NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Contract No. DE-AC36-08GO28308

Heat Capacity Uncertainty 

Calculation for the Eutectic 

Mixture of Biphenyl/Diphenyl 

Ether Used as 

Heat Transfer Fluid

Preprint

Judith C. Gomez, Greg C. Glatzmaier, 

and Mark Mehos

Presented at SolarPACES 2012

Marrakech, Morocco

September 11–14, 2012

Conference Paper

NREL/CP-5500-56446

September 2012
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1 

HEAT CAPACITY UNCERTAINTY CALCULATION FOR THE 

EUTECTIC MIXTURE OF BIPHENYL/DIPHENYL ETHER USED AS 

HEAT TRANSFER FLUID

Judith C. Gomez1, Greg C. Glatzmaier2, and Mark Mehos3

1 PhD in Metallurgy and Materials Engineering. Post-Doctoral Researcher. National Renewable Energy 

Laboratory (NREL). 1617 Cole Blvd. MS1626, Golden, Colorado 80401. USA. Phone: 

+1.303.275.4290, E-Mail: Judith.Gomez@nrel.gov 

2 Senior Engineer. NREL. +1.303.384.7470

3 CSP Principal Program Manager. NREL. +1.303.384.7458

Abstract

The main objective of this study was to calculate the uncertainty at 95% confidence for the experimental values 

of heat capacity of the eutectic mixture of biphenyl/diphenyl ether (Therminol VP-1) determined from 300 to 

370 °C. Twenty-five samples were evaluated using differential scanning calorimetry (DSC) to obtain the sample 

heat flow as a function of temperature. The ASTM E-1269-05 standard was used to determine the heat capacity 

using DSC evaluations. High-pressure crucibles were employed to contain the sample in the liquid state without 

vaporizing. Sample handling has a significant impact on the random uncertainty. It was determined that the fluid 

is difficult to handle, and a high variability of the data was produced. The heat capacity of Therminol VP-1 

between 300 and 370 °C was measured to be equal to 0.0025T+0.8672 with an uncertainty of ± 0.074 J/g.K 

(3.09%) at 95% confidence with T (temperature) in Kelvin. 

Keywords: biphenyl/diphenyl ether, heat capacity, uncertainty, differential scanning calorimetry. 

1. Introduction

The heat transfer characteristics of large-scale solar parabolic trough power plants rely on the thermal properties 

of a high-temperature synthetic oil (eutectic mixture of biphenyl/diphenyl ether) also known by the commercial 

names Therminol VP-1 [1–3] and Dowtherm A. Accurate knowledge of the oil’s properties, in particular heat 

capacity, is important for the efficient operation of concentrating solar power (CSP) plants and thus reduces their 

operating costs. This eutectic mixture has a low melting point of 12 °C, a boiling point of 257 °C, and a 

maximum operating temperature of 400 °C at elevated pressure [3]. For the oil to be in the liquid phase at the 

current operating temperatures (293 – 393 °C), the plants need to operate at high pressure (approximately 1.2–1.5 

MPa).

The experimental evaluation of the thermal properties of liquid biphenyl/diphenyl ether is extremely difficult 

under the plant operating conditions. Cabaleiro et al. experimentally measured the density, viscosity, and thermal 

conductivity of pure diphenyl ether and three different binary mixtures of diphenyl ether and biphenyl, including 

the eutectic mixture, from 288.15 K (15 °C) to 343.15 K (70 °C) [1]. The density was measured at 45 MPa of 

pressure, but viscosity and thermal conductivity were measured at atmospheric pressure.

Just a few articles have reported the experimental heat capacity of this eutectic synthetic oil [4]. The liquid heat 

capacity values reported in the literature [3] are an extrapolation from low temperatures, below its boiling point

of 257 °C. Knowledge of a more accurate value of its heat capacity at high temperatures is extremely important 

for calculating the thermal energy absorbed by the solar collector field at parabolic trough plants. Total 

uncertainty of heat capacity has been reported in the literature for different calorimeter techniques [5–8].
2 

2. Measurement procedure

The heat capacity was measured using a differential scanning calorimeter DSC1 STARe System from MettlerToledo. The instrument measures the difference between heat flows from the sample and reference (empty 

crucible) sides of a sensor as a function of temperature or time. The sensor has 120 thermocouples, which 

guarantee excellent sensitivity.

The specific heat capacity (C) measurements were performed following the standard ASTM E-1269-05. This 

method consists of heating a blank (baseline), the sample, and a sapphire disk (reference material for C 

measurements) through the same temperature range at a fixed rate in a controlled atmosphere (nitrogen flow as 

protective gas at 80 cm3

/min). The difference in heat flow between the blank (reference) and the sample or the 

sapphire, due to energy changes, is continuously recorded. The system provides corrected heat flows for the 

sapphire (HFRef) and for the sample (HFSample). This information is obtained after subtracting the heat flow of 

the blank (baseline) from the sample or sapphire. The software STARe from Mettler-Toledo was used to 

determine the heat capacities of the samples in which the corrected heat flow values are used to calculate the 

unknown heat capacity of the sample (CSample) by using the known values for the heat capacity of the sapphire 

reference material (CRef) and the weights of the reference sapphire (WRef) and the sample (WSample) following 

the equation: 

CSample = CRef ×

HFSample

HFRef

×

WRef

WSample

(1)

Uncertainty calculations for DSC measurements have been a subject of some controversy. Different articles have 

discussed the ways to minimize errors associated with recording data. They have identified that DSC can perform 

thermal properties measurements (phase transition temperatures and their latent heats, heat capacities, etc.) with 

low uncertainty if the calibration of the instrument is carefully performed [5]. This analytical calibration must be 

executed by using high-purity reference materials with well-known melting temperatures and heats of fusion. We 

performed temperature and heat flow calibrations for the DSC by melting indium and zinc and recording the 

onsets and their respective heats of fusion. This calibration was carried out prior to running the heat capacity 

method for the blanks, samples, and sapphires.

As stated by Rudtsch (2002), the repeatability of DSC measurements is in most cases the major source of 

uncertainty. The factors that influence achieving good repeatability are the thermal contact and thus the heat 

transfer conditions between the sample, crucible, sensor/furnace, and the surroundings [6,7]. Therefore, control of 

the atmosphere, sensor cleanliness, and crucible positioning play important roles on the uncertainty. To minimize 

these effects, positioning of the crucibles in the measuring cell was executed by an autosampler; the sensor was 

cleaned carefully using dry air before performing the tests; vibrations and gas flow fluctuations were avoided; 

and three runs per sample were recorded to report the average of the runs per sample. The uncertainty associated 

with the mass of the samples and sapphires was minimized using a balance with a resolution of 0.001 mg. 

3. Heat capacity uncertainty

Nowadays it is commonly accepted that the statement of quantitative results obtained from measurements should 

contain both the values attributed to the measuring process and the associated uncertainty [6]. Uncertainty is the 

preferred term, instead of precision, trueness, etc., used to define the level of confidence or the accuracy of a 

measurement. Uncertainty considers both the random error (precision) and the systematic error (bias). Those 

errors define the band in which the true value of the measurement can be expected to lie with a stated confidence 

level. Error is defined as “the true difference between the true value of the parameter being measured and the 

measurement obtained (measurand)” [9]. As the true value is never known, the error cannot be calculated. 
3 

Knowing the error will allow us to correct the data. Because of this, we need to calibrate the instrument to trade 

the large unknown error we would have without calibration for the expected small errors resulting from the 

calibration process.

Uncertainty is “an estimate of the limits in which we can expect an error to go, under a given set of conditions as 

part of the measurement process” [9]. Random uncertainty sources are those that cause scatter in the data. 

Random uncertainty is obtained using the standard deviation (SX,i) of the elemental random source i, as follows: 

SX,i = �

∑ �Xi,k − X�i� N 2 i

k=1

Ni − 1 �

1

2

(2)

The sum is over k where there are Ni (number of data points averaged for error source i) values of Xi,kwith its 

average X�i. 

What matters the most about an error source is its average effect for a particular experimental error. This 

represents the random standard uncertainty for an error source (SX�,i) or standard error of the mean for error 

source i, and it is calculated as follows: 

SX�,i = SX,i

�Ni

(3)

The combined effect of the several random uncertainties on the average for the test result that needs evaluation 

will define the total random standard uncertainty (SX�,R), which is determined by:

SX�,R = ���SX�,i�

2

Ni

i=1

�

1

2

(4) 

Those sources that do not produce scatter in the results will produce systematic uncertainties (bi) that are constant 

for the duration of the test and are associated with the instrument itself. They will affect every measurement 

equally and are not observable in the test data. It is a common approach for DSC manufacturers to report the 

systematic uncertainty of their instruments (bR) as that associated with the measured heat capacity of stable 

samples in which their heat capacities are well reported in the literature. The manufacturers usually use singlecrystal sapphire disks to report the systematic uncertainty. 

The total uncertainty with 95% confidence (U95) is then calculated using the systematic uncertainty (bR), the total 

random standard uncertainty (SX�,R) with the Student’s t at 95% confidence (t95) as follows: 

U95 = ±t95 �(bR)2 + �SX�,R�

2

�

1

2 (5)

The Student’s t is determined using the degrees of freedom for the sample (v), which is the number of data points 

used to calculate the standard deviation minus one (N-1). With the degree of freedom, the following table is 

employed to determine the value of t95. 
4 

v t95 v t95 v t95

1 12.706 11 2.201 21 2.080

2 4.303 12 2.179 22 2.074

3 3.182 13 2.160 23 2.069

4 2.776 14 2.145 24 2.064

5 2.571 15 2.131 25 2.060

6 2.447 16 2.120 26 2.056

7 2.365 17 2.110 27 2.052

8 2.306 18 2.101 28 2.048

9 2.262 19 2.093 29 2.045

10 2.228 20 2.086 ≥ 30 2

Table 1: Student’s t for 95% confidence [9].

The systematic uncertainty for the DSC1 used in this investigation was determined by performing several heat 

capacity calculations using a sapphire disk as the sample as well as the reference material. The known values of 

heat capacity of sapphire as a function of temperature reported in the standard ASTM E-1269-05 are included in 

the database of STARe software. Those values were considered as the “true” value for that particular sample 

(sapphire). 

The heat flow of seven sapphire samples was measured from 300 to 380 °C at 20 K/min. Isothermals of 10 

minutes were employed before and after the dynamic region. High-pressure crucibles made of stainless steel were 

employed. The heat capacity of these sapphire samples was indirectly measured by STARe software using 

equation 1. The error of the measurement was then determined by subtracting the expected heat capacity value 

(reference) from the measured value. Figure 1 shows the reference values (red diamonds) as well as the measured 

values (blue squares) for the average heat capacity of the seven sapphire runs. The measured values are slightly 

off (bR =0.005 J/g.K) at low temperatures, but the accuracy increases above 360 °C (bR =0.001 J/g.K). The 

average error for the temperature range from 300 to 380 °C was (bR =0.004 J/g.K). 
5 

Fig. 1: Heat capacities of a single-crystal sapphire disk used as the reference and the sample to determine 

the systematic uncertainty of the differential scanning calorimeter DSC1 Stare System from MettlerToledo.

To determine the heat capacity of the synthetic oil Therminol VP-1 (eutectic of biphenyl/diphenyl ether), the 

same temperature method used to determine the systematic uncertainty was employed. As this oil has a boiling 

point of 257 °C and a maximum operating temperature of 400 °C at elevated pressure [3], high-pressure crucibles 

with a capacity of 30 μL were employed to keep the sample in the liquid state. A sample of Therminol VP-1 was 

provided by its manufacturer, Solutia, Inc. High-pressure crucibles maintained the sample in the liquid state at 

constant volume because the containing vessel is rigid and very strong. The test occurred at the saturation 

pressure of the sample where the DSC measured the constant volume specific heat. Constant pressure specific 

heat is virtually equivalent to constant volume specific heat for incompressible liquids. 

Handling of the sample has a significant impact on the random uncertainty. It was determined that Therminol VP1 is difficult to handle, and a high variability of the data was produced. It was found that the placement of the oil 

inside the crucible was a difficult task because of the small amount of mass required. Because the maximum 

temperature in which Therminol VP-1 is stable is 400 °C, the highest temperature for the heat capacity 

measurement was 390 °C. In DSC measurements, there is a thermal lag in the heat flow at the beginning and the 

end of the heating cycle. This artifact of approximately 20 °C makes the recordable heat flow values at these 

temperatures useless. For this reason the heat capacity values reported for Therminol VP-1 are from 300 to 370 

°C.

To decrease the variability of the results, each of the 25 samples tested was run consecutively during three 

heating cycles without removing them from the measuring cell. The average heat capacity for 25 samples is 

shown in Fig. 2 as a function of temperature. Using equations 2 – 5 with the data of Therminol heat capacities 

1.05

1.06

1.07

1.08

1.09

1.1

1.11

1.12

1.13

1.14

1.15

300 310 320 330 340 350 360 370 380

Heat Capacity, J/g.K

Temperature, °C 

STARe reference values

Cp (sapphire as sample)
6 

and the Student’s t for 24 degrees of freedom as 2.064, the total uncertainty at 95% confidence (U95) was 

 ± 0.074 J/g.K (3.09 %). The heat capacity of Therminol VP-1 between 300 and 370 °C was measured to be equal 

to 0.0025T+0.8672 ± 0.074 J/g.K with T (temperature) in Kelvin. 

Fig. 2: Heat capacity of 25 samples of biphenyl/diphenyl ether eutectic (Therminol VP-1). Uncertainty at 

95% confidence (U95) is provided. Solid line represents the extrapolated values from low temperatures 

reported by its manufacturer, Solutia, Inc.

4. Conclusions

The heat capacity of Therminol VP-1 (eutectic of biphenyl/diphenyl ether) from 300 to 370 °C was measured in a 

differential scanning calorimeter (DSC) following the standard ASTM E-1269-05. Three heating cycles were 

used per run per sample to decrease the scatter in the results. Isothermals of 10 minutes were employed before 

and after the dynamic section in which a heating rate of 20 K/min was employed. The uncertainty of the heat 

capacity of Therminol VP-1 was calculated. Both systematic and random uncertainties were determined. The heat 

capacity for 25 samples was found to be 0.0025T+0.8672 with T (temperature) in Kelvin. The total uncertainty of 

± 0.074 (3.09 %) J/g.K was obtained. Volatile samples such as Therminol VP-1 must be carefully handled to 

minimize the uncertainty associated with the scatter of the results and thus obtain accurate thermal properties 

measurements using a DSC. 

Acknowledgements

This work was supported by the U.S. Department of Energy under Contract No. DE-AC36-08-GO28308 with the 

National Renewable Energy Laboratory. 

Heat Capacity = 0.0028T + 1.4867

Heat Capacity = 0.0025T + 1.5497

1.50

1.70

1.90

2.10

2.30

2.50

2.70

2.90

300 310 320 330 340 350 360 370

Heat Capacity, J/g.K

Temperature, °C 

Solutia, Inc.(extrapolated from low temp)

Average of 25 samples

U95 = ± 0.074 J/g.K (3.09 %)
7 

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