(the amount of heat transferred to the liquid when heated)
1. System of actions for obtaining and processing the results of measuring the time of heating a liquid to a certain temperature and changing the temperature of the liquid:
1) check whether an amendment needs to be introduced; if yes, then introduce an amendment;
2) establish how many measurements of a given quantity need to be made;
3) prepare a table for recording and processing observation results;
4) make a set number of measurements of a given value; record the observation results in a table;
5) find the measured value of the quantity as the arithmetic mean of the results of individual observations, taking into account the rule of the spare digit:
6) calculate the absolute deviations of the results of individual measurements from the average:
7) find the random error;
8) find the instrumental error;
9) find the reading error;
10) find the calculation error;
11) find the total absolute error;
12) write down the result indicating the total absolute error.
2. System of actions for constructing a graph of dependence Δ t = f(Δ τ ):
1) draw coordinate axes; The abscissa axis is designated Δ τ , With, and the ordinate axis is Δ t, 0 C;
2) select scales for each of the axes and mark scales on the axes;
3) depict the intervals of Δ values τ and Δ t for every experience;
4) draw a smooth line so that it runs inside the intervals.
3. OG No. 1 – water weighing 100 g at an initial temperature of 18 0 C:
1) to measure temperature we will use a thermometer with a scale up to 100 0 C; To measure the heating time we will use a sixty-second mechanical stopwatch. These instruments do not require corrections;
2) when measuring the heating time to a fixed temperature, random errors are possible. Therefore, we will carry out 5 measurements of time intervals when heated to the same temperature (in calculations this will triple the random error). No random errors were found when measuring temperature. Therefore, we will assume that the absolute error in determining t, 0 C is equal to the instrumental error of the thermometer used, that is, the scale division price 2 0 C (Table 3);
3) create a table for recording and processing measurement results:
| Experience no. | |||||||
| Δt, 0 C | 18 ± 2 | 25 ± 2 | 40 ± 2 | 55 ± 2 | 70 ± 2 | 85 ± 2 | 100 ± 2 |
| τ 1 , s | 29,0 | 80,0 | 145,0 | 210,0 | 270,0 | 325,0 | |
| t 2 , s | 25,0 | 90,0 | 147,0 | 205,0 | 265,0 | 327,0 | |
| t 3 , s | 30,0 | 85,0 | 150,0 | 210,0 | 269,0 | 330,0 | |
| t 4 , s | 27,0 | 89,0 | 143,0 | 202,0 | 272,0 | 330,0 | |
| t 5 , s | 26,0 | 87,0 | 149,0 | 207,0 | 269,0 | 329,0 | |
| t avg, s | 27,4 | 86,2 | 146,8 | 206,8 | 269,0 | 328,2 |
4) the results of the measurements are entered into the table;
5) arithmetic mean of each measurement τ calculated and indicated in the last row of the table;
for temperature 25 0 C:
7) find the random measurement error:
8) in each case, we find the instrumental error of the stopwatch taking into account the full circles made by the second hand (that is, if one full circle gives an error of 1.5 s, then half a circle gives 0.75 s, and 2.3 circles - 3.45 s) . In the first experiment Δ t and= 0.7 s;
9) we take the counting error of a mechanical stopwatch equal to one scale division: Δ t o= 1.0 s;
10) calculation error in in this case equal to zero;
11) calculate the total absolute error:
Δ t = Δ tC + Δ t and + Δ t 0 + Δ tB= 4.44 + 0.7 + 1.0 + 0 = 6.14 s ≈ 6.1 s;
(here the final result is rounded down to one significant figure);
12) write down the measurement result: t= (27.4 ± 6.1) s
6 a) calculate the absolute deviations of the results of individual observations from the average for temperature 40 0 C:
Δ t and= 2.0 s;
t o= 1.0 s;
Δ t = Δ tC + Δ t and + Δ t 0 + Δ tB= 8.88 + 2.0 + 1.0 + 0 = 11.88 s ≈ 11.9 s;
t= (86.2 ± 11.9) s
for temperature 55 0 C:
Δ t and= 3.5 s;
t o= 1.0 s;
Δ t = Δ tC + Δ t and + Δ t 0 + Δ tB= 6.72 + 3.5 + 1.0 + 0 = 11.22 s ≈ 11.2 s;
t= (146.8 ± 11.2) s
for temperature 70 0 C:
Δ t and= 5.0 s;
t o= 1.0 s;
Δ t= Δ tC + Δ t and + Δ t 0 + Δ tB= 7.92 + 5.0 + 1.0 + 0 = 13.92 s ≈ 13.9 s;
12 c) write down the measurement result: t= (206.8 ± 13.9) s
for temperature 85 0 C:
Δ t and= 6.4 s;
9 d) counting error of a mechanical stopwatch Δt o = 1.0 s;
Δt = Δt C + Δt and + Δt 0 + Δt B = 4.8 + 6.4 + 1.0 + 0 = 12.2 s;
t= (269.0 ± 12.2) s
for temperature 100 0 C:
Δ t and= 8.0 s;
t o= 1.0 s;
10 e) the calculation error in this case is zero;
Δ t = Δ tC + Δ t and + Δ t 0 + Δ tB= 5.28 + 8.0 + 1.0 + 0 = 14.28 s ≈ 14.3 s;
t= (328.2 ± 14.3) s.
We present the calculation results in the form of a table, which shows the differences between the final and initial temperatures in each experiment and the time of heating the water.
4. Let’s plot the dependence of the change in water temperature on the amount of heat (heating time) (Fig. 14). When constructing, in all cases the interval of error in time measurement is indicated. The line thickness corresponds to the temperature measurement error.
Rice. 14. Graph of the change in water temperature versus the time of its heating
5. We establish that the graph we obtained is similar to a graph of direct proportionality y=kx. Coefficient value k in this case it is not difficult to determine from the graph. Therefore, we can finally write Δ t= 0.25Δ τ . From the plotted graph we can conclude that the water temperature is directly proportional to the amount of heat.
6. Repeat all measurements for OR No. 2 – sunflower oil
.
The last row in the table shows the average results.
| t, 0 C | 18 ± 2 | 25 ± 2 | 40 ± 2 | 55 ± 2 | 70 ± 2 | 85 ± 2 | 100 ± 2 |
| t 1, c | 10,0 | 38,0 | 60,0 | 88,0 | 110,0 | 136,0 | |
| t 2, c | 11,0 | 36,0 | 63,0 | 89,0 | 115,0 | 134,0 | |
| t 3, c | 10,0 | 37,0 | 62,0 | 85,0 | 112,0 | 140,0 | |
| t 4, c | 9,0 | 38,0 | 63,0 | 87,0 | 112,0 | 140,0 | |
| t 5, c | 12,0 | 35,0 | 60,0 | 87,0 | 114,0 | 139,0 | |
| t avg, c | 10,4 | 36,8 | 61,6 | 87,2 | 112,6 | 137,8 |
6) calculate the modules of absolute deviations of the results of individual observations from the average for temperature 25 0 C:
1) find the random measurement error:
2) we find the instrumental error of the stopwatch in each case in the same way as in the first series of experiments. In the first experiment Δ t and= 0.3 s;
3) the counting error of a mechanical stopwatch is taken equal to one scale division: Δ t o= 1.0 s;
4) the calculation error in this case is zero;
5) calculate the total absolute error:
Δ t = Δ tC + Δ t and + Δ t 0 + Δ tB= 2.64 + 0.3 + 1.0 + 0 = 3.94 s ≈ 3.9 s;
6) write down the measurement result: t= (10.4 ± 3.9) s
6 a) We calculate the absolute deviations of the results of individual observations from the average for temperature 40 0 C:
7 a) we find the random measurement error:
8 a) instrumental error of the stopwatch in the second experiment
Δ t and= 0.8 s;
9 a) counting error of a mechanical stopwatch Δ t o= 1.0 s;
10 a) the calculation error in this case is zero;
11 a) calculate the total absolute error:
Δ t = Δ tC + Δ t and + Δ t 0 + Δ tB= 3.12 + 0.8 + 1.0 + 0 = 4.92 s ≈ 4.9 s;
12 a) write down the measurement result: t= (36.8 ± 4.9) s
6 b) calculate the absolute deviations of the results of individual observations from the average for temperature 55 0 C:
7 b) we find the random measurement error:
8 b) instrumental error of the stopwatch in this experiment
Δ t and= 1.5 s;
9 b) counting error of a mechanical stopwatch Δ t o= 1.0 s;
10 b) the calculation error in this case is zero;
11 b) calculate the total absolute error:
Δ t = Δ tC + Δ t and + Δ t 0 + Δ tB= 3.84 + 1.5 + 1.0 + 0 = 6.34 s ≈ 6.3 s;
12 b) write down the measurement result: t= (61.6 ± 6.3) s
6 c) calculate the absolute deviations of the results of individual observations from the average for temperature 70 0 C:
7 c) we find the random measurement error:
8 c) instrumental error of the stopwatch in this experiment
Δ t and= 2.1 s;
9 c) counting error of a mechanical stopwatch Δ t o= 1.0 s;
10 c) the calculation error in this case is zero;
11 c) calculate the total absolute error:
Δ t = Δ tC + Δ t and + Δ t 0 + Δ tB= 2.52 + 2.1 + 1.0 + 0 = 5.62 s ≈ 5.6 s;
12 c) write down the measurement result: t= (87.2 ± 5.6) s
6 d) calculate the absolute deviations of the results of individual observations from the average for temperature 85 0 C:
7 d) we find the random measurement error:
8 d) instrumental error of the stopwatch in this experiment
Δ t and= 2.7 s;
9 d) counting error of a mechanical stopwatch Δ t o= 1.0 s;
10 d) the calculation error in this case is zero;
11 d) calculate the total absolute error:
Δ t = Δ tC + Δ t and + Δ t 0 + Δ tB= 4.56 + 2.7 + 1.0 + 0 = 8.26 s ≈ 8.3;
12 d) write down the measurement result: t= (112.6 ± 8.3) s
6 e) calculate the absolute deviations of the results of individual observations from the average for temperature 100 0 C:
7 e) we find the random measurement error:
8 d) instrumental error of the stopwatch in this experiment
Δ t and= 3.4 s;
9 d) counting error of a mechanical stopwatch Δ t o= 1.0 s;
10 e) the calculation error in this case is zero.
11 e) calculate the total absolute error:
Δ t = Δ tC + Δ t and + Δ t 0 + Δ tB= 5.28 + 3.4 + 1.0 + 0 = 9.68 s ≈ 9.7 s;
12 d) write down the measurement result: t= (137.8 ± 9.7) s.
We present the calculation results in the form of a table, which shows the differences between the final and initial temperatures in each experiment and the heating time of sunflower oil.
7. Let's plot the dependence of the change in oil temperature on the heating time (Fig. 15). When constructing, in all cases the interval of error in time measurement is indicated. The line thickness corresponds to the temperature measurement error.
Rice. 15. Graph of the change in water temperature versus the time of its heating
8. The constructed graph is similar to a direct proportional graph y=kx. Coefficient value k in this case it is not difficult to find from the graph. Therefore, we can finally write Δ t= 0.6Δ τ .
From the plotted graph we can conclude that the temperature of sunflower oil is directly proportional to the amount of heat.
9. We formulate the answer to the PP: the temperature of the liquid is directly proportional to the amount of heat received by the body when heated.
Example 3. PZ: set the type of dependence of the output voltage on the resistor R n on the value of the equivalent resistance of the circuit section AB (the problem is solved in an experimental setup, circuit diagram which is shown in Fig. 16).
To solve this problem you need to do the following:
1. Create a system of actions for obtaining and processing the results of measuring the equivalent resistance of a circuit section and the voltage across the load R n(see clause 2.2.8 or clause 2.2.9).
2. Create a system of actions to plot the dependence of the output voltage (on the resistor R n) from the equivalent resistance of the circuit section AB.
3. Select OP No. 1 – area with a certain value R n1 and complete all the actions planned in steps 1 and 2.
4. Select a functional dependence known in mathematics, the graph of which is similar to the experimental curve.
5. Write mathematically this functional relationship for the load R n1 and formulate for her an answer to the given cognitive task.
6. Select OP No. 2 – section of the aircraft with a different resistance value R n2 and perform the same system of actions with it.
7. Select a functional dependence known in mathematics, the graph of which is similar to the experimental curve.
8. Write down this functional relationship for resistance mathematically R n2 and formulate for him an answer to the given cognitive task.
9. Formulate the functional relationship between quantities in a generalized form.
Report on identifying the type of dependence of the output voltage on the resistance R n from the equivalent resistance of the circuit section AB
(provided in an abbreviated version)
The independent variable is the equivalent resistance of the circuit section AB, which is measured using a digital voltmeter connected to points A and B of the circuit. The measurements were carried out at a limit of 1000 Ohms, that is, the measurement accuracy is equal to the value of the least significant digit, which corresponds to ±1 Ohm.
The dependent variable was the value of the output voltage taken across the load resistance (points B and C). As measuring instrument a digital voltmeter with a minimum discharge of hundredths of a volt was used.
Rice. 16. Diagram of an experimental setup for studying the type of dependence of the output voltage on the value of the equivalent circuit resistance
The equivalent resistance was changed using keys Q 1, Q 2 and Q 3. For convenience, we will denote the on state of the key as “1”, and the off state as “0”. In this chain, only 8 combinations are possible.
For each combination, the output voltage was measured 5 times.
The following results were obtained during the study:
| Experience number | Key status | Equivalent resistance R E, Ohm | Output voltage, U out, IN | |||||
| U 1,IN | U 2, IN | U 3, IN | U 4, IN | U 5, IN | ||||
| Q 3 Q 2 Q 1 | ||||||||
| 0 0 0 | 0,00 | 0,00 | 0,00 | 0,00 | 0,00 | |||
| 0 0 1 | 800 ± 1 | 1,36 | 1,35 | 1,37 | 1,37 | 1,36 | ||
| 0 1 0 | 400 ± 1 | 2,66 | 2,67 | 2,65 | 2,67 | 2,68 | ||
| 0 1 1 | 267 ± 1 | 4,00 | 4,03 | 4,03 | 4,01 | 4,03 | ||
| 1 0 0 | 200 ± 1 | 5,35 | 5,37 | 5,36 | 5,33 | 5,34 | ||
| 1 0 1 | 160 ± 1 | 6,70 | 6,72 | 6,73 | 6,70 | 6,72 | ||
| 1 1 0 | 133 ± 1 | 8,05 | 8,10 | 8,05 | 8,00 | 8,10 | ||
| 1 1 1 | 114 ± 1 | 9,37 | 9,36 | 9,37 | 9,36 | 9,35 |
The results of experimental data processing are presented in the following table:
| № | Q 3 Q 2 Q 1 | R E, Ohm | U avg, IN | U avg. env. , IN | Δ U avg, IN | Δ U and, IN | Δ U o, IN | Δ U in, IN | Δ U, IN | U, IN |
| 0 0 0 | 0,00 | 0,00 | 0,00 | 0,01 | 0,01 | 0,00 | 0,02 | 0.00±0.02 | ||
| 0 0 1 | 800±1 | 1,362 | 1,36 | 0,0192 | 0,01 | 0,01 | 0,002 | 0,0412 | 1.36±0.04 | |
| 0 1 0 | 400±1 | 2,666 | 2,67 | 0,0264 | 0,01 | 0,01 | 0,004 | 0,0504 | 2.67±0.05 | |
| 0 1 1 | 267±1 | 4,02 | 4,02 | 0,036 | 0,01 | 0,01 | 0,00 | 0,056 | 4.02±0.06 | |
| 1 0 0 | 200±1 | 5,35 | 5,35 | 0,036 | 0,01 | 0,01 | 0,00 | 0,056 | 5.35±0.06 | |
| 1 0 1 | 160±1 | 6,714 | 6,71 | 0,0336 | 0,01 | 0,01 | 0,004 | 0,0576 | 6.71±0.06 | |
| 1 1 0 | 133±1 | 8,06 | 8,06 | 0,096 | 0,01 | 0,01 | 0,00 | 0,116 | 8.06±0.12 | |
| 1 1 1 | 114±1 | 9,362 | 9,36 | 0,0192 | 0,01 | 0,01 | 0,002 | 0,0412 | 9.36±0.04 |
We plot the dependence of the output voltage on the value of the equivalent resistance U = f(R E).
When plotting a graph, the line length corresponds to the measurement error Δ U, individual for each experiment (maximum error Δ U= 0.116 V, which corresponds to approximately 2.5 mm on the graph at the selected scale). The thickness of the line corresponds to the measurement error of the equivalent resistance. The resulting graph is shown in Fig. 17.
Rice. 17. Output voltage graph
from the value of equivalent resistance in section AB
The graph resembles an inverse proportional graph. To verify this, let's plot the dependence of the output voltage on the reciprocal of the equivalent resistance U = f(1/R E), that is, from conductivity σ chains. For convenience, we present the data for this graph in the form of the following table:
The resulting graph (Fig. 18) confirms the assumption made: the output voltage at the load resistance R n1 inversely proportional to the equivalent resistance of the circuit section AB: U = 0,0017/R E.
We select another object of study: OI No. 2 – another value of load resistance R n2, and perform all the same actions. We get a similar result, but with a different coefficient k.
We formulate the answer to the PZ: output voltage across the load resistance R n inversely proportional to the value of the equivalent resistance of a circuit section consisting of three parallel-connected conductors, which can be connected in one of eight combinations.
Rice. 18. Graph of the dependence of the output voltage on the conductivity of the AB circuit section
Note that the scheme under consideration is digital-to-analog converter (DAC) – a device that converts a digital code (in this case, binary) into an analog signal (in this case, into voltage).
Planning activities to solve cognitive problem No. 4
Experimental determination of a specific value of a specific physical quantity(solving cognitive problem No. 4) can be carried out in two situations: 1) the method for finding the specified physical quantity is unknown and 2) the method for finding this quantity has already been developed. In the first situation, there is a need to develop a method (system of actions) and select equipment for its practical implementation. In the second situation, there is a need to study this method, that is, to find out what equipment should be used for the practical implementation of this method and what should be the system of actions, the sequential implementation of which will allow obtaining a specific value of a specific value in specific situation. Common to both situations is the expression of the desired quantity in terms of other quantities, the value of which can be found by direct measurement. They say that in this case a person carries out an indirect measurement.
Values obtained by indirect measurement are inaccurate. This is understandable: they are found based on the results of direct measurements, which are always inaccurate. In this regard, the system of actions to solve cognitive problem No. 4 must necessarily include actions to calculate errors.
To find errors in indirect measurements, two methods have been developed: the method of error boundaries and the method of boundaries. Let's consider the content of each of them.
Error bounds method
The error bounds method is based on differentiation.
Let the indirectly measured quantity at is a function of several arguments: y = f(X 1, X 2, …, X N).
Quantities X 1, X 2, ..., X n measured by direct methods with absolute errors Δ X 1,Δ X 2,...,Δ X N. As a result, the value at will also be found with some error Δ u.
Usually Δ X 1<< Х 1, Δ X 2<< Х 2 , …, Δ X N<< Х n , Δ y<< у. Therefore, we can go to infinitesimal quantities, that is, replace Δ X 1,Δ X 2,...,Δ XN,Δ y their differentials dХ 1, dХ 2, ..., dХ N, dy respectively. Then the relative error
the relative error of a function is equal to the differential of its natural logarithm.
On the right side of the equality, instead of differentials of variable quantities, their absolute errors are substituted, and instead of the quantities themselves, their average values are substituted. In order to determine the upper limit of the error, the algebraic summation of errors is replaced by arithmetic summation.
Knowing the relative error, find the absolute error
Δ at= ε u ּу,
where instead of at substitute the value obtained as a result of the measurement
U ism = f (<X 1>, <Х 2 >, ..., <Х n > ).
All intermediate calculations are performed according to the rules of approximate calculations with one spare digit. The final result and errors are rounded according to general rules. The answer is written in the form
Y = Y meas.± Δ U; ε y = ...
Expressions for relative and absolute errors depend on the type of function u. The main formulas often encountered when performing laboratory work are presented in Table 5.
The same substance in the real world, depending on environmental conditions, can be in different states. For example, water can be in the form of a liquid, in the idea of a solid - ice, in the form of a gas - water vapor.
- These states are called aggregate states of matter.
Molecules of a substance in different states of aggregation are no different from each other. The specific state of aggregation is determined by the location of the molecules, as well as the nature of their movement and interaction with each other.
Gas - the distance between molecules is much greater than the size of the molecules themselves. Molecules in liquids and solids are located quite close to each other. In solids it is even closer.
To change the state of aggregation of the body, it needs to impart some energy. For example, in order to convert water into steam, it must be heated. For steam to become water again, it must give up energy.
Transition from solid to liquid
The transition of a substance from solid to liquid is called melting. In order for a body to begin to melt, it must be heated to a certain temperature. The temperature at which a substance melts is is called the melting point of a substance.
Each substance has its own melting point. For some bodies it is very low, for example, for ice. And some bodies have a very high melting point, for example, iron. In general, melting a crystalline body is a complex process.
Ice Melt Graph
The figure below shows a graph of the melting of a crystalline body, in this case ice.
- The graph shows the dependence of the ice temperature on the time it is heated. Temperature is shown on the vertical axis, and time is shown on the horizontal axis.
From the graph that initially the ice temperature was -20 degrees. Then they started heating it up. The temperature began to rise. Section AB is the section where the ice is heated. Over time, the temperature increased to 0 degrees. This temperature is considered the melting point of ice. At this temperature, the ice began to melt, but its temperature stopped increasing, although the ice also continued to be heated. The melting area corresponds to the BC area on the graph.
Then, when all the ice melted and turned into liquid, the temperature of the water began to increase again. This is shown on the graph by ray C. That is, we conclude that during melting the body temperature does not change, All incoming energy is used for melting.
1. Plot a graph of temperature (t i) (for example t 2) versus heating time (t, min). Make sure that steady state has been achieved.
3. Only for the stationary mode, calculate the values and lnA, enter the calculation results into the table.
4. Construct a graph of the dependence on x i, taking the position of the first thermocouple x 1 = 0 as the reference point (the coordinates of the thermocouples are indicated on the installation). Draw a straight line along the marked points.
5. Determine the average tangent of the angle of inclination or
6. Using formula (10), taking into account (11), calculate the thermal conductivity coefficient of the metal and determine the measurement error.
7. Using a reference book, determine the metal from which the rod is made.
Control questions
1. What phenomenon is called thermal conductivity? Write down its equation. What characterizes the temperature gradient?
2. What is the carrier of thermal energy in metals?
3. What mode is called stationary? Derive equation (5) describing this mode.
4. Derive formula (10) for the thermal conductivity coefficient.
5. What is a thermocouple? How can you use it to measure the temperature at a certain point on the rod?
6. What is the method for measuring thermal conductivity in this work?
Laboratory work No. 11
Manufacturing and calibration of a temperature sensor based on a thermocouple
Goal of the work: familiarization with the method of manufacturing a thermocouple; manufacturing and calibration of a temperature sensor based on a thermocouple; using a temperature sensor to determine the melting point of Wood's alloy.
Introduction
Temperature is a physical quantity that characterizes the state of thermodynamic equilibrium of a macroscopic system. Under equilibrium conditions, temperature is proportional to the average kinetic energy of thermal motion of body particles. The temperature range at which physical, chemical and other processes occur is extremely wide: from absolute zero to 10 11 K and higher.
Temperature cannot be measured directly; its value is determined by the temperature change of any physical property of the substance convenient for measuring. Such thermometric properties can be: gas pressure, electrical resistance, thermal expansion of a liquid, speed of sound propagation.
When constructing a temperature scale, the temperature values t 1 and t 2 are assigned to two fixed temperature points (the value of the measured physical parameter) x = x 1 and x = x 2, for example, the melting point of ice and the boiling point of water. The temperature difference t 2 – t 1 is called the main temperature interval of the scale. The temperature scale is a specific functional numerical relationship between temperature and the values of the measured thermometric property. An unlimited number of temperature scales are possible, differing in thermometric properties, the accepted dependence t(x) and the temperatures of fixed points. For example, there are Celsius, Reaumur, Fahrenheit, etc. scales. The fundamental disadvantage of empirical temperature scales is their dependence on the thermometric substance. This disadvantage is absent in the thermodynamic temperature scale, which is based on the second law of thermodynamics. For equilibrium processes the following equality holds:
where: Q 1 – the amount of heat received by the system from the heater at temperature T 1; and Q 2 is the amount of heat given to the refrigerator at temperature T 2 . The relationships do not depend on the properties of the working fluid and make it possible to determine the thermodynamic temperature using the quantities Q 1 and Q 2 available for measurements. It is generally accepted that T 1 = 0 K – at absolute zero temperature and T 2 = 273.16 K at the triple point of water. Temperature on the thermodynamic scale is expressed in degrees Kelvin (0 K). Introduction T 1 = 0 is an extrapolation and does not require the implementation of absolute zero.
When measuring thermodynamic temperature, one of the strict consequences of the second law of thermodynamics is usually used, which connects a conveniently measured thermodynamic property with thermodynamic temperature. Among such relationships: the laws of ideal gas, the laws of black body radiation, etc. Over a wide temperature range, approximately from the boiling point of helium to the solidification point of gold, a gas thermometer provides the most accurate measurements of thermodynamic temperature.
In practice, measuring temperature on a thermodynamic scale is difficult. The value of this temperature is usually indicated on a convenient secondary thermometer, which is more stable and sensitive than instruments that reproduce a thermodynamic scale. Secondary thermometers are calibrated according to highly stable reference points, the temperatures of which on the thermodynamic scale were previously found by extremely accurate measurements.
In this work, a thermocouple (contact of two different metals) is used as a secondary thermometer, and the melting and boiling points of various substances are used as reference points. The thermometric property of a thermocouple is the contact potential difference.
A thermocouple is a closed electrical circuit containing two junctions of two different metal conductors. If the temperature of the junctions is different, then an electric current due to the thermoelectromotive force will flow in the circuit. The magnitude of the thermoelectromotive force e is proportional to the temperature difference:
where k-const, if the temperature difference is not very large.
The value of k usually does not exceed several tens of microvolts per degree and depends on the materials from which the thermocouple is made.
Exercise 1. Making a thermocouple
Study of the cooling rate of water in a vessel
under different conditions
The command ran:
Team number:
Yaroslavl, 2013
Brief description of the study parameters
Temperature
The concept of body temperature seems simple and understandable at first glance. From everyday experience, everyone knows that there are hot and cold bodies.
Experiments and observations show that when two bodies come into contact, one of which we perceive as hot and the other as cold, changes in the physical parameters of both the first and second bodies occur. “A physical quantity measured by a thermometer and the same for all bodies or parts of the body that are in thermodynamic equilibrium with each other is called temperature.” When the thermometer is brought into contact with the body being studied, we see various kinds of changes: a “column” of liquid moves, the volume of gas changes, etc. But soon thermodynamic equilibrium necessarily occurs between the thermometer and the body - a state in which all quantities characterizing these bodies: their masses, volumes, pressures, and so on. From this moment on, the thermometer shows not only its own temperature, but also the temperature of the body being studied. In everyday life, the most common way to measure temperature is using a liquid thermometer. Here, the property of liquids to expand when heated is used to measure temperature. To measure the temperature of a body, the thermometer is brought into contact with it, and a heat transfer process occurs between the body and the thermometer until thermal equilibrium is established. To ensure that the measurement process does not noticeably change the body temperature, the mass of the thermometer must be significantly less than the mass of the body whose temperature is being measured.
Heat exchange
Almost all phenomena of the external world and various changes in the human body are accompanied by changes in temperature. Heat exchange phenomena accompany all of our daily lives.
At the end of the 17th century, the famous English physicist Isaac Newton expressed a hypothesis: “the rate of heat exchange between two bodies is greater, the more their temperatures differ (by heat exchange rate we mean the change in temperature per unit time). Heat transfer always occurs in a certain direction: from bodies with a higher temperature to bodies with a lower temperature. Numerous observations convince us of this, even at the everyday level (a spoon in a glass of tea heats up, but the tea cools down). When the temperature of the bodies equalizes, the heat exchange process stops, i.e., thermal equilibrium occurs.
A simple and understandable statement that heat independently moves only from bodies with a higher temperature to bodies with a lower temperature, and not vice versa, is one of the fundamental laws in physics, and is called the II law of thermodynamics, this law was formulated in the 18th century by the German scientist Rudolf Clausius.
Studycooling rate of water in a vessel under different conditions
Hypothesis: We assume that the rate of cooling of water in the vessel depends on the layer of liquid (butter, milk) poured onto the surface of the water.
Target: Determine whether the surface layer of butter and the surface layer of milk affect the cooling rate of water.
Tasks:
1. Study the phenomenon of water cooling.
2. Determine the dependence of the cooling temperature of water with a surface layer of oil on time, write the results in the table.
3. Determine the dependence of the cooling temperature of water with the surface layer of milk on time, write the results in the table.
4. Construct dependency graphs and analyze the results.
5. Draw a conclusion about which surface layer on the water has a greater influence on the rate of cooling of the water.
Equipment: laboratory glass, stopwatch, thermometer.
Experimental plan:
1. Determining the value of the thermometer scale division.
2. Measure the water temperature while cooling every 2 minutes.
3. Measure the temperature while cooling the water with a surface layer of oil every 2 minutes.
4. Measure the temperature while cooling the water with the surface layer of milk every 2 minutes.
5. Enter the measurement results into the table.
6. Using the table data, construct graphs of water temperature versus time.
8. Analyze the results and give their rationale.
9. Draw a conclusion.
Completing of the work
First, we heated water in 3 glasses to a temperature of 71.5⁰C. Then we poured vegetable oil into one of the glasses and milk into the other. The oil was distributed over the surface of the water, forming an even layer. Vegetable oil is a product extracted from plant materials and consisting of fatty acids and related substances. The milk was mixed with water (forming an emulsion), this indicated that the milk was either diluted with water and did not correspond to the fat content stated on the package, or was made from a dry product, and in both cases the physical properties of the milk changed. Natural milk, undiluted with water, forms a clot in water and does not dissolve for some time. To determine the cooling time of liquids, we recorded the cooling temperature every 2 minutes.
Table. Study of cooling time of liquids.
|
liquid | |||||||||||
water, t,⁰С | |||||||||||
water with oil, t,⁰С | |||||||||||
water with milk, t,⁰С |
According to the table, we see that the initial conditions in all experiments were the same, but after 20 minutes of the experiment, the liquids have different temperatures, which means they have different cooling rates of the liquid.
This is presented more clearly in the graph.
In the coordinate plane with axes temperature and time, points were marked that display the relationship between these quantities. Averaging the values, we drew a line. The graph shows a linear dependence of the water cooling temperature on the cooling time under various conditions.
Let's calculate the cooling rate of water:
a) for water
0-10 min 
(ºС/min)
10-20 min (ºС/min)
b) for water with a surface layer of oil
0-10 min 
(ºС/min)
10-20 min 
(ºС/min)
b) for water with milk
0-10 min 
(ºС/min)
10-20 min 
(ºС/min)
As can be seen from the calculations, water and oil cooled the slowest. This is due to the fact that the oil layer does not allow the water to intensively exchange heat with the air. This means the heat exchange between water and air slows down, the rate of water cooling decreases, and the water remains hotter longer. This can be used when cooking, for example when cooking pasta; after boiling water, add oil, the pasta will cook faster and will not stick together.
Water without any additives has the fastest cooling rate, which means it will cool faster.
Conclusion: thus, we have experimentally verified that the surface layer of oil has a greater influence on the cooling rate of water, the cooling rate decreases and the water cools more slowly.
