EP2542504A1

EP2542504A1 - Device and method for determining the degree of disinfection of a liquid

Info

Publication number: EP2542504A1
Application number: EP11710399A
Authority: EP
Inventors: Martin Wesian
Original assignee: Wesian Martin
Current assignee: Helioz Research & Development GmbH
Priority date: 2010-03-01
Filing date: 2011-02-17
Publication date: 2013-01-09
Also published as: US20150253184A1; WO2011106808A1; US9012861B2; US20120318997A1; AT509363B1; AT509363A1; US9383257B2

Abstract

The invention relates to a device (1) and also a method for determining the degree of disinfection, and for determining the time point (to) when a defined degree of disinfection is reached by a liquid, in particular drinking water, that is situated in a container (100) which is light-permeable at least in a UV range. The device (1) comprises in this case a UV measuring appliance (2) for measuring the intensity of the UV radiation in the region of the container (100), a data analysis unit (3) to which the values of the UV intensity which are measured by the UV measuring device (2) are fed, and wherein the data analysis unit (3) converts the UV intensity values measured at the start of a measurement at defined time points (t) to form a characteristic (K), and wherein the data analysis unit (3) compares the characteristics (K) determined at defined time points (t) with a predetermined characteristic (Ko), which predetermined characteristic (Ko) corresponds to a defined degree of disinfection of the liquid, and wherein the device (1) comprises at least one signal output appliance (4) which, in the event that the determined characteristic (K) reaches or exceeds the value of the predetermined characteristic (Ko), provides a signal output.

Description

DEVICE AND METHOD FOR DETERMINING THE DISINFECTION GRADE OF ONE

LIQUID

The invention relates to a device for determining the degree of disinfection of a liquid present in a vessel which is transparent at least in a UV region, in particular of drinking water.

Furthermore, the invention relates to a method for determining the degree of disinfection of a liquid present in a vessel which is permeable to light, at least in a UV region, in particular drinking water.

9,000 children and many adults die every day due to the consumption of contaminated water. More than half of all hospital beds in the affected areas are occupied by people suffering from diseases caused by germ-laden water. Every year natural disasters cause organizations such as the "UN" or "Doctors Without Borders" to invest millions of euros in the short-term drinking water supply of the affected countries. In addition to human suffering, the economic damage and the disadvantages for the entire health system are enormous. The "United Nations" have recognized the problem and therefore proclaimed the "Millennium Development Goals", whereby all member states undertook to provide a sufficient supply of drinking water to half of the world's drinking water-deficient population by 2015. This means that each year 125 million people have to be supplied with water on a long-term and sustainable basis, for which the states of the "UN" provide $ 11.3 billion a year. In order to make good use of these funds, the UN and the implementing organizations and states are looking for solutions in the field of drinking water disinfection that are inexpensive and easy to use.

Established is the "Solar Drinking Water Disinfection" (SODIS), which was developed by the ETH Zurich and referred to by the "WHO" and the "UN" as the "most efficient and cost-effective drinking water disinfection". SODIS can refer to already 3 million users internationally, but has disadvantages in the application and the acceptance. Currently, solar direct drinking water disinfection is given a guideline value of 6 hours in direct sunlight and 12-18 hours in partial cloud cover. Of course, this information depends on various factors, such as the position of the sun, the degree of cloud cover, temperature, shadows, wind and precipitation, which make it difficult to estimate the necessary irradiation time and trust in the actual disinfection. Due to the lack of control of the method, the water often does not last long exposed enough to the sun, whereby no complete sterilization takes place. This in turn results in the disease of the users of dysentery, cholera, typhoid, etc.

It is an object of the invention to provide a reliable and easy-to-use way to detect the disinfection of a liquid, especially drinking water.

This object is achieved with a device mentioned in the introduction, which comprises:

a UV measuring device for measuring the intensity of the UV radiation, in particular the UV radiation of the sunlight, in the region of the vessel,

an evaluation unit to which the UV intensity values measured by the UV measuring device are supplied, and wherein

the evaluation unit calculates the measured values for the UV intensity at certain points in time from the beginning of a measurement to form a parameter,

- And wherein the evaluation unit compares the determined at certain times characteristics with a predetermined characteristic, which predetermined characteristic corresponds to a defined degree of disinfection of the liquid, and wherein

- The device comprises at least one signal output device, which outputs a signal in the event that the determined characteristic value reaches or exceeds the value of the predetermined characteristic.

Furthermore, the above object is achieved by a method mentioned, which comprises the following steps:

Measuring the intensity of UV radiation in the region of the vessel,

calculate the values for the UV intensity measured from the beginning of a measurement at certain times to a parameter,

Comparing the parameters determined at specific times with a predetermined parameter, which predetermined parameter corresponds to a defined degree of disinfection of the fluid, and - Outputting a signal in the event that the determined characteristic value reaches or exceeds the value of the predetermined characteristic.

A commercial PET bottle is filled with the contaminated water and then placed in the sun. The UV radiation of the sun kills germs in the water. Depending on sunshine and / or clouds, the water is disinfected after about 1-3 days. Although this method, known as SODIS, is already being used by 3 million people worldwide, some problems of further dissemination are in the way. Among other things, the high training costs can be mentioned, which can not be met for the large number of people affected, especially since these training courses must be repeated regularly.

Furthermore, there is a lack of acceptance of the method, as it seems too simple and the time when the water is really disinfected, is not clearly regulated.

The present invention offers a solution in the form of a low-cost and self-sufficient technical device that measures the optimum UV irradiation time and indicates to users when the solar water disinfection cycle is completed. The device can be produced very cheaply and enable a family to independently obtain safe drinking water for years.

It is particularly advantageous if the device further comprises a temperature measuring device for determining the temperature of the liquid in the vessel.

The determined temperature of the liquid in the vessel can then be taken into account in the determination of the parameter.

The temperature factor can be an important part of accelerating the disinfection. At temperatures above 40 ° C pathogens are already killed by the temperature alone. The temperature disinfection is independent of the UV radiation, but in combination a guarantee for an optimal disinfection.

Technically, a sufficient temperature can be achieved by a dark or reflective surface on which the water-filled PET bottles are stored for disinfection. A temperature measurement is meaningful or expedient only if (sufficient) liquid is present, namely at least enough liquid that the temperature measuring device also contacts the liquid. Therefore, it is expedient if the temperature measuring device is adapted to detect the presence of liquid, and that the temperature is measured only in the presence of liquid.

Otherwise, if the temperature measuring device does not contact the liquid, the temperature of the air in the vessel would be measured, which may be lower. may be significantly higher than the temperature of the liquid. This would lead to a falsified result and in particular to an early indication of the desired disinfection time.

In a specific embodiment of the invention, it is provided that the UV measuring device comprises at least one UV sensor.

For supplying energy to the electrical components of the device, it may be provided that the device has one or more solar cells.

The power supply can also be effected by means of a battery or preferably with a rechargeable battery, wherein the charging of the rechargeable battery can then take place by means of the solar cells.

In a variant of the invention, the UV measuring device comprises one or more solar cells. The solar cell (s) is preceded by a filter which passes through light only in the UV range, in particular only in the UV-A range or in the preferred measurement spectrum. The current supplied by the solar cells can then be used to deduce the UV intensity.

The use of solar cells can be a significantly cheaper solution than those with its own UV sensor. However, in principle it is also conceivable to combine UV sensor and solar cells for the UV measuring device.

In order to determine the parameter K (t), the values for the UV intensity measured per unit time At are summed over the time t or the values of the UV intensity measured as a function of the time t are integrated over the time. It is thus practically the dose of UV radiation (eg in Ws / m ² ) measured and continuously compared with a limit Ko, which limit defines a degree of disinfection at which the liquid (water) is drinkable. In order to optimally take into account the synergy effects of the UV radiation and the prevailing temperature of the liquid for the disinfection or the determination of the time of a particular degree of disinfection, the values of the UV intensity measured before the time unit Δt or as a function of the time t become the UV intensity before the summation or integration with the temperature T (At) measured per unit time At or the temperature T (t) measured as a function of the time t.

In this case, the temperature can actually be measured and taken into account at any point in time t or each time unit Δt at which the UV intensity is measured. However, the measurement of the temperature can also take place at relatively long intervals, since these generally do not vary as much as the UV intensity.

In an easy-to-implement variant of the invention, the evaluation unit comprises a counter or a counter whose count per unit time At by a counter value which is proportional to the measured in this time unit At value for the UV intensity increases, and that the given characteristic value corresponds to a specific value for the meter reading.

If the temperature is taken into account in this variant, the counter value is multiplied by a temperature-dependent proportionality factor, which proportionality factor for a minimum temperature and temperature values below the minimum temperature takes the value 1, and for temperature values above the minimum temperature, a value dependent on the temperature greater than 1 assumes.

In order to be able to arrange the device reliably in the vicinity of or on the vessel, a variant of the device is provided in that it has fastening means for releasably securing the device to the vessel.

The attachment means are e.g. designed in the form of a screw, with which the device can be screwed over the opening of the vessel to this.

Furthermore, it is still advantageous if the device comprises eyelets for fastening the device in the environment and / or on the vessel. In this way, a reliable loss and theft protection is given. Finally, for reasons already described above, it is still expedient if the temperature measuring device is arranged on the device in such a way that the temperature measuring device projects at least partially into the liquid present in the vessel when the device is attached to the vessel.

Advantageously, the temperature measuring device comprises at least one TC element (NTC resistor, "negative temperature coefficient"), which is cheap, robust, and easy to use and with which the temperature can be measured in a known manner via the measurement of the resistance.

In the following the invention is explained in more detail with reference to the drawing. In this shows

1 is a first simple variant of the device according to the invention without temperature measurement in a schematic representations,

2 shows a second variant of the device according to the invention with temperature measurement in a schematic representation,

3a shows a device according to the invention according to FIG. 1 in a schematic, perspective representation before being fastened to a vessel filled with liquid, FIG.

3b shows a device according to the invention according to FIG. 2 in a schematic, perspective view before being fastened to a vessel filled with liquid, FIG.

4a shows the relationship between the decrease in the number of bacteria in a liquid as a function of time and at different UV intensities and temperatures,

Fig. 4b shows the course of the germ reduction as a function of time at constant UV intensity and changing temperatures, and

FIGS. 5a-5c show the course of the parameter K (t) as a function of time for different temperature scenarios.

FIG. 1 shows a device 1 for determining the degree of disinfection (or the time of reaching a certain degree of disinfection) of a liquid, in particular drinking water, contained in a vessel 100 (FIG. 3a) which is transparent at least in a UV region. The vessel 100 is, for example, conventional PET bottles. The device comprises a UV measuring device 2 for measuring the intensity of the UV radiation in the region of the vessel 100 and an evaluation unit 3 to which the values for the UV intensity measured by the UV measuring device 2 are supplied. The evaluation unit 3 calculates the measured values for the UV intensity measured at the beginning of a measurement at a given time t to a parameter K, and compares the parameters K determined at certain times t with a predetermined characteristic K0, which predefined parameter Ko a defined disinfection level Liquid corresponds. If the desired degree of disinfection, which corresponds to the parameter Ko, is reached, then the device 1 emits signals via a signal output device 4, which signal the successful disinfection.

The signal output device 4 may be of an acoustic nature or of an optical nature, e.g. a flashing or lit LED, or a display that shows the relevant information. Of course, a combination on one or more of these display means is possible.

To supply the individual electronic components, a power supply unit 10 is provided, e.g. a battery or a rechargeable battery or one or more solar cells 7 for generating electricity. Preferably, a battery 10 is charged by the solar cells 7.

In order to reliably locate the device 1 on the vessel 100, the variant of the device shown has attachment means 9 for releasably securing the device to the vessel 100, these attachment means e.g. in the form of a screw 9 are formed as shown, with which the device over the opening of the vessel 100, for example, can be screwed to a bottleneck of this.

Furthermore, it is still favorable if the device comprises eyelets 11 for fastening the device in the environment and / or on the vessel. In this way, a reliable loss and theft protection is given.

Furthermore, FIG. 3 a shows a push-button 6 for switching the device 1 on and off or for starting / stopping a measurement,

FIG. 2 and FIG. 3 b show a further variant of the device 1 which has an essentially identical structure to the device of FIG. 1 and FIG. 3 a and further comprises a temperature measuring device 5 for determining the temperature T of the liquid in the vessel 100. The determined temperature T of the liquid in the vessel 100 can then be taken into account in determining the parameter K.

The influence of the temperature on the germ reduction is shown in FIG. 4a. The line labeled "UV" shows the germ reduction as a function of time t, assuming a temperature which does not significantly contribute to the germ reduction, as indicated by "UV + Tl", "UV + T2" and "UV + T3" Curves represent the germ reduction as a function of time with the same UV intensity, but with increasing temperature. As can be seen, the time duration for the germ reduction at a high temperature (assumption: T3> 45 ° C) significantly reduces compared to the other temperatures and in particular in the case without (for disinfection) significant temperature.

Technically, a sufficient temperature can be achieved by a dark or reflective surface on which the water-filled PET bottles are stored for disinfection.

A temperature measurement is meaningful or expedient only if (sufficient) liquid is present, namely at least enough liquid that the temperature measuring device also contacts the liquid. Therefore, it is expedient if the temperature measuring device 5 is adapted to detect the presence of liquid, and that the temperature is measured only in the presence of liquid.

In a specific embodiment of the invention, it is provided that the UV measuring device 2 comprises at least one UV sensor. In a variant of the invention, the UV measuring device 2 comprises one or more solar cells. The solar cell (s) is preceded by a filter which transmits light only in the UV range, in particular only in the UV-A range or in the preferred measurement spectrum. The current supplied by the solar cells can then be used to deduce the UV intensity.

The use of solar cells can be a significantly cheaper solution than those with its own UV sensor. In principle, however, a combination of UV sensor 2 and solar cells 7, as shown in FIG. 3 a, is also conceivable for the UV measuring device 2.

In order to determine the parameter K (t), the values for the UV intensity measured per unit time (At) are summed over the time (t) or the values of the UV intensity measured as a function of the time (t) are integrated over time. Thus, practically the dose of UV radiation (eg in Ws / m ² ) is determined as a function of time and continuously compared with a limit value Ko (for the dose), which limit defines a degree of disinfection at which the liquid (water) is drinkable is.

Fig. 5a shows schematically a corresponding process, wherein a constant UV intensity is assumed and the influence of the temperature is not taken into account. After a time t = to, the parameter K reaches the value Ko, K (t0) = Ko, which is the time at which the desired degree of disinfection is achieved and a signal is output from the device, which gives the user the successful disinfection signaled.

In order to optimally take into account the synergy effects of the UV radiation and the prevailing temperature of the liquid for the disinfection or the determination of the time of a certain degree of disinfection, the values of the UV intensity measured per unit time Δt or as a function of the time t are preferably Summation or integration with the temperature T (At) measured per unit time At or the temperature T (t) measured as a function of the time t.

FIG. 5b shows three different measurements at three different temperatures, with T1 <T2 <T3. As can be seen, with increasing temperature (with the same UV intensity), the curve (straight line) K (t) increases steeply in accordance with a larger gradient and the value to for the disinfection is reached more quickly at a higher temperature. In the cases shown in FIG. 5b, where the temperature is taken into account, but the temperature is assumed to be constant over the entire measurement, the weighting of the values for the UV intensity can also be realized by setting the value Ko by a value Ko * is replaced, which takes the temperature into account. At T3, the value Ko * (T3) would be correspondingly lower than that for eg Ko * (T2) or Ko * (Tl) and, of course, less than Ko.

In realistic measurements, however, the temperature varies, as is still shown in Figure 5c.

In an easy-to-implement variant of the invention, the evaluation unit 3 comprises a counter or a counter whose count per unit time At by a counter value which is proportional to the measured in this time unit At value for the UV intensity increases, and that the predetermined characteristic Ko corresponds to a specific value for the counter reading.

If the temperature is taken into account in this variant, then the counter value is multiplied by a proportionality factor kT dependent on the temperature T, which proportionality factor for a minimum temperature Tmin and temperature values below the minimum temperature Tmin assumes 1, and for temperature values above the minimum temperature Tmin one of the Temperature dependent value greater than 1 assumes.

In a simple reliable variant, e.g. kT = 1 for T> 35 ° Celsius, kT = 1.1 in the range of 35 ° - 40 °, kT = 1,2 for 40 ° - 45 °, and for T> 45 ° kT = 1,3 ,

It should be noted, however, that the numerical values and graphs given here are only to be regarded as exemplary and, of course, can also be adapted accordingly to the situation or newer research results in the field.

The temperature measuring device 5 is arranged on the device 1 in such a way that, when the device 1 is attached to the vessel 100, the temperature measuring device 5 projects at least partially into the liquid present in the vessel 100. Advantageously, the temperature measuring device 5 comprises at least one NTC element (NTC resistor, "negative temperature coefficient"), which is cheap, robust, and easy to use, and with which the temperature is measured in a known manner by measuring the resistance may,

The evaluation unit 3 comprises a microprocessor and memory, which memory may be integrated into the processor. When a measurement is restarted, the memory is checked, and if data from a previous measurement is present, the measured data are read out and recalculated according to internal comparison data. If, for example, a measurement or a disinfection cycle has been aborted before reaching Ko, germs can again accumulate in the liquid. The measurement can therefore not be continued at the last value of K (t) but this enrichment must be taken into account accordingly, since the number of nuclei after a longer interruption of UV radiation increases again and the previous data must therefore be adjusted.

Interruptions of the measurement can arise especially when the energy supply is exclusively via solar cells without intermediate buffering by means of a battery, for example at nightfall.

The device 1 according to the invention thus abstracts and continuously integrates sensor data of the radiation intensity, the irradiated UV dose and the temperature and compares these data with data from scientific studies in order to ensure a suitable germ stage reduction. The synergetic processes of UV-induced killing and thermal inactivation (dose- and time-dependent) with opposing processes by mechanisms of repair of the nuclei are considered. As a result, even under difficult environmental conditions (low light conditions, cloud cover, intermittent rain) it is possible to ensure an optimized disinfection time and a predictable, adequate germ reduction. The characteristic value Ko can be determined correspondingly preferably or among other things from microbiological tests.

Three exemplary microbiological test series are shown below, whereby an artificial UV source was used for solar simulation: The test setup includes, on the one hand, an irradiation unit, the measurement by means of a calibrated UV measuring instrument and the recording by a separate program. At the times indicated in the tables, a sample of the water was taken. Furthermore, in each test, a blank test was attempted with an equal prepared bottle which was not exposed to radiation. Table 1

Table 2

CFU / ml (Kolo¬

Minutes dose Dose forming min. Min. W / m ² J / m ² total units)

0 0 0 0 0 1600000

60 60 3.985 14346.00 14346.00 3600000

105 45 7,071 19091, 70 33437,70 500,000

125 20 10,501 12601, 20 46038,90 22000

140 15 16.601 14940.90 60979.80 12000

155 15 16,691 15021, 90 76001, 70 1360

170 15 10.681 9612.90 85614.60 50

180 10 10,451 6270,60 91885,20 35

200 20 6,975 8370,00 100255,20 0

220 20 6,453 7743,60 107998,80 0

Table 3

CFU / ml (Kolo¬

Minutes dose Dose forming min. Min. W / m ² J / m ² total units)

0 0 0 0 0 1500000

60 60 8,549 30,776.40 30776.40 800000

100 40 13.01 31224.00 62000.40 250000

125 25 22,91 34365,00 96365,40 200000

155 20 16,26 19512,00 115877,40 242500

200 45 5.542 14963.40 130840.80 66000

230 30 12.04 21672.00 152512.80 13500

245 15 10.15 9135.00 161647.80 1953

260 15 10.15 9135.00 170782.80 2315

270 15 843 7688.70 178471, 50 1325

280 10 8,481 5088,60 183560,10 816

295 15 8,545 7690,50 191250,60 1960

305 10 51 50.60 196351, 20 780

315 10 13,74 8244,00 173818,80 700

325 10 13,69 8214,00 182032,80 520

335 10 13.78 8268.00 190300.80 210

345 10 13,67 8202,00 167278,80 0

360 15 13.61 12249.00 145162.80 0

Claims

1. Device (1) for determining the degree of disinfection or for determining the point in time (to) of reaching a certain degree of disinfection of a liquid present in at least one UV-transparent vessel (100), in particular drinking water, wherein the device (1 ) comprises:

a UV measuring device (2) for measuring the intensity of the UV radiation, in particular the UV radiation of the sunlight, in the region of the vessel (100),

- An evaluation unit (3), which are supplied by the UV measuring device (2) measured values for the UV intensity, and wherein

the evaluation unit (3) calculates the measured values for the UV intensity at certain points in time (t) from the beginning of a measurement to a parameter (K),

- And wherein the evaluation unit (3) compares the determined at certain times (t) characteristics (K) with a predetermined characteristic (Ko), which predetermined characteristic (Ko) corresponds to a defined degree of disinfection of the liquid, and wherein

- The device (1) at least one signal output device (4), which in the case that the determined characteristic (K) reaches or exceeds the value of the predetermined characteristic (Ko), outputs a signal.

2. Apparatus according to claim 1, characterized in that it further comprises a temperature measuring device (5) for determining the temperature (T) of the liquid in the vessel (100).

3. A device according to claim 2, characterized in that the temperature measuring device (5) is adapted to detect the presence of liquid, and that the temperature is measured only in the presence of liquid.

4. Device according to one of claims 1 to 3, characterized in that the UV measuring device (2) comprises at least one UV sensor.

5. Device according to one of claims 1 to 4, characterized in that it comprises one or more solar cells (7).

6. Apparatus according to claim 5, characterized in that the UV measuring device (2) comprises one or more solar cells (7).

7. Device according to one of claims 1 to 6, characterized in that the per unit time (At) measured values for the UV intensity over time (t) added up or measured as a function of time (t) values of UV Intensity be integrated over time.

8. The device according to claim 7, characterized in that the per unit time (At) or as a function of time (t) measured values of the UV intensity before the summation or integration with the per unit time (At) measured temperature (T (T) At)) or as a function of time (t) measured temperature (T (t)) are weighted.

9. Apparatus according to claim 7 or 8, characterized in that the evaluation unit (3) comprises a counter or a counter whose count per unit time (At) by a counter value which is proportional to the value measured in this time unit (At) for the UV intensity is increased, and that the predetermined characteristic (Ko) corresponds to a specific value for the meter reading.

10. Apparatus according to claim 8 and 9, characterized in that the counter value is multiplied by a proportional to the temperature (T) proportionality factor (kT), which proportionality factor for a minimum temperature (Tmin) and temperature values below the minimum temperature (Tmin) the value of 1 and assumes a temperature-dependent value greater than 1 for temperature values above the minimum temperature (Tmin).

11. Device according to one of claims 1 to 10, characterized in that it comprises fastening means (9) for releasably securing the device to the vessel (100).

12. Device according to one of claims 2 to 11, characterized in that the temperature measuring device (5) is arranged on the device (1) such that in the vessel (100) fixed state of the device (1), the Temperarurmesseinrichtung (5) protrudes at least partially into the liquid in the vessel (100).

13. Device according to one of claims 2 to 12, characterized in that the temperature measuring device (5) comprises at least one NTC element.

14. A method for determining the degree of disinfection or for determining the point in time (to) of reaching a certain degree of disinfection of a liquid, in particular drinking water, contained in a vessel (100) which is transparent at least in a UV range, comprising the following steps:

Measuring the intensity of the UV radiation in the region of the vessel (100),

calculate the values for the UV intensity measured from the beginning of a measurement at specific times (t) to a parameter (K),

Comparing the characteristic quantities (K) determined at specific times (t) with a predetermined characteristic value (Ko), which predetermined parameter (Ko) corresponds to a defined degree of disinfection of the fluid, and

- Outputting a signal in the event that the determined characteristic (K) reaches or exceeds the value of the predetermined characteristic (Ko).

15. The method according to claim 14, characterized in that further the temperature (T) of the liquid in the vessel (100) and the temperature (T) in the determination of the characteristic (K) is taken into account.

16. The method according to claim 14 or 15, characterized in that the per unit time (At) measured values for the UV intensity over the time (t) added up or measured as a function of time (t) values of the UV intensity over the time to be integrated.

17. The method according to claim 16, characterized in that the per unit time (At) or as a function of time (t) measured values of UV intensity before the summation or integration with the per unit time (At) measured temperature (T (T) At)) or as a function of time (t) measured temperature (T (t)) is weighted.

18. The method according to claim 16 or 17, characterized in that the evaluation unit (3) comprises a counter or a counter whose count per unit time (At) by a counter value which is proportional to the value measured in this time unit (At) for the UV intensity is increased, and that the predetermined characteristic (K0) corresponds to a specific value for the meter reading.

19. The method according to claim 17 and 18, characterized in that the counter value with a temperature (T) dependent proportionality factor (kT) is multiplied, which proportionality factor for a minimum temperature (Tmin) and temperature values below the minimum temperature (Tmin) the value of 1 and for temperature values above the minimum temperature (Tmin) assumes a temperature-dependent value greater than 1.