Thermometer calibration and temperature measurement

Purpose You will 1. calibrate two thermometers (mercury thermometer and Pt-resistance thermometer by immersing them in different equilibrium systems (ice/water, Na2SO4∙10 H2O solid/liquid and boiling point of water) of known temperatures 2. use the stem correction for the mercury thermometer 3. determine the boiling point of an organic liquid by using the previously determined calibration and stem correction function 4. determine the heating curve of an electric cooking plate by an IR- (non-contact) thermometer

Background International Temperature Scale of 1990 (ITS–90) Temperature is a numerical measure of hot and cold. This intensive variable is one of the principal quantities of thermodynamics. The International System of Units (SI) defines unit kelvin (K) and scale for the thermodynamic temperature (symbol T) with absolute zero as the first reference point (0 K), and by using the reliably reproducible temperature of the triple point of water as the second reference point. For historical reasons, the triple point temperature of water is fixed at 273.16 K. Degrees Celsius (°C, symbol θ,  or t) is defined by the equation t / o C  T / K  273.15 The Kelvin and Celsius scales are impractical to use at temperatures that are very different from the triple point of water. Therefore the International Temperature Scale of 1990 (ITS–90) was defined and internationally accepted in 1990. ITS–90 is designed to represent the thermodynamic (absolute) temperature scale as closely as possible throughout its range. It is an approximation of the thermodynamic temperature scale that facilitates the comparison and compatibility of temperature measurements internationally. ITS–90 uses 17 defined calibration points ranging from 0.65 K to approximately 1358 K (-272.5 °C to 1085 °C) and is subdivided into multiple temperature ranges which overlap in some instances. The defined points are based on various thermodynamic equilibrium states. Most of them are phase transitions, specifically the melting/freezing point of very pure (>99.9999%) chemical elements and on the triple point of water. A selection of these defined points is listed in the table.

Substance Defining point in K Defining point in °C State Neon, Ne 24.5561 -248.5939 Triple point Oxygen, O 54.3584 -218.7916 Triple point 2 Argon, Ar 83.8058 -189.3442 Triple point Mercury, Hg 234.3156 -38.8344 Triple point Water, H 0 273.16 0.01 Triple point 2 Gallium, Ga 302.9146 29.7646 Melting point Indium, In 429.7485 156.5985 Freezing point Tin, Sn 505.078 231.928 Freezing point

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Many different thermometer designs are required to cover the entire range. These include helium vapour pressure thermometers, helium gas thermometers, standard platinum resistance thermometers and monochromatic radiation thermometers. ITS–90 uses complex mathematical formulas to interpolate between its defined points. Note, that according to ITS–90 the boiling point of water at standard atmospheric pressure is not 100.00 oC (as it was defined previously), but 99.974 °C. See the vapour pressure of water as function of temperature in the table below.

p / hPa t / °C 701.17 89.976 977.59 98.974 1013.2 99.974 1049.9 100.974 1432.4 109.972

The vapour pressure of water can be approximated in the range 977 – 1013 hPa by the linear equation: t/oC = 71.52132 + 0.028082 × p/hPa Also, in the praxis easily realisable secondary standards are used for thermometer calibration (e.g. melting point of ice at atmospheric pressure).

Temperature measurement Thermometers are devices that measure temperature using a variety of different principles. Most of these rely on measuring some physical property of a working material that varies with temperature. One of the most common devices for measuring temperature is the glass thermometer. The mercury-in-glass or mercury thermometer is based upon the difference between the thermal expansion coefficients of liquid mercury (about 1.8·10-4 K-1) and glass (about 0.2·10-4 K-1). The glass vessel of a mercury thermometer consists of a bulb (i.e. mercury container) and a capillary of uniform diameter. Temperature increase causes the fluid to expand, so the temperature can be determined by measuring the volume of the fluid. The capillary is usually marked at two points (say at 0 °C and 100 °C ) and graduated uniformly in between, on an assumption that the volume of a fixed mass of mercury is a linear function of temperature. The measuring interval of a common mercury thermometer is between -39 °C and +350 °C. Note that the European Union bans mercury from certain electrical, electronic and non-electrical measuring devices, such as thermometers and barometers. The alcohol thermometer is an alternative to the mercury-in-glass thermometer. Unlike the mercury thermometer, the contents of an alcohol thermometer (pure ethanol, toluene, kerosene etc.) are less toxic. Thermometers are not affected by vapour pressure above the capillary column. It is only necessary that the liquid be clearly distinguishable from the volume above the liquid. The glass capillary magnifies the column, and can be shaped to increase the magnification. A gas thermometer measures temperature by the variation in volume or pressure of a gas. The constant volume thermometer consists of a bulb connected by a capillary tube to a manometer. A bimetallic thermometer consists of two strips of different metals (usually steel and copper) which expand to a different degree as they are heated. The strips are joined together throughout their length. The different expansions force the flat strip to bend if

2 temperature changes. The metal with the higher coefficient of thermal expansion is on the outer side of the curve when the strip is heated. Resistance thermometers measure temperature by correlation of resistance with temperature of pure materials, typically platinum, nickel or copper. A thermistor is a type of resistor (in general semiconductor) whose resistance varies significantly with temperature, more so than in standard resistors. A thermocouple is a device consisting of two dissimilar conductors that contact each other at one or more spots. It produces a voltage when the temperature of one of the spots differs from the reference temperature at other parts of the circuit (thermoelectric effect or Seebeck effect). An infrared thermometer is a device which infers temperature from a portion of the blackbody radiation (Stefan–Boltzmann law) emitted in the range of 8 to 14 µm by the object being measured. They are sometimes called non-contact thermometers, since the device is able to measure temperature from a distance. A pyrometer is a type of radiation thermometer used to measure high temperatures. Liquid crystal thermometers contain heat-sensitive (thermochromic) liquid crystals in a plastic strip that change colour to indicate different temperatures.

There are some important sources of error in measuring with mercury (or alcohol) thermometers. 1. Achieving thermal equilibrium needs a good while. Therefore when measuring with mercury thermometer you must wait at least 10 mins before recording temperature values. 2. Glass, not being a crystalline material, cannot adjust its volume promptly to an abrupt drop in temperature. Consequently when you transfer a thermometer from boiling water into an ice/water bath, mercury thermometers tend to show lower than 0 °C for the melting point of ice. This type of error is called zero point depression. (You will not study this effect). 3. The glass capillary that contains the mercury (or any other liquid) thread is never quite even in diameter along its whole length as it should be; on the other hand the scale is uniformly divided. Consequently for precise measurements the thermometer should be calibrated. To obtain proper temperature values we define the correction, ∆t

t  te  tm where te is exact (correct) temperature established by well known phase equilibria and tm is the measured one. The value of ∆t can be either negative or positive number. Measuring the temperatures of some equilibrium systems with well-known temperatures you can get ∆t in the o 0 – 100 C range (in form of table or as ∆t vs. tm plot). Between calibration points, linear interpolation is used. 4. Stem error and correction. Thermometers are normally scaled on the assumption that when the reading is done, the whole thermometer is in thermal equilibrium with its surroundings. In practice however we only immerse the bulb and a part of the capillary in what we want to take a reading of, and therefore part of the thread is practically exposed to room temperature. If the thread temperature is significantly different from that of the bulb an error occurs (stem error), and we need to take a stem correction (∆tstem) using the equation

tstem  k tm  tstem l o o where tm (in C) is the temperature read in the thermometer, tstem (in C) is the mean temperature of the stem measured by an another (auxiliary) thermometer in the middle of the stem (or estimated by another way), and l is the length of the stem outside the vessel (in oC). Constant k depends on the difference of the thermal expansion coefficients of thermometer liquid and glass. In case mercury-in-glass thermometers its value is about 0.00016 oC-1.

3 It can be easily seen from the above mentioned errors that for precise measurements the thermometer should be calibrated and stem correction should be used. With knowledge of both corrections, the true temperature can be calculated by the equation:

tc  tm  t  tstem where tc is the correct value of temperature and tm means the measured one.

Procedure 1. Calibration of thermometers You will calibrate two thermometers  mercury-in-glass-thermometer (3 point calibration). The serial number is on the backside. The reading accuracy should be estimated between marks in increments of 0.01 oC. Wait about 10 mins to reach thermal equilibrium between the system and thermometer. After that, record 5-6 equilibrium temperature values.  Pt-resistance thermometer (2 point calibration). The registration number is on the front side. The reading accuracy is 0.1 oC (digital display). Equilibrium is reached in a short time. To determine the calibration, check your thermometers with the following 3 systems:  ice/water system  Na2SO4∙10 H2O, solid/liquid equilibrium (for mercury-in-glass-thermometer only)  boiling water / water vapour at actual atmospheric pressure

Ice/water system (0.00 °C at a pressure of 1.013∙105 Pa) Prepare an ice/water mixture from ground ice and distilled water in a Dewar flask. Fill the flask to the brim, stir continuously and carefully. Put the thermometers in the flask; you even may put more thermometers in it simultaneously. For the mercury thermometer, use a magnifying glass and small lamp for better reading of the scale. Na2SO4∙10 H2O, solid/liquid system (32.38 °C). To obtain the value of tm you should prepare the solid salt / molten salt equilibrium system: Na2SO4∙10H2O(s) = Na2SO4 (s) + Na2SO4 (aq) To do this, take a clean and dry test tube, place a glass stirrer into it and fill it up to about two- thirds with solid salt (the salt should be properly ground in a mortar beforehand). Heat it gently over a Bunsen burner at constant stirring until half of the salt is melted. After that it should be placed into a bigger glass tube (thermal insulator) and both of these tubes placed into a beaker containing water the temperature of which should be about 32 °C (to thermostat the system). Then immerse your thermometers into the mixture. Stir the melted salt and water bath continuously and carefully in the beaker (see figure). After the measurement clean the thermometers carefully and scrape the molten mixture into the waste container.

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Apparatus for the determination correction in the Na2SO4∙10 H2O solid/liquid system.

Water/water vapour system (about 100 °C depending on the atmospheric pressure). Use the double wall glass apparatus (see figure) for calibration in boiling water. To avoid stem error the whole mercury thermometer must be immersed in the steam. Only a very small part of the scale (about 1 oC) may be out for better reading. In order to calculate the equilibrium boiling temperature, you will have to determine the actual atmospheric pressure with an electronic barometer (measuring principle is piezoresistivity).

Apparatus for the determination of boiling point in the boiling water/water vapour system.

5 2. Using stem correction in case of intentionally wrong temperature measurement Draw out some part of the thermometer above the upper cork level, so that a certain length of the thread will remain outside the mantle, and note it. That length will be referred to as stem length (l). Attach another (auxiliary) thermometer to the middle point of the stem and note its temperature, tstem as well. Read the intentionally wrong temperature shown by the partially immersed thermometer. Your mentor will give the value of stem lengths. 3. Determination of boiling point of organic liquid Using a boiling point apparatus (see figure), determine the boiling point of an organic liquid with the mercury thermometer. Do not forget to put boiling chip under the Cottrell vapour lift. Attach an auxiliary thermometer at suitable height for stem correction. Read the actual stem length (l), as well. After the measurement pour the liquid into the organic waste bin. Do not wash the apparatus with water, leave it open to dry out.

Apparatus for the determination of boiling point of organic liquid

4. Determination of the heating curve of an electric cooking plate by an IR-thermometer The IR-thermometer is already fixed in the lab at an optimal distance from the heating plate. Emission factor of the surface is already adjusted (0.95). Adjust the measuring spot using the double laser beam into the middle of the plate. Switch on the plate at a power given by your mentor. Read temperatures in 5 min interval and write them in a table for about 1 hour. Each student must take part in this series of measurements. Take care – cooking plate is hot!

Calculations 1. Calculate the boiling point of water at the actual atmospheric pressure using vapour pressure table or equation according to ITS–90 (tb). 2. Calculate the correction values of thermometers at the three secondary standard temperatures

t1  0.00 C - tm1

t2  32.38 C -tm2 (mercury thermometer only)

t3  tb - tm3 ,

3. Plot corrections (t) vs. measured temperature (tm) for the mercury thermometer. Connect measuring points by straight lines. Give the results in form of a table, as well. 4. Calculate the stem correction

6 tstem  k tm  tstem l using constant the k = 0.00016 oC-1 of the mercury thermometer. Apply the correction for the measured boiling ponit to obtain the correct value. 5. Calculate the boiling temperature of the organic liquid applying the calibration values and the stem correction. Between the calibration points use linear interpolation. 6. Copy the common table of the heating plate measurement and attach it to your protocol. Plot the temperatures (y) vs. time (t). Fit the equation (exponential saturation) y = A(1 – exp(-Bt)) to the measurement and draw the curve to the graph. A and B are fitting parameters: A is the maximum temperature and B is proportional to the rate of heating.

Results to be given 1. Calibration table with an accuracy of 0.01 oC for mercury thermometer (3 points) and 0.1 oC for Pt-resistance thermometer (2 points). Calibration graph for the mercury thermometer. 2. Stem correction of the thermometer 3. Corrected boiling point of the organic liquid 4. Heating graph of the cooking plate with fitted curve and fitting parameters

Riedel 22. 09. 2016.

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