The custom demos section of the website is used by UO chemistry instructors to schedule demonstrations that are not listed in the database. Fluids Flow Engineering Use experimental data to develop a relationship among the variables: heat, mass, specific heat, and change in temperature. x]Y~_}Z;b7 {}H[-ukZj+d WEVuf:-w Cgcm?S'~+v17k^w/?tNv/_w?h~&LwWb?J'_H1z#M#rl$>IW})*Jw p To relate heat transfer to temperature change. Some students reason "the metal that has the greatest temperature change, releases the most heat". D,T(#O#eXN4r[{C'7Zc=HO~ Th~cX7cSe5c Z?NtkS'RepH?#'gV0wr`? The mole fraction of each oxidation product at the initial oxidation stage of the alloys at the corresponding temperatures was predicted. All rights reservedDisclaimer | Since heat is measured in Joules ( J ), mass in grams ( g ), and temperature in degree Celsius ( C ), we can determine that c = J g C. Therefore, specific heat is measured in Joules per g times degree Celsius. The final equilibrium temperature of the system is 30.0 C. What is the specific heat of the metal sample? 3) Liquid water goes through an unknown temperature increase to the final value of x. 1999-2023, Rice University. 35.334 kJ of heat are available to vaporize water. Therefore, since the temperature of the water at thermal equilibrium is 29.8 C, the final temperature of the metal must be the same (29.8 C). See the attached clicker question. The specific heat equation can be rearranged to solve for the specific heat. Example #7: A ring has a mass of 8.352 grams and is made of gold and silver. Our goal is to make science relevant and fun for everyone. Power Transmission Tech. It produces 2.9 kJ of heat. Economics Engineering A thermometer and stirrer extend through the cover into the reaction mixture. After students have answered the question, use the tongs and grab the hot lead metal and place it in 50 mL of room temperature water. The warmer iron goes down from to 85.0 to x, so this means its t equals 85.0 minus x. In your day-to-day life, you may be more familiar with energy being given in Calories, or nutritional calories, which are used to quantify the amount of energy in foods. The total mass of the cup and the stirrer is 50.0 grams. Specific heat calculations are illustrated. The heat produced by the reaction is absorbed by the water and the bomb: This reaction released 48.7 kJ of heat when 3.12 g of glucose was burned. 117 N when standing in the surface of the moon (This is approximately the amount of energy needed to heat 1 kg of water by 1 C.). This book uses the If the p.d. So, if we want to determine the units for specific heat, we'll just isolate the term in the above formula to get c = q m T. \[c_p = \dfrac{q}{m \times \Delta T} = \dfrac{134 \: \text{J}}{15.0 \: \text{g} \times 38.7^\text{o} \text{C}} = 0.231 \: \text{J/g}^\text{o} \text{C} \nonumber \]. 3.12: Energy and Heat Capacity Calculations is shared under a CK-12 license and was authored, remixed, and/or curated by Marisa Alviar-Agnew & Henry Agnew. Helmenstine, Todd. Because the final temperature of the iron is 73.3C and the initial temperature is 25.0C, T is as follows: T = Tfinal Tinitial = 73.3C 25.0C = 48.3C. The initial teperature of the water, stirrer, and calorimeter is 20.0 C. K). are licensed under a, Measurement Uncertainty, Accuracy, and Precision, Mathematical Treatment of Measurement Results, Determining Empirical and Molecular Formulas, Electronic Structure and Periodic Properties of Elements, Electronic Structure of Atoms (Electron Configurations), Periodic Variations in Element Properties, Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law, Stoichiometry of Gaseous Substances, Mixtures, and Reactions, Shifting Equilibria: Le Chteliers Principle, The Second and Third Laws of Thermodynamics, Representative Metals, Metalloids, and Nonmetals, Occurrence and Preparation of the Representative Metals, Structure and General Properties of the Metalloids, Structure and General Properties of the Nonmetals, Occurrence, Preparation, and Compounds of Hydrogen, Occurrence, Preparation, and Properties of Carbonates, Occurrence, Preparation, and Properties of Nitrogen, Occurrence, Preparation, and Properties of Phosphorus, Occurrence, Preparation, and Compounds of Oxygen, Occurrence, Preparation, and Properties of Sulfur, Occurrence, Preparation, and Properties of Halogens, Occurrence, Preparation, and Properties of the Noble Gases, Transition Metals and Coordination Chemistry, Occurrence, Preparation, and Properties of Transition Metals and Their Compounds, Coordination Chemistry of Transition Metals, Spectroscopic and Magnetic Properties of Coordination Compounds, Aldehydes, Ketones, Carboxylic Acids, and Esters, Composition of Commercial Acids and Bases, Standard Thermodynamic Properties for Selected Substances, Standard Electrode (Half-Cell) Potentials, Half-Lives for Several Radioactive Isotopes. Keith Nisbett, Copyright 2000 - Forgive me if the points seem obvious: Solution Key Number One: We start by calling the final, ending temperature 'x.' We will ignore the fact that mercury is liquid. Therefore: (It is important to remember that this relationship only holds if the calorimeter does not absorb any heat from the reaction, and there is no heat exchange between the calorimeter and the outside environment.). These values are tabulated and lists of selected values are in most textbooks. What was the initial temperature of the water? This site shows calorimetric calculations using sample data. Since the solution is aqueous, we can proceed as if it were water in terms of its specific heat and mass values. T = 20 C T = T final - T initial T final = T inital + T T final = 10 C + 20 C T final = 30 C Answer: The final temperature of the ethanol is 30 C. For example: Say you add 75.0 Joules of energy to 2.0 grams of water, raising its temperature to 87 C. In a simple calorimetry process, (a) heat, Chemical hand warmers produce heat that warms your hand on a cold day. The influence of the laser radiation flux on the metal nanolayer can lead to its significant heating and to the same heating of the adjacent water layers. Thermodynamics (Assume a density of 0.998 g/mL for water.). This is opposite to the most common problem of this type, but the solution technique is the same. Hardware, Metric, ISO Want to cite, share, or modify this book? Determination Of Mean Metal Temperature - posted in Industrial Professionals: While Designing a STHE, BEM type, with the following process data for normal operating case : Shell Side Fluid: Cooling Water Shell Side Flow : 29000 kg/hr Shell Side Inlet : 33 deg C Shell Side Inlet : 45 deg C Fouling Factor : 0.0004 m2.hr.C/kcal Tube Side Fluid: Nitrogen Tube Side Flow : 7969 kg/hr Tube Side Inlet . Plug the given values into your equation: 75.o J = 2.0 g x (4.184 J/gC) x (87 C - t0). Identify what gains heat and what loses heat in a calorimetry experiment. State any assumptions that you made. Because energy is neither created nor destroyed during a chemical reaction, the heat produced or consumed in the reaction (the system), qreaction, plus the heat absorbed or lost by the solution (the surroundings), qsolution, must add up to zero: This means that the amount of heat produced or consumed in the reaction equals the amount of heat absorbed or lost by the solution: This concept lies at the heart of all calorimetry problems and calculations. if you aren't too fussy about significant figures. Dec 15, 2022 OpenStax. Students are asked to predict what will happen to the temperature of water and the temperature of the metals. 2. Measure and record the temperature of the water in the calorimeter. Record the temperature of the water. The specific heat of water is 4179 J/kg K, the amount of heat required to raise the temperature of 1 g of water by 1 Kelvin. A 10.3 g sample of a reddish-brown metal gave off 71.7 cal of heat as its temperature decreased from 97.5C to 22.0C. Each different type of metal causes the temperature of the water to increase to a different final temperature. Example #3: Determine the final temperature when 20.0 g of mercury at 165.0 C mixes with 200.0 grams of water at 60.0 C. Feedback Advertising If the amount of heat absorbed by a calorimeter is too large to neglect or if we require more accurate results, then we must take into account the heat absorbed both by the solution and by the calorimeter. Step 1: List the known quantities and plan the problem. This is what we are solving for. When the metal is nearly finished heating, place another thermometer into the calorimeter and record the initial temperature of the water. 2) Use 35.334 kJ and the heat of vaporization of water to calculate moles and then mass of water vaporized: mass H2O = (0.869225 mol) (18.015 g/mol) = 15.659 g, Bonus Example: A 250. gram sample of metal is heated to a temperature of 98.0 C. Curriculum Notes Specific heat capacity: Aluminum 0.91 J/gC Copper 0.39 J/gC Silver 0.240 J/gC Lead 0.160 J/gC Heat Lost from metal = Heat Gained by water. across them is 120V, calculate the charge on each capacit He holds bachelor's degrees in both physics and mathematics. In Fig. That's why water is so useful in moderating the temperature of machinery, human bodies and even the planet. are not subject to the Creative Commons license and may not be reproduced without the prior and express written When an endothermic reaction occurs, the heat required is absorbed from the thermal energy of the solution, which decreases its temperature (Figure 5.11). The formula is Cv = Q / (T m). Noting that 75/25 = 3, we arrive at: 38.25 0.45x = 12.552x 251.04 then 13.002x = 289.29 The answer is 22.25 C if you aren't too fussy about significant figures. When the ring has been heated to 94.52 C and then dropped into 13.40 g water at 20.00 C, the temperature of the water after thermal equilibrium was reached was 22.00 C. More expensive calorimeters used for industry and research typically have a well-insulated, fully enclosed reaction vessel, motorized stirring mechanism, and a more accurate temperature sensor (Figure 5.13). 2023 Leaf Group Ltd. / Leaf Group Media, All Rights Reserved. There's one important exception to keep in mind. The caloric content of foods can be determined by using bomb calorimetry; that is, by burning the food and measuring the energy it contains. Substitute the known values into heat = mcT and solve for c: \(c \,\mathrm{=\dfrac{-71.7\: cal}{(10.3\: g)(-75.5^\circ C)}}\). Divide the heat supplied/energy with the product. Remove the Temperature Probe and the metal object from the calorimeter. Next, we know that the heat absorbed by the solution depends on its specific heat, mass, and temperature change: To proceed with this calculation, we need to make a few more reasonable assumptions or approximations. \: \text{J/g}^\text{o} \text{C}\). At the end of the experiment, the final equilibrium temperature of the water is 29.8C. . For example, when an exothermic reaction occurs in solution in a calorimeter, the heat produced by the reaction is absorbed by the solution, which increases its temperature. Final Temperature After Mixing When you mix together two substances with different initial temperatures, the same principles apply. Under these ideal circumstances, the net heat change is zero: This relationship can be rearranged to show that the heat gained by substance M is equal to the heat lost by substance W: The magnitude of the heat (change) is therefore the same for both substances, and the negative sign merely shows that qsubstance M and qsubstance W are opposite in direction of heat flow (gain or loss) but does not indicate the arithmetic sign of either q value (that is determined by whether the matter in question gains or loses heat, per definition). The change in temperature is given by \(\Delta T = T_f - T_i\), where \(T_f\) is the final temperature and \(T_i\) is the initial temperature. C. If energy goes into an object, the total energy of the object increases, and the values of heat T are positive. Place 50 mL of water in a calorimeter. Assuming the use of copper wire ( = 0.004041) we get: If you are redistributing all or part of this book in a print format, 3. The colder water goes up in temperature, so its t equals x minus 20.0. You can plug in all the other values that you're given, then solve for t0. It is 0.45 J per gram degree Celsius. Bending the disk creates nucleation sites around which the metastable NaC2H3O2 quickly crystallizes (a later chapter on solutions will investigate saturation and supersaturation in more detail). Table \(\PageIndex{1}\) lists the specific heats for various materials. Randy Sullivan, University of Oregon Compare the heat gained by the water in Experiment 1 to the heat gained by the water in experiment 2. If this occurs in a calorimeter, ideally all of this heat transfer occurs between the two substances, with no heat gained or lost by either its external environment. The Law of Conservation of Energy is the "big idea" governing this experiment. 1 gives the specific heat of iron as 0.108 cal/gC. This demonstration assess students' conceptual understanding of specific heat capacities of metals. Harrington, D.G. consent of Rice University. Specific heat is the amount of heat per unit of mass needed to raise a substance's temperature by one degree Celsius. Heat the metals for about 6 minutes in boiling water. A computer animation depicting the interaction of hot metal atoms at the interface with cool water molecules can accompany this demonstration (see file posted on the side menu). then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a digital format, A common reusable hand warmer contains a supersaturated solution of NaC2H3O2 (sodium acetate) and a metal disc. When in fact the meal with the smallest temperature change releases the greater amount of heat. << /Length 4 0 R /Filter /FlateDecode >> (credit: modification of work by Science Buddies TV/YouTube). This means: Please note the use of the specific heat value for iron. . Stir it up. This indicates that each metal has a different ability to absorb heat energy and to transfer heat energy. These easy-to-use coffee cup calorimeters allow more heat exchange with the outside environment, and therefore produce less accurate energy values. The water specific heat will remain at 4.184, but the value for the metal will be different. Determine the specific heat and the identity of the metal. Use the graph of temperature versus time to find the initial temperature of the water and the equilibrium temperature, or final temperature, of the water and the metal object after the object warms up and the water cools . Initial temperature of water: 22.4. Please note the starting temperature of the metal is above the boiling point of water. The specific heat of cadmium, a metal, is fairly close to the specific heats of other metals. Have students predict what will happen to the temperature of the water in the two calorimeters when hot lead is added to one and hot aluminum is added to the other. The final temperature of the water was measured as 42.7 C. Whether you need help solving quadratic equations, inspiration for the upcoming science fair or the latest update on a major storm, Sciencing is here to help. Copyright 2012 Email: The specific heat of water is approximately 4.184 J/g C, so we use that for the specific heat of the solution. The initial temperature of the water is 23.6C. .style1 { Calculate the value of q for this reaction and explain the meaning of its arithmetic sign. First heat a 10 gram aluminum metal in beaker of boiling water for at least 10 minutes so that the metal's . Most of the problems that I have seen for this involve solving for C, then solving for k, and finally finding the amount of time this specific object would take to cool from one temperature to the next. Journal of Chemical Education, 88,1558-1561. Place 50 mL of water in a calorimeter. Again, you use q = mcT, except you assume qaluminum = qwater and solve for T, which is the final temperature. Use experimental data to develop a conceptual understanding of specific heat capacities of metals. Relatively inexpensive calorimeters often consist of two thin-walled cups that are nested in a way that minimizes thermal contact during use, along with an insulated cover, handheld stirrer, and simple thermometer. Explanation: did it on edgunity. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . Assume no water is lost as water vapor. 7_rTz=Lvq'#%iv1Z=b Downloads One calorie (cal) = exactly 4.184 joules, and one Calorie (note the capitalization) = 1000 cal, or 1 kcal. The specific heat equation doesn't work during a phase change, for example, from a liquid to a gas or a solid to a liquid. The university expressly disclaims all warranties, including the warranties of merchantability, fitness for a particular purpose and non-infringement. (b) The foods nutritional information is shown on the package label. (+=8y(|H%= \=kmwSY $b>JG?~cN12t_8 F+y2_J~aO,rl/4m@/b3t~;35^cOMw_:I?]/\ >R2G Where Q is the energy added and T is the change in temperature. 3) This problem could have been solved by setting the two equations equal and solving for 'x. For a physical process explain how heat is transferred, released or absorbed, at the molecular level. 3) Total heat given off by the metal sample: 4) Determine the specific heat of the metal sample: Go to calculating final temperature when mixing metal and water problems 1 - 15. Two different metals, aluminum and lead, of equal mass are heated to the same temperature in a boiling water bath. The sample is placed in the bomb, which is then filled with oxygen at high pressure. What is the final temperature of the crystal if 147 cal of heat were supplied to it? Having this information, you can also calculate how much energy you need to supply to a sample to increase or decrease its temperature. An instant cold pack consists of a bag containing solid ammonium nitrate and a second bag of water. What was the initial temperature of the metal bar, assume newton's law of cooling applies. Applications and Design When we use calorimetry to determine the heat involved in a chemical reaction, the same principles we have been discussing apply. Helmenstine, Todd. Elise Hansen is a journalist and writer with a special interest in math and science. For example Carla Prado's team at University of Alberta undertook whole-body calorimetry to understand the energy expenditures of women who had recently given birth. How much heat did the metal . Beam Deflections and Stress URL:https://media.pearsoncmg.com/bc/bc_0media_chem/chem_sim/calorimetry/Calor.php. Calorimetry is used to measure amounts of heat transferred to or from a substance. This type of calorimeter consists of a robust steel container (the bomb) that contains the reactants and is itself submerged in water (Figure 5.17). After a few minutes, the ice has melted and the temperature of the system has reached equilibrium. A chilled steel rod (2.00 C) is placed in the water. Engineering Calculators Which takes more energy to heat up: air or water? In fact, water has one of the highest specific heats of any "common" substance: It's 4.186 joule/gram C. VvA:(l1_jy^$Q0c |HRD JC$*m!JCA$zy?W? (credit a: modification of work by Rex Roof/Flickr), Francis D. Reardon et al. When using a calorimeter, the initial temperature of a metal is 70.4C. Richard G. Budynas The melting point (or, rarely, liquefaction point) of a solid is the temperature at which a sustance changes state from solid to liquid at atmospheric pressure. The 38.5 was arrived at in the same manner as the 1.8 just above. Note that the specific heat for liquid water is not provided in the text of the problem. ;?C2w%9iW/k-gN1WiuK; A/rNJTem'mzRUE|QG9^GdXK|oe3IX;{#y?h9b6hFV,^u$e`rm`DqXO]eBuwHUIv33BEh;P7kju~U)S\K}l2($_h(T=>`` V; font-size: 12px; This specific heat is close to that of either gold or lead. 7. Calculate the specific heat of cadmium. Analysis 1. The initial temperature of each metal is measured and recorded. Go to calculating final temperature when mixing metal and water: problems 1 - 15, Go to calculating final temperature when mixing two samples of water. "Calculating the Final Temperature of a Reaction From Specific Heat." 2 0 obj Comment: none of the appropriate constants are supplied. Flat Plate Stress Calcs Absolutely, The k is a ratio that will vary for each problem based on the material, the initial temperature, and the ambient temperature. If theaccompanying computer animation is displayed students can gain a conceptual understandingof heat transfer between a hot sample ofmetal and the cool water at the particle level (atom level). Structural Shapes The metal standard often allow for this by specifying low temperature tests for metals to be used at lower temperatures. How about water versus metal or water versus another liquid like soda? Hardware, Imperial, Inch A small electrical spark is used to ignite the sample. Design and conduct an experiment in which you can calculate the specific heat of aluminum by creating a thermal equilibrium system in which two different with different initial temperatures reach a final temperature that is the same for both. 1. The calorimeters described are designed to operate at constant (atmospheric) pressure and are convenient to measure heat flow accompanying processes that occur in solution. The metals are added to two insulated cups or calorimeters, each containing the same amount of water initially at room temperature. At the end of the experiment, the final equilibrium temperature of the water is 29.8C. 6. Example #8: A 74.0 g cube of ice at 12.0 C is placed on a 10.5 kg block of copper at 23.0 C, and the entire system is isolated from its surroundings. The EBSD images of phase distribution of as-HPed FG (unimodal) and bimodal Mo-Si-B alloys are shown in Figs. C What is the temperature change of the metal? ), (10.0) (59.0 x) (4.184) = (3.00) (x 15.2) (0.128). During her time at the National Bureau of Standards, research chemist Reatha Clark King performed calorimetric experiments to understand the precise heats of various flourine compounds. };md>K^:&4;[&8yZM:W02M6U|r|_(NzM#v: *wcbjBNT That is the initial temperature of the metal. Training Online Engineering, Fusion - Melting Change of Liquid State Thermodynamics, Critical Temperature and Melting Point for Common Engineering Materials, Atomic Numbers Weights Melting Temperatures. (23.0 x) (4042.5) = 26578.18 + 309.616x, x = 15.2 C (to three sig figs, I followed the rule for rounding with 5), Example #9: How many grams of water can be heated form 25.0 C to 35.0 C by the heat released from 85.0 g of iron that cools from 85.0 C to 35.0 C? A 360-g piece of rebar (a steel rod used for reinforcing concrete) is dropped into 425 mL of water at 24.0 C. A simple calorimeter can be constructed from two polystyrene cups. It would be difficult to determine which metal this was based solely on the numerical values. A nutritional calorie (Calorie) is the energy unit used to quantify the amount of energy derived from the metabolism of foods; one Calorie is equal to 1000 calories (1 kcal), the amount of energy needed to heat 1 kg of water by 1 C. Calculate the initial temperature of the piece of copper. What is the specific heat of the metal? Background. Electric Motor Alternators Given appropriate calorimetry data for two metals, predict which metal will increase the temperature of water the most. (The specific heat of gold is 0.128 J/g C. The question gives us the heat, the final and initial temperatures, and the mass of the sample. Example #4: 10.0 g of water is at 59.0 C. Suppose we initially have a high-temperature substance, such as a hot piece of metal (M), and a low-temperature substance, such as cool water (W). \(\Delta T = 62.7^\text{o} \text{C} - 24.0^\text{o} \text{C} = 38.7^\text{o} \text{C}\), \(c_p\) of cadmium \(= ? The heat given off by the reaction is equal to that taken in by the solution. Civil Engineering Stir it up. q = (50.0 g) (10.0 C) (0.092 cal g1 C1). Specific heat: Al 0.903 J/gC Pb 0.160 J/gC. More recently, whole-room calorimeters allow for relatively normal activities to be performed, and these calorimeters generate data that more closely reflect the real world. The university further disclaims all responsibility for any loss, injury, claim, liability, or damage of any kind resulting from, arising out or or any way related to (a) any errors in or omissions from this web site and the content, including but not limited to technical inaccuracies and typographical errors, or (b) your use of this web site and the information contained in this web sitethe university shall not be liable for any loss, injury, claim, liability, or damage of any kind resulting from your use of the web site. The specific heat capacities of each metal is displayed to students: Al 0.903 J/gC Pb 0.160 J/gC. Welding Stress Calculations What is the direction of heat flow? with rxn and soln used as shorthand for reaction and solution, respectively. Insert the values m = 100 kg and c = 800 J/kg C to find T = (7.35106 J) (100 kg)(800 J/kgC) = 92C T = ( 7.35 10 6 J) ( 100 kg) ( 800 J/kg C) = 92 C. Discussion The initial oxidation products of the alloys are . .style2 {font-size: 12px} This demonstration assess students' conceptual understanding of specific heat capacities of metals. %PDF-1.3 UO Libraries Interactive Media Group. If the final temperature of the system is 21.5 C, what is the mass of the steel bar? Note: 1.00 g cal g1 C1 is the specific heat for liquid water. 3. The equation that relates heat \(\left( q \right)\) to specific heat \(\left( c_p \right)\), mass \(\left( m \right)\), and temperature change \(\left( \Delta T \right)\) is shown below. "Do not do demos unless you are an experienced chemist!" If we make sure the metal sample is placed in a mass of water equal to TWICE that of the metal sample, then the equation simplifies to: c m = 2.0 ( DT w / DT m ) This enables the accurate determination of the heat involved in chemical processes, the energy content of foods, and so on. 1) The basic equation to be used is this: 2) The two masses associated with the gold and the silver rings: The 1.8 is arrived at thusly: 23.9 22.1. If the temperature were to rise to 35 Celsius, we could easily determine the change of resistance for each piece of wire. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. Friction Formulas Apps The calibration is accomplished using a reaction with a known q, such as a measured quantity of benzoic acid ignited by a spark from a nickel fuse wire that is weighed before and after the reaction. Most values provided are for temperatures of 77F (25C). Bomb calorimeters require calibration to determine the heat capacity of the calorimeter and ensure accurate results. Legal. Which metal will reach 60C first? This solution uses 0.901 for aluminum and 4.18 for water: Todd Helmenstine is a science writer and illustrator who has taught physics and math at the college level. Friction Engineering Subtract the final and initial temperature to get the change in temperature (T). status page at https://status.libretexts.org. (Cp for Hg = 0.14 J per gram degree Celsius.). Substitute the known values into heat = mcT and solve for amount of heat: \[\mathrm{heat=(150.0\: g)\left(0.108\: \dfrac{cal} {g\cdot {^\circ C}}\right)(48.3^\circ C) = 782\: cal} \nonumber \]. Spring Design Apps When you mix together two substances with different initial temperatures, the same principles apply. Calculate the initial temperature of the piece of rebar. If the materials don't chemically react, all you need to do to find the final temperature is to assume that both substances will eventually reach the same temperature. If energy is coming out of an object, the total energy of the object decreases, and the values of heat and T are negative. Click on this link to view how a bomb calorimeter is prepared for action. In our previous studies, the approximation of the infinite absorption coefficient of the sensor nanolayer was considered by the example of gold.