?
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HOW ?
opted to separate electrical calibration fromradiation measurements to optimize the conditionsfor each, i.e...
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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
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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=
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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)
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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)
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TmcE pΔ=
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Determination of Mass :- test mass in Dural® for control of stability- air buouyancy correction- relative uncertainty 2 parts in 105
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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
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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
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t
TIDEAL DISTRIBUTION
T
Determination of Temperature
nV
UI
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t
TIDEAL DISTRIBUTION
REAL DISTRIBUTION
T
Determination of Temperature
nV
UI
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t
TIDEAL DISTRIBUTION
REAL DISTRIBUTION
T
Determination of Temperature
nV
UI
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t
TIDEAL DISTRIBUTION
REAL DISTRIBUTION
T
Determination of Temperature
nV
UI
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24.503
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0 50 100 150 200 250 300
(T-2
73.1
5) /
K
t / s
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Transfer coefficient
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Ambient temperature…
…and initial temperature
• transfer coefficient
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0 50 100 150 200 250 300
Losses
• transfer coefficient• ambient temperature• initial temperature
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0 50 100 150 200 250 300
Heat input
• transfer coefficient• ambient temperature• initial temperature• losses
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• transfer coefficient• ambient temperature• initial temperature• losses• heat input
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-100-80-60-40-20
020406080
100
0 50 100 150 200 250 300
RESIDUALS
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But how do we deal with the losses by radiation transfer ?
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« High » reflectivity of innersurface
But how do we deal with the losses by radiation transfer ?
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« 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 ?
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« 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 ?
![Page 38: “Determination of the Specific Heat Capacity of … C - Graphite...“Determination of the Specific Heat Capacity of Graphite Using Absolute and Differential Methods” Susanne Picard](https://reader031.vdocuments.mx/reader031/viewer/2022022004/5aa781cc7f8b9a424f8c659d/html5/thumbnails/38.jpg)
)( 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 ?
![Page 39: “Determination of the Specific Heat Capacity of … C - Graphite...“Determination of the Specific Heat Capacity of Graphite Using Absolute and Differential Methods” Susanne Picard](https://reader031.vdocuments.mx/reader031/viewer/2022022004/5aa781cc7f8b9a424f8c659d/html5/thumbnails/39.jpg)
))()(()( 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 ?
![Page 40: “Determination of the Specific Heat Capacity of … C - Graphite...“Determination of the Specific Heat Capacity of Graphite Using Absolute and Differential Methods” Susanne Picard](https://reader031.vdocuments.mx/reader031/viewer/2022022004/5aa781cc7f8b9a424f8c659d/html5/thumbnails/40.jpg)
))()(()( 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 ?
![Page 41: “Determination of the Specific Heat Capacity of … C - Graphite...“Determination of the Specific Heat Capacity of Graphite Using Absolute and Differential Methods” Susanne Picard](https://reader031.vdocuments.mx/reader031/viewer/2022022004/5aa781cc7f8b9a424f8c659d/html5/thumbnails/41.jpg)
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
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?
?
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
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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….
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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]
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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
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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
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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
![Page 48: “Determination of the Specific Heat Capacity of … C - Graphite...“Determination of the Specific Heat Capacity of Graphite Using Absolute and Differential Methods” Susanne Picard](https://reader031.vdocuments.mx/reader031/viewer/2022022004/5aa781cc7f8b9a424f8c659d/html5/thumbnails/48.jpg)
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
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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
![Page 50: “Determination of the Specific Heat Capacity of … C - Graphite...“Determination of the Specific Heat Capacity of Graphite Using Absolute and Differential Methods” Susanne Picard](https://reader031.vdocuments.mx/reader031/viewer/2022022004/5aa781cc7f8b9a424f8c659d/html5/thumbnails/50.jpg)
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
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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
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?
?
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
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?
?
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
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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
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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
![Page 56: “Determination of the Specific Heat Capacity of … C - Graphite...“Determination of the Specific Heat Capacity of Graphite Using Absolute and Differential Methods” Susanne Picard](https://reader031.vdocuments.mx/reader031/viewer/2022022004/5aa781cc7f8b9a424f8c659d/html5/thumbnails/56.jpg)
ab
lossab
iiigab
ab
ab
TEmccm
TE
Δ++=
Δ ∑ma mb
Principle of differential measurement…
![Page 57: “Determination of the Specific Heat Capacity of … C - Graphite...“Determination of the Specific Heat Capacity of Graphite Using Absolute and Differential Methods” Susanne Picard](https://reader031.vdocuments.mx/reader031/viewer/2022022004/5aa781cc7f8b9a424f8c659d/html5/thumbnails/57.jpg)
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…
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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…
![Page 59: “Determination of the Specific Heat Capacity of … C - Graphite...“Determination of the Specific Heat Capacity of Graphite Using Absolute and Differential Methods” Susanne Picard](https://reader031.vdocuments.mx/reader031/viewer/2022022004/5aa781cc7f8b9a424f8c659d/html5/thumbnails/59.jpg)
X
lossX
iiigX
X
X
TEmccm
TE
Δ++=
Δ ∑
T
E/ΔT
y = b m + a
T = 22 °C
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X
lossX
iiigX
X
X
TEmccm
TE
Δ++=
Δ ∑
T
E/ΔT
y = b m + a
T = 22 °C
![Page 61: “Determination of the Specific Heat Capacity of … C - Graphite...“Determination of the Specific Heat Capacity of Graphite Using Absolute and Differential Methods” Susanne Picard](https://reader031.vdocuments.mx/reader031/viewer/2022022004/5aa781cc7f8b9a424f8c659d/html5/thumbnails/61.jpg)
X
lossX
iiigX
X
X
TEmccm
TE
Δ++=
Δ ∑
T
E/ΔT
y = b m + a
T = 22 °C
![Page 62: “Determination of the Specific Heat Capacity of … C - Graphite...“Determination of the Specific Heat Capacity of Graphite Using Absolute and Differential Methods” Susanne Picard](https://reader031.vdocuments.mx/reader031/viewer/2022022004/5aa781cc7f8b9a424f8c659d/html5/thumbnails/62.jpg)
X
lossX
iiigX
X
X
TEmccm
TE
Δ++=
Δ ∑
T
E/ΔT
y = b m + a
T = 22 °C
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X
lossX
iiigX
X
X
TEmccm
TE
Δ++=
Δ ∑
T
E/ΔT
y = b m + a
T = 22 °C
![Page 64: “Determination of the Specific Heat Capacity of … C - Graphite...“Determination of the Specific Heat Capacity of Graphite Using Absolute and Differential Methods” Susanne Picard](https://reader031.vdocuments.mx/reader031/viewer/2022022004/5aa781cc7f8b9a424f8c659d/html5/thumbnails/64.jpg)
X
lossX
iiigX
X
X
TEmccm
TE
Δ++=
Δ ∑
T
E/ΔT
y = b m + a
T = 22 °C
![Page 65: “Determination of the Specific Heat Capacity of … C - Graphite...“Determination of the Specific Heat Capacity of Graphite Using Absolute and Differential Methods” Susanne Picard](https://reader031.vdocuments.mx/reader031/viewer/2022022004/5aa781cc7f8b9a424f8c659d/html5/thumbnails/65.jpg)
9.011.013.015.017.019.021.023.0
0.013 0.018 0.023 0.028m g / kg
l / [
JK-1
]RESULTS
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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:
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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:
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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
![Page 69: “Determination of the Specific Heat Capacity of … C - Graphite...“Determination of the Specific Heat Capacity of Graphite Using Absolute and Differential Methods” Susanne Picard](https://reader031.vdocuments.mx/reader031/viewer/2022022004/5aa781cc7f8b9a424f8c659d/html5/thumbnails/69.jpg)
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
![Page 70: “Determination of the Specific Heat Capacity of … C - Graphite...“Determination of the Specific Heat Capacity of Graphite Using Absolute and Differential Methods” Susanne Picard](https://reader031.vdocuments.mx/reader031/viewer/2022022004/5aa781cc7f8b9a424f8c659d/html5/thumbnails/70.jpg)
Test of the experimental method and analysis…
Al2O3
…using a sapphire sample
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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
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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.
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Susa
nne
Pica
rd D
avid B
urns
Philip
pe R
oger
BIP
M
Graphite sample in a copper recepient, inside the vacuum container
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Susa
nne
Pica
rd D
avid B
urns
Philip
pe R
oger
BIP
M
Temperature stabilized cabinhousing the vacuum chamber