Theoretical and experimental assessment of a novel method to establish the complete measurement range of the calorimeter and its limit ofdetection and quantification

Vesna Krsti?

Mining and Metallurgy Institute Bor,Zeleni Bulevar 35,19210 Bor,Serbia

University of Belgrade,Technical Faculty Bor,VJ 12,19210 Bor,Republik of Serbia

Keywords:Benzoic acid Certified reference material The limit of detection/quantification Measurement range Quality control Calorimeter Environmental protection

ABSTRACT For determining the accuracy of a calorimeter over the instrument’s entire measuring range,a novel method has been established.For this new approach,(a)benzoic acid(C6H5CO2H)as a certified reference material(CRM),(b)SiO2 and(c)a mixture of CRM benzoic acid and SiO2 have been used.To illustrate the essential difference between 1)the novel analytical method for control of the entire measurement range and 2) the calorimeter calibration,both applications of benzoic acid (BA) have been demonstrated.An experimental result showed that BA was successfully used to check the whole calorimeter measurement range.The results also showed that the same new method was successfully applied to determine the limit of detection and quantification.A new instrument testing process and a new measurement technique have thus been established.In this way,the cost of using CRM to control the accuracy of measuring the entire measuring range of the calorimeter,as shown in this paper,is minimized.The requirements of the ISO/IEC 17025:2017 standard are satisfied.ISO/IEC 17025:2017,together with ISO 9001:2015(quality management systems),ISO 14001:2015 (relate to environmental protection) and ISO 45001:2018 (occupational safety),constitute an integrated quality system by which a testing laboratory may also accredit.

1.Introduction

A calorimeter is a measuring instrument for determining the amount of heat that is released or consumed during physical–chemical processes.It is also used to determine the specific heat capacity.Since the time when the first calorimetric bomb was made,it has undergone many technical changes [1,2].The latest generations have very sophisticated computer programs for processing data obtained from the combustion of a sample.Meschel(2020) [3] gave a historical overview of the calorimeters used by Antoine Lavoisier (1789),by Kawakami (1927),by Kubaschewski and Walter (1939),by Calvet (1950),by Ticknor and Bever(1954),by Kleppa from(1955)to(2006),by Gachon(1979),by Cacciamani (1995),by Jung (2003) and by Navrotsky (2016).Meschel(2020) briefly described the different types of calorimeter measurements [3].More recently,the emphasis has been on developing instruments that work quickly,with a small sample amount.Technical improvements of the calorimeter have been the subject of research over the last years.These have been recorded so that the application of the method for measurements of both a) the calorimeter and b) the method used,has improved.From these developments,the so-called standard method for different substrates emerges such as the testing of solid and liquid fuels,waste testing,food testing and metabolic studies and testing of explosives [4,5].Lately,researchers have developed a new concept of a calorimeter for the detection of high-energy cosmic rays in space[6,7].Calorimetric determinations have been applied in many branches of research and technology.They are essential for understanding and interpreting many physical–chemical processes.Also serve to determine the heat capacity of matter,the energy value of fuel,biomass,food and other applications.

With the advent of ISO/IEC (the International Organization for Standardization/International Electrotechnical Commission)17025 from 1999,which replaced EN 45001 and the ISO/IEC Guide 25,the competence of all the laboratories applying this standard was assessed and registered internationally.The application of the ISO/IEC 17025:2017[8]standard involves method verification.This means providing evidence on the capacity of each laboratory to successfully test the methods and the capacity to test and to determine the characteristics that describe the different results(repeatability,reproducibility,and measurement uncertainty).

The heat capacity is the value which characterizes every calorimeter.It must be checked periodically,and this check must be repeated whenever the calorimeter’s work conditions change for any reason.Heat capacity is determined by benzoic acid(C6H5-CO2H)as a CRM(certified reference material).Benzoic acid is usually used for calorimeter testing because it has a crystalline structure that can be obtained with high purity.The use of CRM is one of the requirements of ISO/IEC 17025:2017 standard[8].Reference materials play a valuable role in the standard method and can be divided into two groups (a) certified reference materials(CRMs) and (b) laboratory reference materials (RMs) [9].CRM and RM packages are also used to assess the measurement uncertainty,for determining the accuracy and precision of measurements,determining the limits of quantification,the limit of detection,the range of measuring and other measurement parameters of the device.

Jovanovi?et al.[10,11]have given their explanation about how ISO/IEC 17025 [8] has been introduced into the laboratories of Eastern European countries.For good conduct the laboratory tests,it is necessary that in addition to the requirements of ISO/IEC 17025:2017 [8],laboratory tests should also be the requirements of ISO 14001:2015 [12] and ISO 45001:2018 [13].The mentioned three standards,together with the basic ISO 9001:2015 [14] standard,form one integral quality system.These confirm the quality of testing in one laboratory.The control of the measuring range of the calorimeter is usually performed using several different CRMs,selected so that their combustion heat corresponds to various intervals of measurement of the apparatus.CRMs are expensive chemicals.Therefore CRMs are chosen that most closely corresponds to the measurement range that is more or most commonly used,for testing a particular type of sample.In this way,it is unthinkable to check the entire measuring range of the calorimeter,because it would be too expensive.For this reason laboratories that use a calorimeter usually opt for the purchase of one or two CRMs.The value of the CRM is chosen according to the possibilities and the measuring range of the calorimeter.So the one or two different points on the entire measuring range of the calorimeter are checked.

However,the experiments presented in this paper provide an opportunity to solve the problem of controlling the measuring range of the calorimeter at each point on the curve representing the measuring range,using a single CRM,benzoic acid.It gives maximum savings and control of the accuracy of the calorimeter over the entire measuring range.In addition,benzoic acid can be applied to determine the performance of different types of calorimeter equipment[15,16]and at this moment there has been no known prior published work that covers the scope of the studies reported in this paper.

Based on the requirements of the ISO/IEC 17025:2017,this paper presents a theoretical model with calculated and expected results.The results obtained experimentally were based on a theoretical model,using (a) CRM benzoic acid,(b) SiO2and,(c) mixtures of CRM benzoic acid and SiO2.Silicon dioxide was chosen as a supplement to benzoic acid,since its heat of combustion is zero,and it behaves like an inert material during the incineration of mixed samples.The results obtained were used to control the entire measuring range of the calorimeter.

A part of the same obtained results served to determine the lower and upper limit of calorimeter detection.The results obtained were also used for calculating the limit of quantification.This experiment indicates the possibility of using the minimum amount of benzoic acid while fully providing confidence in the quality of the results tested.

2.Methodology

2.1.Calorimeter system

Two different standards were used,ISO 1928:2009 [17] from Europe and ASTM (American Society for Testing and Materials)D5865/D5865M–19 [18] from the USA for determination of the gross calorific value.Sample preparation for analysis is the same in both standard norms.ISO and ASTM standards for the use of calorimeters have a different approach,but the final results are the same.Fig.1 represents the principle of operation of a calorimeter [19,20].

Fig.2 shows the main parts of the calorimeter C5000 produced by IKA Werke(the factory No.:01.666060)with the names of components.The cooling and oxygen supply system are also parts of the calorimeter.The whole system is used to determine the gross calorific value of the sample.

Fig.1.Schematic representation of the principle of operation of a classical calorimeter.Modified after Chemistry LibreTextsTM[19] and Operating Instructions [20].

Fig.2.Schematic representation of measurement cell,calorimeter C5000 and calorimetric bomb C5010.Modified after Operating Instructions [20].

The working principle of the calorimeter is based on the bomb,immersed in water,Fig.2.In a bomb,the sample ignites and burns with the help of oxygen.The heat from the bomb is transferred to the water.The software system(calorimeter C5000)automatically calculates the upper calorific value of the sample.

2.2.Calibration of the calorimeter

Combustion of benzoic acid (BA) under specified conditions(to gaseous carbon dioxide and liquid water)serves to make a change in the temperature of the calorimeter of one unit interpretable in defined units of energy.The classical type of combustion by a calorimeter can be maintained unchanged over extended periods in terms of mass(heat capacity),geometry and heat exchange surfaces.It allows the calibration of an instrument to be carried out as a separate series of measurements,establishing the efficient heat capacity,i.e.the calibration constant (ε) of the calorimeter [17]For systems where the quantity of water in the calorimeter vessel is kept the same in all tests,the calibration constant (ε) is calculated,as shown in Eq.(1):

Where ε is the efficient heat capacity,expressed in joules per kelvin;mbais the mass,expressed in grams,of BA;qV,bais the certified gross calorific value,expressed in joules per gram,at constant volume for the BA;Qfuseis the contribution,expressed in joules,from the combustion of the fuse;Qignis the contribution,expressed in joules,from the oxidation of the ignition wire;QNis the contribution,expressed in joules,from the formation of nitric acid from liquid water and gaseous nitrogen and oxygen;θ is the corrected temperature rise,expressed in Kelvins.

2.3.Calorimetric procedure

Calorimetry is a measuring method for determining the amount of heat.Unlike the temperature measurement,calorimetry measures the amount of heat energy that binds to or is released during a physical or chemical process.Calorimetry is based on observing the effects that heat produces (Fig.3).

The change in temperature during the monitoring of the sample combustion in the calorimeter is shown graphically in Fig.3[17,21] The main period or what we refer to as the period of sample combustion is marked with the number 3 in Fig.3.This sample combustion period begins by igniting the sample in the presence of oxygen,and it is represented in the graph by point 5 ortiperiod.The number 1 ortjindicates the jacket temperature,while the numbers 2 and 4 show the before-period and after-period respectively.The calorimetric determination consists of two different combustion tests.The first one use for the calibration of calorimeter where usually use BA.Then the value of BA combustion is about 11,000 J?K-1(Table 1).The second one use for samples analysis when BA can use as an unknown sample.Then the value of BA combustion is approximately 26,500 J?g-1.The calorimetric procedure for both types of tests is essentially the same,but the calculations,and the results are different,as shown in this paper.

Fig.3.The time-temperature curve of heat produced.Modified after ISO 1928:2009 [17] and Operating Instructions [20].

Table 1 Calibration of a calorimeter for each bomb of the calorimeter

3.Experimental

The experiments carried out with samples of (a) pure benzoic acid as a standard CRM material,(b) silicon (IV)-oxide,and the(c) mixture of benzoic acid and silicon (IV)-oxide.The term ‘‘pure benzoic acid”is used in this paper when referring to benzoic acid that is not combined with SiO2.Benzoic acid is the CRM material used for the calibration of the calorimeter.According to ISO 1928:2009 [17] benzoic acid is used for the determination of the gross calorific value.Benzoic acid with Ref.No33045,production by AlliedSignal Riedel-de Ha?n (ELINCS-Nr.:200-618-2) has the heat of combustion of (26,461 ± 40) J?g-1.Silicon (IV)-oxide,SiO2,was used as a Pro-analysis quality,obtained from‘‘Hemos production”,with a granular size from 0.2 to 0.5 mm and declaration No202 K4.

Samples with mixtures of BA and SiO2,with a total mass of 1 g,were prepared with a different BA proportion,from 0.05 g to 0.80 g.Each sample mixed was labelled according to the mass of benzoic acid as 0.05–0.80BA/SiO2.[22].Specimens of pure BA have different masses on average 1.00 g,1.25 g and 1.50 g.These samples were called 1.00BA,1.25BA and 1.50BA,as shown in Table 2.

The method of determining the heat value,using both ISO 1928[17]and ASTM D5865[18]standard norms,was carried out on the calorimeter C5000 by IKA Werke,with the factory No01.666060.The calorimeter was used in the adiabatic mode.This means that the process of heat exchange with the external environment is negligible so that the adiabatic process itself does not depend on external conditions.It also means that the calorimetric bomb has a constant volume.The calorimeter bomb used in this experiment was model C5010,with a capacity of 0.260 L and characteristics of 23 MPa and 323 K(Fig.2).

The sample tested was measured on a balance,then transferred to the bomb and burned in the calorimeter under high pressure in the presence of oxygen.The pressure of the oxygen was about 3 MPa and according to the Operating Instructions,No71 900 01a,IKA WERKE[20],the pressure must not exceed 4 MPa.The quality of pure oxygen was 99.95 or 3.5.The heat generated is calculated from the increase the water temperature and the heat capacity of the bomb(Fig.2).The data obtained from the combustion processing of samples was recorded by using an implemented software program ‘‘IKA?C5000 Control”,Version 2.21.Samples were measured by the calibrated analytical balance,model ‘‘Sartorius BP 61S”,with an accuracy of ±0.0001 g on-line connected with the calorimeter.

4.Results and Discussion

4.1.Calibration of the calorimeter

To ensure the precision and accuracy of the results,calibration of the calorimeter is a routine maintenance inspection.It is desirable to carry out this calibration every six months,also every time the device has an intervention due to device failure.Table 1 presents the results of the calibration for each calorimeter bomb used in experiments.Combustion of BA(about 1 g)for the calibration is carried out under the same conditions as the combustion of BA as a sample,according to ISO 1928 [17,22].

Table 1 shows the calibration results (ε),measured and corrected according to Eq.(1),of the calorimeter for each bomb used.In this way a closer observation can undertake of the difference in a)the use of benzoic acid in the calibration process and b)the use of benzoic acid in the new method of controlling the entire measuring range of the calorimeter.When the calibration is by determining each bomb,the result was about 10,700 J?K-1.It is the value thatentered into the calorimeter program for each bomb,according to Table 1.It serves for the operation of the calorimeter for further data processing.When the calorific value of the BA is determined as the unknown sample,the value obtained was about 26,450 J?g-1.Since the certified CRM BA value has achieved,it means that calibration of the calorimeter has successfully carried out.

Table 2 The theoretical model of gross calorific value (GCV),for mixed samples of benzoic acid (X) and SiO2 (Y);and pure specimen of benzoic acid and SiO2

4.2.The novel analytical method for the control of the entire calorimeter measurement range

Due to the generally high price of CRMs,a new &highly accurate method has been investigated to accurately allow a calorimeter,to be used for measurements in the range from 0 to 40 kJ?g-1.By using the knowledge of physical chemistry,and experience with different instrumental laboratory measurement techniques,the idea has been developed about how this problem could resolve.The newly developed method would give more accuracy in obtaining results.

Table 2 shows the expected or ideal theoretical results of the heat of combustion,calculated both for samples with pure BA(the measurement of the GCV only of BA)and the mixture samples(the mixture of BA and SiO2).It is to highlight that the amount of combustion heat comes only from BA.To examine the measurements of the combustion heat with the range above the value of certified BA (higher than (26,461 ± 40) J?g-1),the mass of benzoic acid gives the proper amount of heat that was calculated theoretically.

The experiment has been conducted,by calculating the amount of BA that is needed to be in the samples.To obtain higher amounts of heat per one gram of benzoic acid,than the certified values of BA,the mass for every specific specimen,should be calculated.This information is of great practical importance because it shows which mass of the sample of BA may use when working with the device to get closer to the upper limit of the calorimeter.The upper limit of the calorimeter,given by the manufacturer is 40,000 J?g-1and value above this can damage the equipment.For example,to obtain the heat of combustion of 40,000 J?g-1,a sample that contains exactly 1.5117 g of BA should be burnt,Table 2.But data is given for the software program of calorimeter C5000 indicates that there is only 1 g of BA.Only in this way,using false information for the mass of the sample (manipulation),it is possible to obtain the heat of combustion which differs from the certified value of BA.It is the crucial moment when performing the trial and it must be remembered that this fact should be kept in mind.Using this‘‘false value”is critical and the whole experiment based on this idea.The obtained results are appropriate,according to ISO/IEC 17025 [8].

Fig.4.Theoretical model of GCV for (a) pure samples of BA as a standard material and(b)BA used in a specific manner of the entire calorimeter measurement range.

The results of the theoretical model from Table 2,shown in Fig.4.The theoretical expectation of heat combustion of certified benzoic acid is 26,461 J?g-1.For any mass of the different sample of BA from Table 2,values are constant and amount to 26,461 J?g-1over the entire measuring range,as shown in Fig.4,curve (a).All kind CRM materials (for coal,food,etc.) have the same certified value for different sample weights,as shown here in the example of BA,Fig.4 (a).Linear curve (b),Fig.4,shows the different values of heat combustion of BA for the entire calorimeter measurement range.These values were obtained by preparing samples as previously described in Section 3.

Table 3 shows the experimental results of the gross calorific values of different samples [17] The specimen measured in duplicate(Z1,Z2),and consisting of either only BA and only SiO2or a mixture of mass fraction BA (X1,X2) and mass fraction of SiO2(Y1,Y2)expressed in grams to four decimal places,since the samples were measured on the weight of 4 decimal places.It has been known that the heat of combustion of SiO2is equal to zero,which is experimentally confirmed by the results obtained of the heat of combustion of the sample 1.00 SiO2,Table 2.It means that the entire thermal value of the mixed samples,BA/SiO2,comes only from the mass fraction of BA in the specimen.

Initially,only a part of the measuring range analysed for the values of the heat of combustion of BA was less than the certified value since the idea of mixed samples was used (BA and SiO2)[21]However,since the input of heat of combustion(of BA)higher than the certified value(26,461 J?g-1)is not possible,it was necessary to investigate an alternative method to solve this problem.Thus it was imperative to solve this problem.

When it comes to the heat of combustion of CRMs,each sample mass provides a value corresponding to the certified heat combustion.This is because the newer software programs are programmed so that each sample weight recalculates to 1 g.To obtain values different from the certified one,for sample weights greater than 1 g,the mass is calculated theoretically.Table 2 shows how much BA each sample should contain,to cover the measuring range of the calorimeter above the certified value up to its upper limit of measurement.In this way,it is possible to prevent any damage to the calorimeter.The theoretical values calculated,as shown in Table 2,where benzoic acids are measured,tableted and transferred into the calorimeter for analyses,are shown in Fig.2 and Fig.4.In the software program of the calorimeter,the data is always entered equal to 1 g regardless of the real mass of the samples.Only in this way,by using simulated (false,inaccurate) data on the value of the sample mass,it is possible to obtain a heat of combustion differing from the certified amount of BA.

Table 3 Experimental results of GCV (Z1 and Z2) corrected for HNO3,for mixed samples of BA (X1 and X2),and SiO2 (Y1 and Y2)

This is achieved when,for example,the mass of a sample of tableted BA of 0.4370 g is measured,then a value is entered in the calorimeter program as if analyzing a specimen of 1 g.It is a procedure that is repeated for each point on the curve in the entire measuring range of the calorimeter,Fig.5.In the same way,instead of the curve(a) in Fig.4,the curve (b)is obtained.When the mass of BA is measured to approximately 1 g and the real(correct)value of the weight is entered in the calorimeter program,the exact certified amount of(26,461±40)J?g-1is obtained.This is represented by the value of the intersection of two lines in Fig.4.Whenever the apparatus analyzes a sample with the real mass of the specimen,the same certified value of BA is always obtained,Fig.4 (a),even though the amount of the sample is variable.In the same way the points on the curve (b),Fig.4,above the certified value of(26,461 ± 40) J?g-1are shown.Combustion heat of 40,000 J?g-1should be obtained if a sample containing 1.5117 g of BA.The software program of the calorimeter is programmed as if the analysis had been performed with a specimen of 1 g mass,which represents a false value,given that the actual mass of the sample was 1.5117 g.

The results obtained using mixed samples and samples only with BA,which used a simulated (false) mass entered in the soft-ware program,mean that it is possible to cover any point on the curve that represents the measuring range of the calorimeter.This is shown by the slope of the curve in Fig.4 (b) and Fig.5.In this way,it is possible to control the accuracy of measuring for each specific calorific value of the sample and ensure the reliability of the results,which is a requirement of the standard ISO/IEC 17025:2017.

The method of the least squares and regression analysis was employed using a calculation based on the mass fraction of BA in the specimen and the heat of combustion obtained.The difference between the measurements obtained from the combustion heat value and exact values calculated from the regression equation,Fig.5,served to calculate the standard deviation of the whole series of the specimens,which is±111.29 J?g-1with a confidence level of 68.26%.

Standard deviation with the given level of confidence of 95.46%(forn-1=19,p=1.729)is±43.03 J?g-1,Table 3.Thus the standard deviation of ±43.03 J?g-1applies to the entire range of measurement of the heat of combustion of the samples tested,at the same time the heat of combustion of each specimen serves as a control of the whole measurement range of the calorimeter.The samples tested were measured in duplicate to ensure the repeatability of the results of each measurement.Other statistical data of these experiments are given in Table 3.Based on the regression equation and the values of the coefficient of determination(R2=0.9999),the linear function depends on the mass and heat of combustion confirmed,as shown in Fig.5.

Fig.5.Experimental results for the heat combustion of benzoic acid and mixed samples (benzoic acid and SiO2) as a function of benzoic acid mass.

The uncertainty of measurement results (characterized by a value interval in which the exact value) is most probably within the specified confidence level [23,24] The result of an evaluation of the measurement uncertainty should be the best approximation to the exact range of values[11].The measurement uncertainty of BA,by AlliedSignal Riedel-de Ha?n,is±40 J?g-1.The result obtained from the measurement of uncertainty for the whole curve is±43.03 J?g-1based on experimental data in the same order of magnitude as given by the manufacturer,and as such is acceptable.The resulting curve,see Fig.5,in addition to being used to determine the control of the calorimeter C5000 over the entire measuring range,is also used for determining the limit of detection and the limit of quantification as the lowest value of heat combustion which the calorimeter can measure with a certain precision.

With the sample of 0.05BA/SiO2,the lowest point at which the heat of combustion can be measured is shown in Table 3.In the same table,we see that the heat of combustion of the sample 0.04BA/SiO2has not been registered by the calorimeter,although the sample burned.The sample of 1.00SiO2is not burned,which confirms that its heat of combustion is equal to zero.Therefore,these two samples were not included in the statistical analysis but were taken as the limit of detection which the calorimeter can register.

4.3.Determination of limit of detection and limit of quantification

The repeatability of results is confirmed by the combustion of 6 samples type 0.05BA/SiO2[21],with the mass ratio of benzoic acid and SiO2is approx.0.05% (mass).The same result was obtained when only 0.05 g BA was used,and the calorimeter was set to analyze the sample with a value of 1 g.The processing of the data obtained is shown in Table 4.For statistical processing of the measurement results,repeatability of 6 measurements was also carried out for samples 1.00BA and 1.50BA in the same way,Table 4.

According to ISO 11843-1[24]the criterion of detection(CD)is defined as the lowest value for which the required confidence interval can be said to be different from zero.If the formula (2) is used to calculate the criteria of detection,the CD would be 73.74 J?g-1(where df is the number of degrees of freedom for the value 5,t95%=2.015 andSblanc=33.88,n=6).

The CD value calculated is the value which cannot be measured experimentally by the calorimeter.The limit of detection,LoD (for the calorimeter)is the lowest amount of the combustion heat that the calorimeter can detect in this sample but it is not necessary to be quantified [25] The limit of detection (LoD) is typically calculated as twice the value of the CD (2 × CD).If the 2CD applied in the case of the calorimeter C5000 IKA Werke the limit of detection should be equal to 147.48 J?g-1.The experimental value of the LoDis～1180 J?g-1,according to Table 4.This value can be measured experimentally with adequate accuracy.Therefore it is more suitable than the value of the limit of detection obtained by calculating the afore-mentioned formula.Since the CD is half of the LoD,the experimental value of CD would be 590 J?g-1.This value is significantly different from the value obtained by calculation using the formula mentioned,and the 147.48 J?g-1is not a value measurable by the calorimeter C5000.It is not the limit of detection because it is still not the lowest amount of combustion heat of the sample that can be determined with acceptable precision and accuracy.It is not the lowest level at which the relative standard deviation is still admissible [26,27] Hubertet al.[28] were a pioneer of this concept and used it for the validation of chromatographic methods.If the Eq.(3)is used to calculate the LoQ[29]its value is a measurable size for the calorimeter C5000.The LoQ is 1575 J?g-1,and this value can be measured on the calorimeter.However,this value is significantly higher than those obtained experimentally.The experimental determination of LoQ by using the calorimeter C5000 gives a value of～1200 J?g-1.This value for the C5000 calorimeter is measurable.

Table 4 Measured results of GCV corrected for HNO3,for samples 0.05BA,1.00BA and 1.50BA with calculated statistical value.

The standard deviation,with the confidence level of 95% for samples 0.05BA is ±33.88 J?g-1according to Table 4 which is practically the same order of magnitude as the value of the measuring uncertainty of the whole curve of the measuring range of±43.03 J?g-1.In other words,the result obtained using Eq.(3) is approximately 1600 J?g-1.Considering that the standard deviation for a confidence level of 95%is achieved at the lowest experimental point,it is virtually the same order of magnitude as the standard deviation of the same confidence level of the whole curve.A value obtained experimentally of～1200 J?g-1has been taken as the limit of quantification.

5.Conclusions and Future Perspectives

Environmental protection is a priority of today’s man.The new method is in accord with ISO/IEC 17025:2017,ISO 9001:2015,ISO 14001:015,ISO 45001:2018 and other accompanying ISO and ASTM standards related to the laboratory use a calorimeter.It is confirmed the quality of laboratory testing.Benzoic acid(BA)with the certified heat of combustion (26,461 ± 40) J?g-1,was used in a novel method for testing the calorimeter over the entire operating range.Using a series of samples with different weights of BA,a curve was formed.The curve was obtained by measuring the appropriate amount of BA for each specimen.The software program of the calorimeter,the method of manipulation (simulation)was applied in such a way as the value set as the amount for each sample is always exactly 1 g.The lower and upper detection limit and the quantification limit are determined using the same curve.Also,the same sample weights were used to designate the accuracy of the calorimeter operation over the entire measuring range.

With this experiment,we obtained a linear dependence for the whole measuring range.That suggesting that the calorimeter works with satisfying precision and accuracy throughout the entire measurement range.Also,a different CRM can be used,with a specific heat of combustion,but that would only cover a measuring range at a certain point,depending on the combustion heat of a given CRM.However,in this way,it is not possible to control every part of the measuring scale of the calorimeter.This novel analytical method provides good results for laboratory testing using the calorimeter and is economically acceptable.The laboratory staff can purchase 1 or 2 CRMs for a given type of materials (fuel or food) and confirm the accuracy of the calorimeter in the certified CRM value.After that,the testing laboratory no longer has to purchase other CRMs.That is because the device can be checked in the future by this new method (using only the BA).

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors gratefully acknowledge the funding by the Ministry of Education and Science,the Republic of Serbia for Registration(No.451-03-68/2022-14/200052).The author is also grateful to Marjan Gori?ek,Jim Fleming and Prof.Nicola Bolton for their overall support and generosity.

Nomenclature

dfthe number of degrees of freedom

GCV gross calorific value,J?g-1

LoD the limit of detection

LoQ the limit of quantification

mbathe mass,expressed in grams,of BA

S the standard deviation for the confidence levee of 95%

s standard deviation

Qfusethe contribution,expressed in joules,from the combustion of the fuse

Qignthe contribution,expressed in joules,from the oxidation of the ignition wire

QNthe contribution,expressed in joules,from the formation of nitric acid from liquid water and gaseous nitrogen and oxygen

t95%t-test at 95% confidence level

ε the efficient heat capacity,J?K-1

θ the corrected temperature rise,expressed in Kelvins