Determination of the Specific Heat Capacity of Graphite Using Absolute and Differential Methods Susanne Picard David Burns Philippe Roger BIPM

Transcription

1 Determination of the Specific Heat Capacity of Graphite Using Absolute and Differential Methods Susanne Picard David Burns Philippe Roger BIPM Absorbed Dose and Air Kerma Dosimetry Workshop - Paris 9-11 May 2007

2 Outline Why? How? First, direct method to measure specific heat capacity Second, differential method. Test of method on sapphire Conclusion

3 Outline Why? How? First, direct, method to measure specific heat capacity Second, differential, method. Test of method on sapphire Conclusion

4 Desired quantity is absorbed dose to water, D w Two techniques in use: ionometry (BIPM primary standard) calorimetry (NMIs)

5 ionometry calorimetry WATER GRAPHITE

6 ionometry calorimetry WATER GRAPHITE + Long term stability Sensitivity Precision - Need for cavity theory or interaction coefficients

7 ionometry calorimetry WATER GRAPHITE + Long term stability Sensitivity Precision - Need for - cavity theory or interaction coefficients + +/- +/-

8 ionometry + Long term stability Sensitivity Precision calorimetry WATER GRAPHITE - +/- Need for - cavity theory or interaction coefficients + +/- WHY graphite calorimetry?

9 ionometry + Long term stability Sensitivity Precision calorimetry WATER GRAPHITE - +/- Need for - cavity theory or interaction coefficients + +/- WHY graphite calorimetry? Heat defect Heating of probes Compactness and simplicity - +

10 ionometry + Long term stability Sensitivity Precision calorimetry WATER GRAPHITE - +/- Need for - cavity theory or interaction coefficients + +/- WHY graphite calorimetry? Heat defect Heating of probes Compactness and simplicity - +

11 HOW?

12 HOW? opted to separate electrical calibration from radiation measurements to optimize the conditions for each, i.e...

13 HOW? opted to separate electrical calibration from radiation measurements to optimize the conditions for each, i.e... need to determine the temperature response for a known quantity of injected energy

14 HOW? opted to separate electrical calibration from radiation measurements to optimize the conditions for each, i.e... need to determine the temperature response for a known quantity of injected energy = Specific heat capacity E = mc pδt

15 Precautions to reduce heat loss due to Conduction Q = -A k dt/dx Convection Q = A h (T 1 - T sur ) Radiation heat transfer Q = A ε σ F (T 14 - T 24 )

16 Precautions to reduce heat loss due to Conduction Convection Q = -A k dt/dx Q = A h (T 1 - T sur ) VACUUM Radiation heat transfer Q = A ε σ F (T 14 - T 24 )

17 E = mc pδt

18 Determination of Mass : - test mass in Dural for control of stability - air buouyancy correction - relative uncertainty 2 parts in 10 5

19 Determination of Mass : - test mass in Dural for control of stability - air buouyancy correction - relative uncertainty 2 parts in 10 5 Determination of Energy : - thermistor as heating element -use DAQ card - high sampling rate of I and U -2 parts in 10 5 resolution - integration over time of I x U - transform electric energy into thermal energy - minimize thermal losses nv I U

20 Determination of Mass : - test mass in Dural for control of stability - air buouyancy correction - relative uncertainty 2 parts in 10 5 Determination of Energy : - thermistor as heating element -use DAQ card - high sampling rate of I and U -2 parts in 10 5 resolution - integration over time of I x U - transform electric energy into thermal energy - minimize thermal losses nv I U

21 IDEAL DISTRIBUTION Determination of Temperature T I U t nv

22 IDEAL DISTRIBUTION Determination of Temperature T I U REAL DISTRIBUTION t nv

23 IDEAL DISTRIBUTION Determination of Temperature T I U REAL DISTRIBUTION t nv

24 IDEAL DISTRIBUTION Determination of Temperature T I U REAL DISTRIBUTION t nv

25 (T ) / K t / s

26

27

28 Transfer coefficient

29 transfer coefficient Ambient temperature and initial temperature

30 transfer coefficient ambient temperature initial temperature Losses

31 transfer coefficient ambient temperature initial temperature losses Heat input

32 transfer coefficient ambient temperature initial temperature losses heat input

33 RESIDUALS

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

35 But how do we deal with the losses by radiation transfer? «High» reflectivity of inner surface

36 But how do we deal with the losses by radiation transfer? «High» reflectivity of inner surface Most emitted radiation from the black sample is re-absorbed

37 But how do we deal with the losses by radiation transfer? «High» reflectivity of inner surface Most emitted radiation from the black sample is re-absorbed The shiny surrouning emits only a small quantity

38 But how do we deal with the losses by radiation transfer? «High» reflectivity of inner surface Most emitted radiation from the black sample is re-absorbed The shiny surrouning emits only a small quantity 4 ( T 4 1 T2 )

39 But how do we deal with the losses by radiation transfer? «High» reflectivity of inner surface Most emitted radiation from the black sample is re-absorbed The shiny surrouning emits only a small quantity ( T1 T2 ) = ( T1 + T2 )( T1 + T2 )( T1 T2 )

40 But how do we deal with the losses by radiation transfer? «High» reflectivity of inner surface Most emitted radiation from the black sample is re-absorbed The shiny surrouning emits only a small quantity ( T1 T2 ) = ( T1 + T2 )( T1 + T2 )( T1 T2 ) change by 5 parts in 10 5 when heating by 10 mk

41 c p of a graphite sample using 10 windings to avoid injected energy losses, correcting for added impurities cp / [J kg -1 K -1 ] (T ) / K

42 Uncertainty budget I II u(y)/y u(y)/y? statistical uncertainties energy determination (including calibration of heating circuit resistance and DAQ, integration method, influence of resolution and sample speed) mass added impurity correction absolute temperature calibration relative temperature calibration simulation of temperature curve long term stability of power supply voltmeter calibration, time stability < <1 10? u c (y)/y

43 Different number of windings c g / [Jkg -1 K -1 ] (T ) / K

44 c g / [Jkg -1 K -1 ] (T ) / K

45 c p measured for sample H for n windings arrangement corrected for added impurities cp / [Jkg -1 K -1 ] number of windings

46 c p measured for sample H for n windings arrangement corrected for added impurities cp / [Jkg -1 K -1 ] number of windings

47 c p measured for sample H for n windings arrangement corrected for added impurities cp / [Jkg -1 K -1 ] number of windings

48 c p measured for sample H for n windings arrangement corrected for added impurities cp / [Jkg -1 K -1 ] number of windings

49 c p measured for sample H for n windings arrangement corrected for added impurities cp / [Jkg -1 K -1 ] number of windings

50 c p measured for sample H for n windings arrangement corrected for added impurities cp / [Jkg -1 K -1 ] number of windings

51 c p measured for sample H for n windings arrangement corrected for added impurities cp / [Jkg -1 K -1 ] (5) J kg K number of windings

52 Uncertainty budget I II u(y)/y u(y)/y? statistical uncertainties energy determination (including calibration of heating circuit resistance and DAQ, integration method, influence of resolution and sample speed) mass added impurity correction absolute temperature calibration relative temperature calibration simulation of temperature curve long term stability of power supply voltmeter calibration, time stability < <1 10? u c (y)/y

53 Uncertainty budget I II u(y)/y u(y)/y? statistical uncertainties energy determination (including calibration of heating circuit resistance and DAQ, integration method, influence of resolution and sample speed) mass added impurity correction absolute temperature calibration relative temperature calibration simulation of temperature curve long term stability of power supply voltmeter calibration, time stability < <1 10? u c (y)/y Contribution from loss via wires At 10: 4 x 10-3

54 I: DIRECT MEASUREMENT I II u(y)/y u(y)/y statistical uncertainties ? 4 energy determination (including calibration of heating circuit resistance and DAQ, integration method, influence of resolution and sample speed) mass added impurity correction absolute temperature calibration relative temperature calibration simulation of temperature curve long term stability of power supply voltmeter calibration, time stability < < losses from heat source < u c (y)/y < ? 4

55 I: DIRECT MEASUREMENT II: DIFFERENTIAL MEASUREMENT I II u(y)/y u(y)/y statistical uncertainties ? 4 energy determination (including calibration of heating circuit resistance and DAQ, integration method, influence of resolution and sample speed) mass added impurity correction absolute temperature calibration relative temperature calibration simulation of temperature curve long term stability of power supply voltmeter calibration, time stability < < losses from heat source < u c (y)/y < ? 4

56 Principle of differential measurement m a m b E ΔT ab ab = m ab c g + i c m i i + E ΔT loss ab ab

57 Principle of differential measurement m a m b E ΔT ab ab = m ab c g + i c m i i + E ΔT loss ab ab m a Ea ΔT a = m c a g + i c m i i + E ΔT loss a a

58 Principle of differential measurement m a m b E ΔT ab ab = m ab c g + i c m i i + E ΔT loss ab ab m a Ea ΔT a = m c a g + i c m i i + E ΔT loss a a y = b m + a

59 E ΔT X X = m X c g + i c m i i + E ΔT loss X X E/ΔT y = b m + a T T = 22 C

60 E ΔT X X = m X c g + i c m i i + E ΔT loss X X E/ΔT y = b m + a T T = 22 C

61 E ΔT X X = m X c g + i c m i i + E ΔT loss X X E/ΔT y = b m + a T T = 22 C

62 E ΔT X X = m X c g + i c m i i + E ΔT loss X X E/ΔT y = b m + a T T = 22 C

63 E ΔT X X = m X c g + i c m i i + E ΔT loss X X E/ΔT y = b m + a T T = 22 C

64 E ΔT X X = m X c g + i c m i i + E ΔT loss X X E/ΔT y = b m + a T T = 22 C

65 RESULTS l / [JK -1 ] m g / kg

66 RESULTS l / [JK -1 ] m g / kg DIFFERENTIAL: 706.9(6) J kg -1 K -1

67 RESULTS l / [JK -1 ] m g / kg DIFFERENTIAL: 706.9(6) J kg -1 K -1 DIRECT: 707.8(9) J kg -1 K c g / J kg -1 K H R

68 I: DIRECT MEASUREMENT II: DIFFERENTIAL MEASUREMENT I II u(y)/y u(y)/y statistical uncertainties ? 4 energy determination (including calibration of heating circuit resistance and DAQ, integration method, influence of resolution and sample speed) mass added impurity correction absolute temperature calibration relative temperature calibration simulation of temperature curve long term stability of power supply voltmeter calibration, time stability < < losses from heat source < u c (y)/y < ? 4

69 I: DIRECT MEASUREMENT II: DIFFERENTIAL MEASUREMENT I II u(y)/y u(y)/y statistical uncertainties energy determination (including calibration of heating circuit resistance and DAQ, integration method, influence of resolution and sample speed) mass added impurity correction absolute temperature calibration relative temperature calibration simulation of temperature curve long term stability of power supply voltmeter calibration, time stability < < losses from heat source < u c (y)/y <

70 Test of the experimental method and analysis Al 2 O 3 using a sapphire sample

71 Agreement and relative uncertainty of 7 parts in Results at 22 C cp / [Jkg -1 K -1 ] part in BIPM value this work [4] [12] Grønvold et al Compilation by Archer

72 Conclusion Specific heat capacity determined for a sample to 9 parts in 10 4 ; Method tested on sapphire, result agree with other groups better than 7 parts in 10 4 ; This uncertainty is not the limiting factor in the determination of absorbed dose to water.

73 Graphite sample in a copper recepient, inside the vacuum container Susanne Picard David Burns Philippe Roger BIPM

74 Temperature stabilized cabin housing the vacuum chamber Susanne Picard David Burns Philippe Roger BIPM