Abstract: A method for feeding a cored wire into molten metal contained in a vessel comprises positioning the cored wire at a first position wherein a leading tip of the cored wire is proximate an entry point of the vessel, the entry point being above a surface of the molten metal, the cored wire comprising an optical fiber and a cover laterally surrounding the optical fiber; feeding the cored wire at a first speed for a first duration from the first position to a second position wherein the leading tip of the cored wire is immersed within the molten metal and lies within a measuring plane, such that a leading tip of the optical fiber projects from the cover and is exposed to the molten metal; and subsequently feeding the cored wire at a second speed for a second duration to take a first measurement of the molten metal.

Abstract: A device for measuring the temperature of a melt, particularly of a molten metal, includes an optical fiber and a guiding tube having an immersion end and a second end opposite to the immersion end. The optical fiber is partially arranged in the guiding tube. An inner diameter of the guiding tube is larger than an outer diameter of the optical fiber. A first plug is arranged at the immersion end of or within the guiding tube proximate the immersion end of the guiding tube. The optical fiber is fed through the first plug and the first plug reduces a gap between the optical fiber and the guiding tube.

Abstract: System, method and apparatus for measuring electrolysis cell operating conditions and communicating the same are disclosed. The system includes a selectively positionable member coupled to an analytical apparatus, wherein the selectively positionable is configured to move the analytical apparatus into and out of physical communication with a bath. The system may also include a crust breaker for breaking the surface of a bath and an electronic device for measuring bath level.

Abstract: An immersion device for measuring the temperature of a melt with an optical fiber, preferably a metal coated optical fiber, in a metallurgical vessel includes a feeding channel, feeding means for feeding an optical fiber into a disposable guiding tube and for feeding the disposable guiding tube together with the optical fiber into the melt, and control means for monitoring the position of an end of the optical fiber relative to an end of the disposable guiding tube. The relative position determines the quality of a temperature measurement.

Abstract: A device for measuring the temperature of a melt, particularly of a molten metal, includes an optical fiber and a guiding tube having an immersion end and a second end opposite to the immersion end. The optical fiber is partially arranged in the guiding tube. An inner diameter of the guiding tube is larger than an outer diameter of the optical fiber. A first plug is arranged at the immersion end of or within the guiding tube proximate the immersion end of the guiding tube. The optical fiber is fed through the first plug and the first plug reduces a gap between the optical fiber and the guiding tube.

Abstract: A metallurgical probe has a probe longitudinal axis and an open end face. The probe is fitted within a bearing point in such a manner that the open end face faces a predetermined insertion direction. The bearing point has probe centering elements to hold the probe in a predetermined probe position as seen transversely with respect to the probe longitudinal axis. A device inserts an end of the contact rod into a contact rod centering device, in an insertion direction running transversely with respect to the probe longitudinal axis, until the end of the contact rod is positioned, on account of the insertion into the contact rod centering device, in a predetermined contact rod position, in which the end of the contact rod is opposite the open end face. The contact rod is then moved in a direction of the probe longitudinal axis and is inserted into the probe.

Abstract: System, method and apparatus for measuring electrolysis cell operating conditions and communicating the same are disclosed. The system includes a selectively positionable member coupled to an analytical apparatus, wherein the selectively positionable is configured to move the analytical apparatus into and out of physical communication with a bath. The system may also include a crust breaker for breaking the surface of a bath and an electronic device for measuring bath level.

Abstract: A device for measuring the temperature of molten metal irrespective of the nature of the metal, particularly, an immersion/contact type temperature sensing device involving optical fiber which can be universally used for different materials and would be adapted for safe and repetitive immersion in molten metal for measurement of molten metal temperatures and the like. The proposed immersion/contact type temperature sensing device involves combination two-color and multi-color pyrometric detection technique is capable of cost effective and discrete-time temperature measurement of molten metal. The advancement is thus directed to serve as a ready and fast accurate measurement of molten metal temperature and the like.

Abstract: A sensor arrangement is provided for temperature measurement in melts, in particular in metal or cryolite melts having a melting point above 600° C., using a temperature sensor. A method for the measurement with this sensor arrangement is also provided.

Abstract: A method, device and apparatus are provided for measuring the temperature of a melt, particularly of a molten metal, with an optical fiber, fed into the melt through a disposable guiding tube. The optical fiber and an immersion end of the tube are immersed into the melt and have feeding speeds which are independent from each other. An elastic plug is arranged within the tube or at an end of the tube opposite the immersion end. The optical fiber is fed through the elastic plug, and the elastic plug reduces a gap between the optical fiber and the tube, which has a larger inner diameter than the outer diameter of the optical fiber. The apparatus includes a fiber coil and a feeding mechanism for feeding the optical fiber and the tube, including at least two independent feeding motors, one for feeding the optical fiber and one for feeding the tube.

Abstract: A portable temperature sensing probe having a plurality of thermocouples is inserted into a tank mounted on a truck or other receptacle at the time of loading a hot liquid, e.g., molten sulfur. The probe and at least a portion of the associated wiring or leads are attached to the loading pipe and/or discharge nozzle, and the probe is inserted into the interior of the tank before the molten sulfur is discharged. The signals from the plurality of thermocouples are amplified and the corresponding temperature information is transmitted to a display and control device. Due to the significant differential between the temperature of the rising molten sulfur and the vapors in the tank overhead space, the signals generated indicate which of the thermocouple are in contact with molten sulfur or the vapor zone. The generated signals adjust the shut-off valve that controls the flow of molten sulfur into the tank.

Abstract: A measuring device is provided for measurement of parameters, in particular for measuring the temperature, in molten masses, in particular in molten metal or molten cryolite masses having a melting point above 500° C. The measuring device has an optical fiber for receiving radiation from the molten mass and a cable reel having an external circumference for winding up the optical fiber and an internal space surrounded by the external circumference. A distributor and a mode filter for the optical fiber are arranged in the internal space.

Abstract: A device for measuring the temperature in molten metals contains a thermocouple arranged in a ceramic tube that is closed on one side, and has an external protective body that surrounds the tube, forming an annular space between the outer surface of the tube and the inner surface of the protective body. The protective body is formed of a mixture containing 75 to 90% by weight aluminum oxide, 2 to 10% by weight silicon oxide, 7 to 15% by weight graphite, 0.1 to 1% by weight Fe2O3, 0.1 to 1% by weight (K2O+Na2O), and 0.1 to 1% by weight MgO.

Abstract: Disclosed is a container for the thermal analysis of cast iron that enables a reduction in the amount of tellurium used in thermal analysis. By forming a plurality of fine spaces in the interior of a base plate (12) and sidewalls (11), thermal insulating properties are maintained in the base plate (12) and the sidewalls (11) and the temperature of a sample of the cast iron melt placed in the interior of the container (1) is prevented from cooling down. As a result, even if the amount of a sample supplied for thermal analysis is reduced, the speed by which the temperature of the sample drops is suppressed, and a constant temperature is maintained by the heat from the latent heat of solidification. Accordingly, the amount of tellurium used in thermal analysis can be reduced by reducing the amount of the sample supplied for thermal analysis.

Abstract: A measuring device is provided having a protective cover and a sensor arranged in the protective cover. The protective cover has a carrier tube made of metal and closed on one end. A first coating made of an aluminum non-wettable material is arranged on an outer surface of the carrier tube, and a further coating made of aluminum-wettable material is applied on the first coating.

Abstract: A container for molten metal includes an outlet for outflow of the molten metal from the container and a temperature measuring device fixed in a wall of the container. The temperature measuring device includes a plug, an outer protective sheath having a closed end, and an inner protective tube having a closed end. The inner protective tube is arranged within the outer protective sheath. A thermocouple is arranged within the inner protective tube. The plug includes a substantially refractory material and the outer protective sheath consists essentially of substantially refractory metal oxide and graphite. The outer protective sheath extends away from the first end of the plug and projects into a recessed portion of the wall of the container. The closed end of the outer protective sheath is arranged in the recessed portion. A junction of the thermocouple is proximate to the closed end of the inner protective tube.

Abstract: A temperature T of a metal melt in a furnace is precisely determined without contact using at least one burner gun unit fed through a furnace wall of the furnace above the metal melt into a furnace chamber and at least one temperature measuring unit downstream of the burner gun unit.

Abstract: A temperature measurement tube is composite and comprises a rigid shaft (1), which is cooled so as to shield it from corrosion and from the melt, and an end-fitting (15) housing a thermocouple (9) on the end of the tube and constructed from a noble metal, which is resistant to corrosion and to the high melting point. An alumina coating (13) is placed between the two metals in order to prevent any corrosion-inducing electrochemical exchange between them.

Abstract: A portable temperature sensing probe (10) having a plurality of thermocouples (18) is inserted into a tank (16) mounted on a truck or other receptacle at the time of loading a hot liquid, e.g., molten sulfur (14). The probe and at least a portion of the associated wiring or leads are attached to the loading pipe (22) and/or discharge nozzle, and the probe is inserted into the interior of the tank before the molten sulfur (14) is discharged. The signals from the plurality of thermocouples (18) are amplified and the corresponding temperature information is transmitted to a display and control device (30). Due to the significant differential between the temperature of the rising molten sulfur (14) and the vapors in the tank overhead space (26), the signals generated indicate which of the thermocouple (18) are in contact with molten sulfur (14) or the vapor zone (32). The generated signals adjust the shut-off valve (38) that controls the flow of molten sulfur (14) into the tank (16).

Abstract: A temperature measuring device for molten metal includes a porous plug with a first end and an opposed second end, an outer protective sheath with a closed end, an inner protective tube with a closed end, and a thermocouple arranged within an interior of the inner protective tube. The outer protective sheath extends away from the first end of the plug and the inner protective tube is arranged within an interior of the outer protective sheath. The porous plug comprises a substantially refractory material and the outer protective sheath consists essentially of substantially refractory metal oxide and graphite. A junction of the thermocouple is proximate to the closed end of the inner protective tube.

Abstract: A sensor arrangement is provided for temperature measurement in melts, in particular in metal or cryolite melts having a melting point above 600° C., using a temperature sensor. A method for the measurement with this sensor arrangement is also provided.

Abstract: The invention relates to a converter with a container for receiving molten metal and with a measurement device for the optical temperature determination of the molten metal. The converter has an optical waveguide for guiding electromagnetic radiation emitted by the metal to an optical detector for determining the temperature of the metal from an analysis of the electromagnetic radiation. The converter further has a line arranged between the optical detector and the container through which fluid flows for guiding and transporting the optical waveguide. The optical detector is arranged, spaced apart from the container, in a region in which the surrounding temperature is less than 150 DEG C. The invention further relates to a method for the temperature determination of the molten metal in such a converter.

Abstract: A device is provided for temperature measurement in metal melts, particularly in iron or steel melts, having a thermoelement, which is arranged in a thermoelement tube, and having an exterior protective body, which is essentially formed of graphite and metal oxide. The thermoelement tube is arranged in the protective body with a spacing, forming an intermediate space, and an insulating material and an oxygen-reducing material are arranged in the intermediate space. The insulating material and the oxygen-reducing material, as a powder mixture, form a tube (2), which surrounds the thermoelement tube (3) with a spacing and/or which is surrounded by the protective body (1) with a spacing.

Abstract: An apparatus is provided for the determination of at least one parameter of a molten metal or a slag layer lying on top of the molten metal. The apparatus has a carrier tube, a measuring head arranged on one end of the carrier tube with a body fixed in the carrier tube. An A/D converter is arranged within the measuring head or the carrier tube, and the A/D converter is connected to at least one sensor arranged in or on the measuring head. The measuring head has a contact piece, which is electrically connected via its contact terminals to the signal output of the A/D converter, and the contact piece is connected to a lance inserted into the carrier tube. No more than two signal lines are arranged within the lance, the signal lines each being connected at one end via a contact terminal of the contact piece to the A/D converter and at an opposite end to a computer or an analysis device.

Abstract: A measuring device is provided having a protective cover and a sensor arranged in the protective cover. The protective cover has a carrier tube made of metal and closed on one end. A first coating made of an aluminum non-wettable material is arranged on an outer surface of the carrier tube, and a further coating made of aluminum-wettable material is applied on the first coating.

Abstract: A method is provided for measuring a parameter of a molten metal bath by an optical fiber surrounded by a cover. The optical fiber is immersed in the molten bath, and the radiation absorbed by the optical fiber in the molten bath is fed to a detector, wherein the optical fiber is heated when immersed in the molten bath. The heating curve of the optical fiber has at least one point P(t0, T0), wherein the increase ?T1 in the temperature T of the optical fiber over the time ?t in a first time interval t0??t up to the temperature T0 is smaller than the increase ?T2 in the temperature of the optical fiber over the time ?t in an immediately following second time interval t0+?t.

Abstract: A thermocouple shield assembly comprising a first tube having an upper portion and a lower portion with a lower end, the first tube including a first elongated cavity closed at the lower end and receiving the thermocouple, a second tube having a second elongated cavity with at least one open end and receiving the upper portion while a part of the lower portion containing the thermocouple extends out of the open end, and a gap between adjacent walls of the second elongated cavity and of the first tube such as to allow independent thermal deformations of the first and second tubes. In use, at least a portion of the part of the lower portion of the first tube is subjected to a given temperature while the second tube is subjected to a different temperature. Methods of manufacturing and of assembling such a thermocouple shield assembly are also presented.

Abstract: A guide system for signal lines includes a guide tube, through which the signal lines are guided, a cooling system which laterally surrounds the guide tube and has at least one coolant chamber and at least one inlet and at least one outlet for the coolant. The coolant chamber is tubular in construction and is hermetically sealed by a seal at least at one end face.

Abstract: A temperature measuring device for molten metal includes a porous plug with a first end and an opposed second end, an outer protective sheath with a closed end, an inner protective tube with a closed end, and a thermocouple arranged within an interior of the inner protective tube. The outer protective sheath extends away from the first end of the plug and the inner protective tube is arranged within an interior of the outer protective sheath. The porous plug comprises a substantially refractory material and the outer protective sheath consists essentially of substantially refractory metal oxide and graphite. A junction of the thermocouple is proximate to the closed end of the inner protective tube.

Abstract: A method of sensing the temperature of a heated object includes obtaining past temperature data relating to the heated object, capturing a thermal image of the heated object, obtaining a reference temperature of the heated object, and calculating a normalized hotspot temperature.

Abstract: A method is provided for measuring a temperature of a molten metal bath by an optical fiber surrounded by a cover. The optical fiber is immersed in the molten bath, and the radiation absorbed by the optical fiber in the molten bath is fed to a detector, wherein the optical fiber is heated when immersed in the molten bath. The heating curve of the optical fiber has at least one point P(t0, T0), wherein the increase ?T1 in the temperature T of the optical fiber over the time ?t in a first time interval t0??t up to the temperature T0 is smaller than the increase ?T2 in the temperature of the optical fiber over the time ?t in an immediately following second time interval t0+?t.

Abstract: The present invention provides a sampling device for thermal analysis of molten metal, in particular molten cast iron, said sampling device being intended to be filled with liquid metal to be analysed, said sampling device being a container having an upper side and a lower side, said container comprising one common filling inlet on the upper side of said container and at least two cavities, each cavity having a protective tube adapted for enclosing a temperature responsive sensor member, characterised in that said common filling inlet is branched into at least two filling channels ending in said cavities. The invention also provides a kit of parts intended for thermal analysis of solidifying metal, said kit comprising a temperature responsive sensor means and a sampling device as disclosed above.

Abstract: A device is provided for temperature measurement in metal melts, particularly in iron or steel melts, having a thermoelement, which is arranged in a thermoelement tube, and having an exterior protective body, which is essentially formed of graphite and metal oxide. The thermoelement tube is arranged in the protective body with a spacing, forming an intermediate space, and an insulating material and an oxygen-reducing material are arranged in the intermediate space. The insulating material and the oxygen-reducing material, as a powder mixture, form a tube (2), which surrounds the thermoelement tube (3) with a spacing and/or which is surrounded by the protective body (1) with a spacing.

Abstract: The system developed for the continuos temperature measurement of molten metal (1), like in the case of the continuous casting machine tundish (2), uses an optical process to control the continuous casting machine speed, and it consists of an optical infra-red sensor (8) protected by a cooled jacket (30). This two-color sensor (8), fitted with optical fiber (9) and an optical signal converter (10), is focused inside a high thermal and light conductivity ceramic tube (15), and it enables accurate temperature readings of molten steel (1) in the tundish (2). This practical device avoids the inconvenience of the method currently being used. It reduces the operator's high temperature exposure time, lowers maintenance downtime, minimizes the operating risks, improves safety and enables fast, simple replacement, resulting in improved slab quality and, as a consequence, lower costs.

Abstract: A device is provided for temperature measurement in metal melts, particularly in iron or steel melts, having a thermoelement, which is arranged in a thermoelement tube, and having an exterior protective body, which is essentially formed of graphite and metal oxide. The thermoelement tube is arranged in the protective body with a spacing, forming an intermediate space, and an insulating material and an oxygen-reducing material are arranged in the intermediate space. The insulating material and the oxygen-reducing material, as a powder mixture, form a tube (2), which surrounds the thermoelement tube (3) with a spacing and/or which is surrounded by the protective body (1) with a spacing.

Abstract: A method is provided for measuring a parameter of a molten metal bath by an optical fiber surrounded by a cover. The optical fiber is immersed in the molten bath, and the radiation absorbed by the optical fiber in the molten bath is fed to a detector, wherein the optical fiber is heated when immersed in the molten bath. The heating curve of the optical fiber has at least one point P(t0, T0), wherein the increase ?T1 in the temperature T of the optical fiber over the time ?t in a first time interval t0-?t up to the temperature T0 is smaller than the increase ?T2 in the temperature of the optical fiber over the time ?t in an immediately following second time interval t0+?t.

Abstract: A milliwave melter monitoring system is presented that has a waveguide with a portion capable of contacting a molten material in a melter for use in measuring one or more properties of the molten material in a furnace under extreme environments. A receiver is configured for use in obtaining signals from the melt/material transmitted to appropriate electronics through the waveguide. The receiver is configured for receiving signals from the waveguide when contacting the molten material for use in determining the viscosity of the molten material. Other embodiments exist in which the temperature, emissivity, viscosity and other properties of the molten material are measured.

Abstract: A device is provided for measuring the cooling curve of melts and/or the heating curve of melt samples with an optical fiber, wherein an immersion end of the optical fiber having an at least partially free surface is surrounded with a spacing by a temperature-resistant sample-receiving chamber. The optical fiber is immersed with its immersion end in the melt, and a sample is thereby formed in the sample-receiving chamber. The sample-receiving chamber with the sample and the optical fiber are thereafter pulled out of the molten metal. The cooling curve of the sample and/or, after previous solidification of the sample, the temperature profile during heating is measured with reference to a signal obtained by the optical fiber and forwarded to a measurement device.

Abstract: A system and method for a multi-temperature indicator stick. The multi-temperature indicator stick includes an elongated stick configured to indicate two or more predetermined temperatures. The elongated stick includes a first temperature indication material configured to indicate a first predetermined temperature upon being subjected to the first predetermined temperature. The elongated stick also includes a second temperature indication material configured to indicate a second predetermined temperature upon being subjected to the second predetermined temperature. The first temperature indication material and the second temperature indication material share a common interface extending longitudinally along the elongated stick.

Abstract: A device for measuring temperature and analyzing melt in metallurgical vessels with a channel pipe KN arranged on a side wall of a vessel KV, extending with a lower end thereof into this wall, and ending with an upper open end thereof above the vessel KV for taking a melt probe, which has, above an opening, an air inlet with an associated inlet/outlet valve VT and above it, a rotary valve DS that opens a cross-section of the channel pipe KN for introducing measuring probes, laser, or temperature feeler, and closes it.

Abstract: An expendable immersion device for sensing characteristics of molten metal has a contact block and a receptacle tube. The contact block is slidingly disposed at least partially within a distal end of the receptacle tube. The expendable immersion devices includes a sensing element and a heat resistant tube. A distal end of the heat resistant tube is mounted to the sensing element. The sensing element extends partially into the interior of the heat resistant tube. A proximal end of the heat resistant tube is mounted over a distal end of the receptacle tube. A spring element is positioned over a proximal end of the contact block and abuts against the receptacle tube such that a force between the contact block and the sensing element is reduced when the heat resistant tube and sensing element are connected to the distal end of the contact block during assembly.

Abstract: The invention relates to a converter with a container for receiving molten metal and with a measurement device for the optical temperature determination of the molten metal. The converter has an optical waveguide for guiding electromagnetic radiation emitted by the metal to an optical detector for determining the temperature of the metal from an analysis of the electromagnetic radiation. The converter further has a line arranged between the optical detector and the container through which fluid flows for guiding and transporting the optical waveguide. The optical detector is arranged, spaced apart from the container, in a region in which the surrounding temperature is less than 150 DEG C. The invention further relates to a method for the temperature determination of the molten metal in such a converter.

Abstract: A temperature measurement tube is composite and comprises a rigid shaft (1), which is cooled so as to shield it from corrosion and from the melt, and an end-fitting (15) housing a thermocouple (9) on the end of the tube and constructed from a noble metal, which is resistant to corrosion and to the high melting point. An alumina coating (13) is placed between the two metals in order to prevent any corrosion-inducing electrochemical exchange between them.

Abstract: The invention provides an apparatus for measuring the temperature of a molten bath comprising a) a refractory mounting sleeve (1,1?) having an outer surface (2) for contacting the molten bath and an inner cavity (3), said inner cavity having an inner surface (4), an outer opening (6) and an inner closed end (5); and b) an optical pyrometer (7) attached to the mounting sleeve and adapted to measure the thermal radiation emitted by a measurement zone (10) located inside the inner cavity of the mounting sleeve and under the molten bath level. The inner cavity outer opening (6) is adapted to receive fixedly the optical pyrometer (7). The apparatus is characterized in that the mounting plate (8) is adapted to engage in a complementary recess located at the inner cavity outer opening (6) of the mounting sleeve (1,1?). Thereby, the accuracy and reproducibility of the measure is greatly increased.

Abstract: A measuring probe is provided for measurement in molten metal, the probe having a measuring head arranged on an immersion end of a carrier tube. A bath contact and at least one sensor for determining a component of the molten metal are arranged on the immersion end. The bath contact, viewed in the immersion direction, has a first bath contact region with two surface areas extending parallel to the immersion direction on opposite sides of the bath contact.

Abstract: A method is provided for measuring the cooling curve of melts and/or the heating curve of melt samples with an optical fiber, wherein an immersion end of the optical fiber having an at least partially free surface is surrounded with a spacing by a temperature-resistant sample-receiving chamber. The optical fiber is immersed with its immersion end in the melt, and a sample is thereby formed in the sample-receiving chamber. The sample-receiving chamber with the sample and the optical fiber are thereafter pulled out of the molten metal. The cooling curve of the sample and/or, after previous solidification of the sample, the temperature profile during heating is measured with reference to a signal obtained by the optical fiber and forwarded to a measurement device. In addition, a corresponding device is provided for the measuring method.

Abstract: A temperature sensor temperature sensing tube and its fabrication method comprised of a step that provides for a tubular blank of an appropriate length, a step in which a curvilinear semifinished product of the tube member bottom section aperture is formed, a step in which a semifinished product of the neck base and the neck body is formed, a step in which a semifinished product of the neck base and the neck body is further formed, and a step in which a finished product having an outer conoidal hem and an inner conoidal hem is formed. Executing each step completes the fabrication of the temperature sensing tube.

Abstract: The present invention provides a novel method and a system of modules for carrying out thermal analysis of cast iron melts. The characterizing step of the method is de-termination of the position of the thermocouples used for recording cooling curves. The system comprises a thermocouple unit, a thermocouple holder, and a sampling unit. The system comprises means for ensuring that the thermocouples are correctly positioned before starting the thermal analysis. The system also comprises means for automatically transferring calibration data regarding the thermocouples.

Abstract: A device (10) for continuous measurement of the temperature of molten metal in a furnace or recipient for its production and treatment comprises a heat analysis instrument (14) placed in a lance (12) which blows inert gas and/or high-pressure compressed air against a surface of metal slag (18) of a furnace or recipient (20).

Abstract: The invention relates to a regulation method for an electrolytic cell for the production of aluminium by means of reduction of alumina dissolved in a molten cryolite bath and comprises the addition, in the electrolyte bath, during pre-determined time intervals p referred to as “periods”, of a determined quantity Q(p) of aluminium trifluoride (AlF3) determined by the following equation: Q(p)=Qint(p)?Qc1(p)+Qt(p), where Qint(p) is an integral (or “self-adaptive”) term which represents the total actual AlF3 requirements of the cell and which is calculated from a mean Qm(p) of the actual AlF3 supplies made during the last N periods, Qc1 is a compensating term corresponding to the so-called “equivalent” quantity of AlF3 contained in the alumina added to the cell during the period p, and Qt(p) is a corrective term which is a typically increasing function of the difference between the measured bath temperature T(p) and the set-point temperature To.