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Thermal Diffusivity and Specific Heat Capacity of Linear Alkylbenzene

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Thermal Diffusivity and Specific Heat Capacity of Linear Alkylbenzene Thermal diffusivity and specific heat capacity of linear alkylbenzene Wenjie Wu1;2y, Guolei Zhu3y, Qingmin Zhang4, Xiang Zhou1z, Yayun Ding5, Haoxue Qiao1 and Jun Cao5 1 Hubei Nuclear Solid Physics Key Laboratory, Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education, and School of Physics and Technology, Wuhan University, Wuhan 430072, China 2 Key Laboratory of Particle & Radiation Imaging (Tsinghua University), Ministry of Education, Tsinghua University, Beijing 100084, China 3 School of Marine Science and Technology, Northwestern Polytechnical University, Xian 710072, China 4 Department of Nuclear Science and Technology, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an 710049, China 5 Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China E-mail: [email protected] Abstract. We report the measurements of the thermal diffusivity and the isobaric specific heat capacity of linear alkylbenzene at about 23 ◦C with the standard atmosphere, which are measured for the first time. The conductivity, heat capacity ratio, and speed of sound were derived from our measurements based on thermodynamic relations. The temperature dependence of heat capacity ratio and isobaric specific heat capacity were calculated and relevant results were discussed. Keywords: neutrino detector, linear alkylbenzene, specific heat capacity, thermal diffusivity, speed of sound Submitted to: Phys. Scr. arXiv:1904.12147v1 [physics.ins-det] 27 Apr 2019 y These authors contributed equally to this work z Corresponding author Thermal characteristics of LAB 2 1. Introduction 10, 11]. LAB is a mixture of organic compounds with the formula of C6H5CnH2n+1 (n = 10 ∼ 13) [12]. Liquid scintillator (LS) is applied to neutrino detection Alkylbenzenes with different numbers of alkyls have since the first observation of neutrino in 1956 [1]. It varied properties. Thus LABs in two batches could plays an important role in various neutrino researches have different performance. For constructing a gigantic such as the solar neutrino problem [2], precise detector, a large quantity of LAB is required. The measurements of the third mixing angle θ13 [3, 4, temperature difference between the experimental hall 5], and the detection of neutrino-less double beta and the detector would cause a large amount of decay [6]. In order to collect enough signals, the heat transfer. Hence the heat capacity of LAB is fiducial mass of the neutrino target should be as needed to estimate the requirements to the filling and large as possible, since neutrinos are interacting with cooling processes for controlling the temperature of the matter via the weak interaction only. Meanwhile, the detector. In addition, the hydrodynamic motion inside radioactive backgrounds of LS are required to be as the detector should be well-studied for possible physics low as possible to gain sensitivity. For a monolithic analysis. The thermal diffusivity is one of the input gigantic detector, the thermal equilibrium condition for parameters to do the computational fluid dynamics LS is difficult to achieve. A nonuniform distribution of simulation. temperature could cause the convection of LS inside In this paper, we report the measurements of the detector. The convection is an obstacle to the the thermal diffusivity and the isobaric specific heat detection of low energy and rare events since it would capacity of LAB at about 23 ◦C with 1 atm. We have bring peripheral backgrounds, such as 210Pb, to the deduced the thermal conductivity, heat capacity ratio central volume of the detector. and speed of sound based on these measurements. Recently, the non-equilibrium phenomenon is observed by Borexino, which appeares as an annual 2. Experimental method modulation in the spatial distribution of 210Po inside the detector filled with about 280 tonnes LS [7]. The 2.1. The thermal diffusivity correlation between environmental temperature and background distribution indicates that the migration of The thermal diffusivity α was measured by a dynamic backgrounds is driven by the fluid transportation due light scattering (DLC) method, and the schematic to thermal convection. One of the main goals of the diagram can be found in literature [13]. The light last operation phase of Borexino is the observation of emitted from a laser was split in two. The more intense the CNO solar neutrinos whose dominant radioactive one was guided to transmit the sample and the weaker background is 210Bi. The purified LS after phase one was used as a reference to make the apparatus one and the thermal insulation of the detector working at the heterodyne mode. Mixed light of the give a possibility to achieve this goal. Precise scattered light and the reference light was limited by determination of 210Bi concentration is essential to two pin holes to make sure that only light scattered by the sensitivity of CNO neutrinos. The β− decay of a small volume was detected by the photon counting − 2 bismuth is indistinguishable from the νe-e elastic head. The time autocorrelation function G (τ) was scattering. Conversely, the α decay of polonium measured by a digital correlator in the cross correlation 2 can be effectively picked out through Pulse-Shape mode. Based on a least-squares fitting of G (τ), the Discrimination techniques. Thus the concentration of decay constant τR can be determined and the thermal 2 210Bi can be determined through the selection of 210Po diffusivity was calculated by α = 1=(q τR), where while the secular equilibrium is reached. A stable q is the modulus of scattering vector which can be condition of 210Po is of importance to the high precision derived from the wavelength and incident angle of 210Bi concentration. Many efforts have been devoted incident light [13]. The pressure of the sample was to monitor and control the thermal environment of controlled by a pump system and was monitored by Borexino [7]. Other LS detectors could also be suffered a pressure transmitter (Rosemont 3051S). An electric from the stability problem of backgrounds caused by heater was deployed in the sample container and a thermal convection. Therefore, the thermal quantities platinum resistance thermometer was used to measure of LS are necessary to be measured for studying the the temperature. The relative uncertainties are 3:76 × −5 performance of the detector. 10 , 0.001, 0.015 for the measurements of wavelength, LS usually consists of a solvent and a scintillating incident angle and the decay constant respectively. solute. Linear alkylbenzene (LAB) is one kind of The relative uncertainty of thermal diffusivity is ±1.5% solvent which is used in Daya Bay, RENO and which was derived through error propagation [13]. SNO+ [3, 4, 6, 8]. It is taken into consideration for the next generation neutrino experiments as well, such as JUNO, Jinping Neutrino Experiment and LENA [9, Thermal characteristics of LAB 3 2.2. The isobaric specific heat capacity where βP is the isobaric thermal expansion coefficient and κ is the isothermal compressibility. β and κ The isobaric specific heat capacity c was measured T P T P were analyzed based on the variance of density with by a flow calorimeter, and the schematic diagram can respect to temperature or pressure [15]. be found in literature [14]. The apparatus consists The heat capacity ratio γ for LAB is defined as of a plunger type pump, a preheater, a calorimeter c and a container for the measured sample. The pump γ = P = 1:182 ± 0:005: (5) c (Scientific Systems, Series 1500 HPLC Pump) and V the preheater were used to provide samples with The uncertainty of γ is dominated by the measure- controlled flow rate, pressure and temperature. A ments of βP ; ρ and κT since the correlated uncertainty micro-heater was deployed inside the calorimeter as from cP are canceled. The relative uncertainty of γ a heat source. The temperature increment of the reaches 0.4%. sample entering and exiting the calorimeter ∆T was The adiabatic compressibility κS can be derived measured by two platinum resistance thermometers as κT −4 −1 (PRT, Fluke Corporation). Due to the inefficiency κS = = (6:553 ± 0:039) × 10 MPa ; (6) of the heat absorption of the sample, a fraction of γ the heat was absorbed by the calorimeter. The where κT is the isothermal compressibility which has sample collected by the container was weighed to been measured in the literature [15]. calibrate the flow rate with an analytical balance According to the Newton-Laplace formula, the (ME204, Mettler Toledo). Then the isobaric heat thermodynamic speed of sound in LAB can be capacity can be determined by the relative difference calculated as of the thermal power of the micro-heater with respect 1 −1 vsound = p = 1336:34 ± 3:97 m · s : (7) to the variance of the flow rate once ∆T is fixed. κSρ High accuracy was reached by keeping the calorimeter adiabatic from the environment. The experimental 3.3. Estimation of the temperature dependence of γ uncertainties are ±0.0001 W, ±0.001 g/s and ±0.01 K and cP for the measurement of thermal power, flow rate and Different experiments may work at different tempera- temperature respectively. The relative uncertainty of tures. The temperature dependence of γ and c can isobaric heat capacity is ±0.98% which was derived P be useful. According to a previous research [15], the through error propagation [14]. density at different temperatures with 0.1 MPa was described as 3. Results ρ(t) = ρ0[1 − β0(t − t0)]; (8) ◦ 3.1. Measurement results where t is the celsius temperature, t0 is 23 C, ρ0 is The thermal diffusivity α was measured by the DLC the density at t0 with 0.1 MPa. And the isobaric method at 22.98 ◦C with 1 atm to be thermal expansion coefficient at different temperatures was described as α = (7:245 ± 0:109) × 10−8 m2 · s−1: (1) β0 The isobaric specific heat capacity cP was βP (t) = ; (9) 1 − β0(t − t0) measured by the flow method at 23.15 ◦C with 1 atm to be where β0 is the isobaric expansion coefficient at t0 with −1 ◦ −1 0.1 MPa.
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