Heat capacity anomaly near the lower critical consolute point of triethylamine–water

Abstract

The heat capacity of the binary liquid mixture triethylamine-water has been measured near its lower critical consolute point using a scanning, adiabatic calorimeter. Two data runs are analyzed to provide heat capacity and enthalpy data that are fitted by equations with background terms and a critical term that includes correction to scaling. The critical exponent a was determined to be critical exponents. These values, for the most part, agree very well with experimental results. _-3 Several universal amplitude ratios have also been predicted and many have also been experimentally tested with mixed results. 5 A particularly powerful observation is that only two critical exponents are linearly independent, and that the leading amplitudes are interrelated using only two scale factors.l-3 Thus the universality of the exponents could be used with two experiments to determine all the leading critical behavior of a given system.The heat capacity provides a delicate probe of the system near a critical point and can determine essential amplitude and exponent values. In particular, a precise measurement of the heat capacity of the binary fluid mixture triethylamine and water will help settle a dispute in the literature about the amplitude in the one-phase region and its effect on the universal ratio X, measure the universal ratio of the amplitudes above and below the critical temperature, andgive the first attempt in binary liquid mixtures at using a new "universal" amplitude relation R_, to reduce the number of fitting parameters while testing theoretical predictions.The heat capacity has a weak divergence near the critical point that is governed by the critical exponent _, has a critical contribution Be to the background heat capacity, and has correction to scaling terms that extend the theoretical description further from the critical point. 3'6 The critical point influences the system properties over a global region. 78 however, this experiment measures behavior near the critical point and we will use the simpler formalism that is appropri-8048

Critical behavior of binary mixture of {x C6H5CN + (1 −x) CH3(CH2)12CH3}: Measurements of coexistence curves, turbidity, and heat capacity

“…The value of R B calculated from equations (27) and (28) was À0.58 ± 0.02. The value of R B calculated by equation (26) from our experimental results was À0.513 ± 0.003, which is in good agreement with the experimental values reported by Jacobs [42,43] and our previous work [15], but smaller than both the prediction of Bagnuls and Bervillier and that of equation (27).…”

Critical behaviour of binary mixture of {xC6H5CN+(1−x)CH3(CH2)7CH3}: Measurements of coexistence curves, light scattering, and heat capacity

“…It was found that the variation of 0.01 in a caused the changes of about 16%, 11%, 5%, and 1.6% in A + , A À , A + /A À , and C p0 , respectively, while the contribution of the variations of T c and E within their uncertainties to the changes of the adjusting parameters were negligible. It was reported that the theoretical predictions gave the values of A + /A À being (0.537 ± 0.019) for d = 3 expansion [1], (0.530 ± 0.003) for high-temperature series [2], (0.527 ± 0.037) for e expansion [1], and (0.55 ± 0.01) for Monte Carlo simulation [33], while the experimental values were ranged between 0.52 and 0.59 [26,28,30,32,[34][35][36][37][38][39]. The value of A + /A À determined in this study in the temperature range of ±2.8 K from the critical point is 0.533, which is in excellent agreement with the theoretical prediction of 0.530 for hightemperature series.…”

“…The value of X was predicted to be (0.01966 ± 0.00017) from an expansion of d = 3 [41], and (0.01880 ± 0.00008) from high-temperature series [2], respectively. Recent experimental determinations have found X to be in the range between 0.019 and 0.028 [28,30,34,36,39,[42][43][44]. Our measurements in the range (T À T c ) = (0 to 2.8) K gave the values of amplitude n 0 of the correlation length and amplitude A + of the heat capacity to be (0.287±0.005) nm and (0.01365 ± 0.00009) J Á K À1 Á cm À3 , respectively.…”

Heat capacity and turbidity near the critical point of succinonitrile–water

“…The heat capacity of a critical mixture was measured using an adiabatic calorimeter similar to that used previously for studies in triethylamine-water 24 and anilinecyclohexane. 20 Our calorimeter was used in a ''step'' mode, where a fixed energy was added to the cell and the resulting temperature step was measured.…”