Saturated Vapor Pressure Curve Research Articles

The energy-limited water loss of an alpine shrubland on the northeastern Qinghai-Tibetan Plateau, China

Study regionAlpine shrubland on the northeastern Qinghai-Tibetan Plateau. Study focusWater provision ability is a pivotal ecological service of high-altitude alpine regions and is controlled by precipitation, evapotranspiration (ET), and soil water storage whereas the underlying ecohydrological processes remain highly unquantified. Here, we investigated continuous 19-year flux measurements to quantify the temporal patterns of ET and water budget (precipitation minus ET, P−ET), as well as 0-20 cm soil water storage change (ΔSWS). New hydrological insights for the regionAt a monthly scale, ET peaked in July (96.7 ± 26.4 mm, Mean ± S.D.) and averaged 41.7 ± 31.9 mm, whose variations were determined by the slope of the saturation vapor pressure curve at air temperature, air and soil temperatures, regardless of vegetation growth stage. P−ET averaged 18.3 ± 26.3 mm in August and September while stayed deficit during the other months. The variations in P−ET were controlled by precipitation in the May-October growing season whereas by ET in the non-growing season from November to April. ΔSWS peaked in May (28.8 ± 11.2 mm) and September (3.0 ± 2.7 mm) and almost accumulated to zero over the whole season. At annual scales, none of ET, P−ET, and ΔSWS changed significantly. ET averaged 512.2 ± 68.4 mm and exceeded precipitation (459.1 ± 58.4 mm), likely due to the lateral flow supply of uphill locations. The variations in ET were regulated directly by bulk canopy resistance and indirectly by net radiation. P−ET averaged −53.2 ± 95.4 mm and demonstrated a clear water deficit (−51.6 ± 21.0 mm) during the non-growing season. The variations of P−ET were driven jointly by precipitation and ET, with opposite but equivalent effects. The dominance of thermal conditions and energy availability on ET variability manifested an energy-limited feature of water loss in the alpine shrubland. The temporal patterns in P−ET elucidated that the alpine shrubland plays the water retention rather than water provision function through transforming variable precipitation input into stable ET loss.

Derivation of the Penman–Monteith Equation with the Thermodynamic Approach. II: Numerical Solutions and Evaluation

A review of the derivation of the Penman–Monteith equation with the thermodynamic approach of Monteith is presented in a companion manuscript. The resultant set of equations (expressed in terms of latent heat flux, lf, sensible heat flux, qf, final air temperature, Ta, and the slope parameter related to the saturation vapor pressure curve, Δ) represents a coupled system. Thus, a pair of alternative numerical solutions, with different levels of complexity, were developed and evaluated in the study reported here. Results showed that the alternative models (labeled as model 1 and 2) produced outputs that are essentially identical and also in close agreement with a reference solution. Intercomparison of the alternative models based on the criteria of numerical efficiency and robustness suggests that each model represents a comparable alternative to the other to estimate evaporation. However, owing to its simplicity, model 1 was selected for further consideration. A comparison of the outputs of model 1 with those of the conventional model (i.e., the approach widely used to evaluate the Penman–Monteith set of equations), based on data sets covering a range of evaporation conditions, showed that the difference in the approaches implemented in the two models has a significant effect on estimates of qf, a limited effect on lf, and a negligible effect on Ta. Notably, the results also showed that the mean absolute residual for latent heat flux, lf (i.e., the mean of the absolute residuals between estimates obtained with model 1 and the conventional model) is relatively small (only about 8.2%), suggesting that differences between lf estimates computed with model 1 and the conventional model should generally be within the margin of error of the conventional model.

Evaluation of a low-GWP and nonflammable blend as a new alternative for R134a in the heat pump system

R134a is a refrigerant widely used in heat pump systems, which has a high global warming potential (GWP) and cannot be used for a long time. In this study, a new mixed refrigerant, named RGT2 (GWP = 560), has been proposed as an alternative refrigerant to R134a in heat pump systems. RGT2 is a mixture composed of R134a/R1234yf/R161 (54%/43%/3% wt%) without toxicity. Firstly, the basic properties of RGT2 were tested, including flammability, miscibility, and saturated vapor pressure. The results showed that RGT2 is non-flammable and is well miscible with polyol ester (POE) oil and polyvinyl ether (PVE) oil. Moreover, the saturated vapor pressure curve of RGT2 is close to that of R134a in the range of -20∼80 °C. Secondly, the cycle performance of RGT2 and R134a were compared and analyzed by theoretical calculations and experiments. The cooling capacity of the heat pump system filled with RGT2 is close to R134a, and the coefficient of performance (COP) is 3.8% lower than that of R134a. Considering that RGT2 is more environmentally friendly and safer, and its thermophysical properties and cycle performance are close to R134a, it can be used as a substitute refrigerant for R134a in heat pump systems.

The Space Density Distribution of Alkali Metal Atoms in a SERF Atomic Magnetometer

The number density of alkali atoms in vaper cell is an important parameter for atomic magnetometer. The vapor cell is usually heated to a high temperature for the number density exceed to 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">18</sup> m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> to achieve the spin-exchange-relaxation-free (SERF) process. The optical rotation of multichannel atomic magnetometers is affected by the number density distribution. We present an effective method for monitoring and analyzing the spatial distribution homogeneity of the atomic number density in the alkali metal cell within the SERF magnetometer. The numerical results from researching the model of electric heating films and ovens show that the temperature gradient increases with an increase in the cell temperature. This causes an nonuniform number density distribution based on the saturated vapor pressure curve. We present a laser absorption spectroscopy method by using the high-resolution beam profiling camera to record the power of the beam before and after the cell. An optimized optical system of the atomic magnetometer has been established by measuring the the number density variation in the spatial distribution in mm scale. The number density variation coefficient, which is introduced to evaluate the distribution homogeneity, increases from 0.0257 to 0.0333 when the temperature of the oven wall rises from 140°C to 190 °C, showing the same trend as the simulation results. The optical rotation distribution is calculated according to the magnetometer output signal formula. This study is of great interest for optimizing the oven structure and improving the stability of atomic spin polarization and sensitivity of the multichannel magnetometer.

New equations of state describing both the dynamic viscosity and self-diffusion coefficient for potassium and thallium in their fluid phases

Experimental data on the viscosity and self-diffusion coefficient of two metallic compounds in their fluid phases, that is, potassium and thallium, are modeled using the translational elastic mode theory, which has been successfully applied to the case of water. It is shown that this theory allows the experimental data to be accounted for in accordance with their uncertainties and, above all, it allows the different variations observed between the different authors to be explained. Particularly in the case of thallium, this theory makes it possible to represent viscosity data with much better precision than the so-called reference equation of state. The dilute-gas limit laws connecting various parameters of the theory obtained in the case of water are confirmed here and thus give them a universal character. The elastic mode theory is accompanied by the development of new equations of state, mainly to describe properties along the saturated vapor pressure curve, which greatly extend the temperature range of application of these equations compared to those found in the literature. The whole analysis thus makes it possible to propose precise values of various thermodynamic parameters at the melting and boiling temperature corresponding to atmospheric pressure.

Study on environmentally friendly refrigerant R13I1/R152a as an alternative for R134a in automotive air conditioning system

Abstract Aiming at solving the problem of high global warming potential of R134a, a new mixed refrigerant R13I1/R152a (molar fraction ratio of 35:65) with no ozone depletion potential and low global warming potential was proposed as a substitute for R134a in automotive air conditioning. The computational models for the thermodynamic properties of R13I1/R152a were established by using the PR equation of state combined with the vdW mixing rule. Based on these models, the cycle performance of this working fluid was calculated, which was also compared with that of R134a and R1234yf under the different operating conditions. The results show that R13I1/R152a is a near azeotropic refrigerant whose temperature glide is approximately 0, and the saturated vapor pressure curve of which is equivalent to that of R134a. Moreover, compared to R134a, R13I1/R152a has an average 5.7% improvement in coefficient of performance as well as similar volumetric cooling capacity. The average coefficient of performance and volumetric cooling capacity of R13I1/R152a are significantly higher than those of R1234yf by 13.8% and 12.0%, respectively. However, the average discharge temperature of R13I1/R152a is approximately 13.3 K higher than that of R134a, but it is also within reasonable limits. Hence, the application of the proposed refrigerant R13I1/R152a in automotive air conditioning system is technically feasible.

Uncertainty assessment of potential evapotranspiration in arid areas, as estimated by the Penman-Monteith method

The Penman-Monteith (PM) method is the most widely used technique to estimate potential worldwide evapotranspiration. However, current research shows that there may be significant errors in the application of this method in arid areas, although questions remain as to the degree of this estimation error and how different surface conditions may affect the estimation error. To address these issues, we evaluated the uncertainty of the PM method under different underlying conditions in an arid area of Northwest China by analyzing data from 84 meteorological stations and various Moderate Resolution Imaging Spectroradiometer (MODIS) products, including land surface temperature and surface albedo. First, we found that when the PM method used air temperature to calculate the slope of the saturation vapor pressure curve, it significantly overestimated the potential evapotranspiration; the mean annual and July-August overestimation was 83.9 and 36.7 mm, respectively. Second, the PM method usually set the surface albedo to a fixed value, which led to the potential evapotranspiration being underestimated; the mean annual underestimation was 27.5 mm, while the overestimation for July to August was 5.3 mm. Third, the PM method significantly overestimated the potential evapotranspiration in the arid area. This difference in estimation was closely related to the underlying surface conditions. For the entire arid zone, the PM method overestimated the potential evapotranspiration by 33.7 mm per year, with an overestimation of 29.0 mm from July to August. The most significant overestimation was evident in the mountainous and plain nonvegetation areas, in which the annual mean overestimation reached 5% and 10%, respectively; during July, there was an estimation of 10% and 20%, respectively. Although the annual evapotranspiration of the plains with better vegetation coverage was slightly underestimated, overestimation still occurred in July and August, with a mean overestimation of approximately 5%. In order to estimate potential evapotranspiration in the arid zone, it is important that we identify a reasonable parameter with which to calibrate the PM formula, such as the slope of the saturation vapor pressure curve, and the surface albedo. We recommend that some parameters must be corrected when using PM in order to estimate potential evapotranspiration in arid regions.

In situ determination of alkali metal density using phase-frequency analysis on atomic magnetometers

The alkali number density inside the sealed vapor cell restricts the fundamental sensitivity of the atomic magnetometer and may decrease in the long term, thus motivating the investigation of an in situ density determination method on atomic magnetometers. This paper presents a method to measure the alkali number density, which is proportional to the spin-exchange relaxation rate, through phase-frequency analysis. The magnetic resonance response of the atomic magnetometer was actively strengthened at low polarization by increasing the oscillating field amplitude. To downplay the side effect of the transverse field broadening, phase-frequency analysis was applied to extract the transverse relaxation time limited by spin-exchange collisions. The experimental results coincided well with the saturated vapor pressure curve ranging from 413 K to 463 K. Calculated densities were approximately 0.779–0.992 times those of predictions. The density measurement accuracy was improved compared to traditional methods.

On-site monitoring of atomic density number for an all-optical atomic magnetometer based on atomic spin exchange relaxation.

We present a method for monitoring the atomic density number on site based on atomic spin exchange relaxation. When the spin polarization P ≪ 1, the atomic density numbers could be estimated by measuring magnetic resonance linewidth in an applied DC magnetic field by using an all-optical atomic magnetometer. The density measurement results showed that the experimental results the theoretical predictions had a good consistency in the investigated temperature range from 413 K to 463 K, while, the experimental results were approximately 1.5 ∼ 2 times less than the theoretical predictions estimated from the saturated vapor pressure curve. These deviations were mainly induced by the radiative heat transfer efficiency, which inevitably leaded to a lower temperature in cell than the setting temperature.

Evaluating the complementary relationship of evapotranspiration in the alpine steppe of the Tibetan Plateau

AbstractThe complementary relationship (CR) of evapotranspiration allows the estimation of the actual evapotranspiration rate (ETa) of the land surface using only routine meteorological data, which is of great importance in the Tibetan Plateau (TP) due to its sparse observation network. With the highest in situ automatic climate observation system in a typical semiarid alpine steppe region of the TP, the wind function of Penman was replaced by one based on the Monin‐Obukhov Similarity theory for calculating the potential evapotranspiration rate (ETp); the Priestley‐Taylor coefficient, α, was estimated using observations in wet days; and the slope of the saturation vapor pressure curve was evaluated at an estimate of the wet surface temperature, provided the latter was smaller than the actual air temperature. A symmetric CR was obtained between the observed daily actual and potential evapotranspiration. Local calibration of the parameter value (in this order) is key to obtaining a symmetric CR: α, wet environment air temperature (Twea), and wind function. Also, present symmetric CR contradicts previous research that used default parameter values for claiming an asymmetric CR in arid and semiarid regions of the TP. The effectiveness of estimating the daily ETa via symmetric CR was greatly improved when local calibrations were implemented. At the same time, an asymmetric CR was found between the observed daily ETa and pan evaporation rates (Epan), both for D20 aboveground and E601B sunken pans. The daily ETa could also be estimated by coupling the Epan of D20 aboveground and/or E601B sunken pan through CR. The former provided good descriptors for observed ETa, while the latter still tended to overestimate it to some extent.

Experimental characterization of CVOC removal from fractured clay during boiling

A series of experiments was conducted to evaluate the mass transport of a chlorinated volatile organic compound (CVOC) at boiling temperatures in low permeability clays where 20–100% of the pore water was removed. A kaolin clay matrix saturated with water containing 1,2-dichloroethane (DCA) and bromide (Br−) was packed into two columnar cells, a rigid-wall and a flexible-wall tube, which created different external boundary conditions. Both cells were heated to boiling temperatures and the recovered outflow was condensed and analyzed for DCA and bromide, and the clay remaining in the cell was cooled and analyzed for water and DCA content. Clay in the vertically oriented rigid-wall cell was heated to 130°C with a power density of ∼80kW/m3 and then depressurized at its upper end. DCA was nearly completely removed in approximately 15min after 0.3 of pore volume water was recovered. The recovered condensate was enriched to more than 10 times the DCA concentration of the pore water. The flexible-wall cells were heated to 110°C with a lower power density of ∼44kW/m3. These tests resulted in slower recovery rates, and condensate concentrations that were approximately twice the pore concentration of DCA. The concentration of DCA in the clay was reduced by two orders of magnitude after approximately 0.5 of the pore volume was removed. Boiling was inferred to occur within the clay matrix because (a) DCA concentrations were enriched; (b) pressure and temperature conditions in the clay intersected the saturated vapor pressure curve; (c) Br− was absent from all but the initial outflow; (d) change in DCA and water content was roughly uniformly distributed over the length of the cell. Fractures appeared to have formed during heating, increasing the permeability, dropping the internal pressure and enabling stripping of DCA during boiling.

Experimental method for characterizing CVOC removal from fractured clays during boiling

Conventional remediation methods that rely on contact with contaminants can be ineffective in fractured media, but thermal methods of remediation involving CVOC stripping at boiling temperature show promise. However, limited experimental data are available to characterize thermal remediation because of challenges associated with high temperature. This research reports an experimental method using uniformly contaminated clay packed into two types of experimental cells, a rigid-wall stainless steel tube and a flexible-wall Teflon tube in a pressurized chamber. Both tubes are 5 cm in diameter and approximately 25 cm long. This laboratory apparatus was developed as a 1D physical model for contaminant transport in a cylindrical matrix towards a fracture, which is represented by one end of the cylinder and serves as the outlet of vapor and contaminant. The clay was contaminated with dissolved 1,2-dichloroethane (DCA) and bromide, and the columns were heated to more than 100 °C and then the top end was depressurized to atmospheric pressure to induce boiling. The outflow was condensed and analyzed for contaminant mass. The flexible-wall cell was confined to 100 kPa (gage), allowing equilibrium boiling temperatures of approximately 120 °C to be maintained. The clay was sampled before and after heating and extracted to determine the DCA distribution along the length of the column. During a typical test in the rigid-wall cell, internal temperatures and pressures along the column during heating reached the saturated vapor pressure curve. DCA concentrations in the recovered condensate were up to 12 times of the initial pore concentration in the clay. Less than 5% of non-volatile bromide was recovered. Significant removal of DCA and water occurred along the entire length of the clay column. This suggests that boiling was occurring in the clay matrix.

A study of the quantitative relation between the radial distribution function and saturated vapor pressure curve in the series of n-alkanes on the basis of a modified linear dynamic model

A new approach to the determination of the quantitative relations between the structure and properties of molecules on the basis of a modified linear dynamic model is suggested. The dependence between the radial distribution function and saturated vapor pressure curve in the series of n-alkanes was studied. It was found that the suggested model could be used not only to reveal correlation dependences between the structure and activity of molecules but also to obtain information about the three-dimensional structure of molecules with the required properties.

The hydrothermal decomposition of calcium monosulfoaluminate 14-hydrate to katoite hydrogarnet and β-anhydrite: An in-situ synchrotron X-ray diffraction study

We apply in-situ synchrotron X-ray diffraction to study the transformation of calcium monosulfoaluminate 14-hydrate Ca 4Al 2O 6(SO 4)·14H 2O [monosulfate-14] to hydrogarnet Ca 3Al 2(OH) 12 on the saturated water vapor pressure curve up to 250 °C. We use an aqueous slurry of synthetic ettringite Ca 6Al 2(SO 4) 3(OH) 12·26H 2O as the starting material; on heating, this decomposes at about 115 °C to form monosulfate-14 and bassanite CaSO 4·0.5H 2O. Above 170 °C monosulfate-14 diffraction peaks slowly diminish in intensity, perhaps as a result of loss of crystallinity and the formation of an X-ray amorphous meta-monosulfate. Hydrogarnet nucleates only at temperatures above 210 °C. Bassanite transforms to β-anhydrite (insoluble anhydrite) at about 230 °C and this transformation is accompanied by a second burst of hydrogarnet growth. The transformation pathway is more complex than previously thought. The mapping of the transformation pathway shows the value of rapid in-situ time-resolved synchrotron diffraction.

Modeling the phase behavior of ternary systems ionic liquid + organic + CO2 with a Group Contribution Equation of State

AbstractThis work presents the results of the use of a Group Contribution Equation of State (GC‐EOS) to model experimental data obtained for ternary systems of the type bmim[BF4] + organic solute + CO2 with four different organic compounds, namely acetophenone, 1‐phenylethanol, 4‐isobutylacetophenone, and 1‐(4‐isobutylphenyl)‐ethanol. Our results show that the GC‐EOS is able to qualitatively predict not only L+V→L but also L1+L2→L phase transitions. As the two two‐phase boundaries L+V and L1+L2 of the experimentally found three‐phase region L1+L2+V almost coincide with the saturated vapor pressure curve of pure CO2, the phase transitions L+V→L1+L2+V and L1+L2+V→L1+L2 have been represented as this vapor‐pressure curve by the model. The average absolute deviations between experimental and predicted values for all phase transitions have been found to be very satisfactory. © 2009 American Institute of Chemical Engineers AIChE J, 2009

New findings about the complementary relationship-based evaporation estimation methods

Summary A novel approach has been found to estimate the equilibrium surface temperature (Te) of wet environment evaporation (Ew) on a daily basis. Employing this temperature in the Priestley–Taylor equation as well as in the calculation of the slope of the saturation vapor pressure curve with pan measurements improved the accuracy of long-term mean evaporation (E) estimation of the Advection–Aridity (AA) model when validated by Morton’s approach. Complementarity of the potential evaporation (Ep) and E terms was considered both on a daily and a monthly basis with the involved terms always calculated daily from 30 yr of hourly meteorological measurements of the 1961–1990 period at 210 SAMSON stations across the contiguous US. The followings were found: (a) only the original Rome wind function of Penman yields a truly symmetric Complementary Relationship between E and Ep which makes the so-obtained Ep estimates true potential evaporation values; (b) the symmetric version of the modified AA model requires no additional parameters to be optimized; (c) for a long-term mean value of evaporation the modified AA model becomes on a par with Morton’s approach not only in practical applicability but also in its improved accuracy, especially in arid environments with possible strong convection; (d) the latter two models yielded long-term mean annual evaporation estimates with an R2 of 0.95 for the 210 stations, which is all the more remarkable since they employ very different approaches for their Ep calculations; (e) with identical apparent Ep values the two models yielded practically identical long-term mean annual evaporation rates; (f) with the proper choice of the wind function to estimate apparent Ep the long-term mean annual E estimates of the modified AA model are still very close (R2 = 0.93) to those of the Morton approach.

Cavitation in Liquid Helium Observed in a Flow Due to a Vibrating Quartz Fork

A quartz fork vibrating at high amplitude is used to study cavitation in He I and He II along the saturated vapor pressure (SVP) curve and at slightly elevated pressures. Cavitation is observed as a breakdown of the resonance response at critical velocity when slowly sweeping the frequency of the drive across the resonance and confirmed by visual observation of a bubble occurring in He II in the space between the prongs of the fork. On decreasing the temperature from 4.2 K along the SVP curve the critical velocity slowly increases from about 0.4 m/s to 1 m/s, until a steep increase up to about 2 m/s occurs within about 20 mK just below the superfluid transition. We discuss our results, including the measured dependence of the critical velocity versus overpressure at fixed bath temperature.

The Role of Relative Humidity in Radiative–Convective Equilibrium

AbstractThe following conditions are derived for the existence of a radiation limit of tropospheric origin in a nongray atmosphere, extending the work on a gray atmosphere by Nakajima et al.: 1) the atmosphere must become sufficiently optically thick, and 2) the temperature must become only a function of optical depth at each frequency, independent of surface temperature. The first condition is satisfied at high temperatures even in a window region as long as there is weak but nonzero absorption, because the optical depth of the entire atmosphere roughly scales as saturation vapor pressure. At high temperatures, the pseudoadiabatic temperature structure asymptotes to the saturation vapor pressure curve, satisfying the second condition at each frequency. A rapidly decreasing vertical gradient of water vapor mixing ratio allows temperature to asymptote faster in optical depth coordinates than in pressure coordinates.Analyses using a radiative–convective model show that interactive relative humidity can give rise to a different kind of runaway greenhouse effect and multiple equilibria, if the strength of relative humidity feedback exceeds a critical value. The results suggest that this mechanism may be able to explain the runaway greenhouse effect found by Rennó et al. and radiative–convective multiple equilibria by Rennó. The framework employed in this study will serve as a diagnostic tool for further research on the runaway greenhouse effect and radiative–convective multiple equilibria.

A physical model for the interdigitated fuel drivability index sensor

An on-board drivability index (DI) sensor has been invented at Delphi Corporation. It is anticipated that the sensor could be used to reduce exhaust emission and improve engine performance during cold starts. During a DI measurement, the initial amount of fuel captured in the sensor declines as the sensor temperature is raised by built-in heating elements. A volatilization curve, a plot of the fuel level versus the sensor temperature, is thus obtained and the DI of the test fuel can be estimated. In this work, a model is proposed that simulates the curves obtained from the DI sensor measurement. This model assumes that the saturated vapor pressure curve for the test fuel determines the shape of its volatilization curve. The model suggests that mass transfer of fuel constituents to the liquid–air interface could be a rate-determining factor for the volatilization process.

Hydrothermal formation of the calcium silicate hydrates, tobermorite (Ca 5Si 6O 16(OH) 2·4H 2O) and xonotlite (Ca 6Si 6O 17(OH) 2): an in situ synchrotron study

In situ energy-dispersive X-ray diffraction (XRD) techniques have been employed to study the hydrothermal formation of crystalline tobermorite and xonotlite. Alkoxide gels of tobermorite composition with varying aluminium contents (Al/(Al+Si)=0 to 0.15) were reacted with a saturated calcium hydroxide solution at temperatures varying from 190°C to 310°C on the saturated vapour pressure curve. Reaction products consisted of tobermorite, xonotlite or a mixture of both. Tobermorite is stabilised by increasing aluminium content and decreasing temperature, whereas xonotlite forms at higher temperature and lower aluminium contents. Reaction times ranged from 3 to 5 h, with the first Bragg peaks forming within the first 10 min. The formation mechanism involves a two-stage process. Firstly, a poorly crystalline C–S–H gel phase forms, which has good periodicity parallel to the ab plane but is poorly ordered parallel to the c direction. The second stage involves the ordering of the C–S–H gel along the (001) direction to form ordered crystalline tobermorite or xonotlite. Kinetic analysis indicates that the reaction rate is increased with increasing aluminium content and increasing temperature. Activation energies for these reactions at different aluminium contents were calculated from two datasets; firstly, from the change in 2 θ position of the tobermorite(220)/xonotlite(320) peak during the reaction (19–30 kJ/mol) and secondly, from the rate at which the background hump intensity decreases for each experiment (26–33 kJ/mol).