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In the process of boiling a liquid, preheated to the boiling point, the energy imparted to it goes
1) to increase the average speed of the molecules
2) to increase the average speed of movement of molecules and to overcome the forces of interaction between molecules
3) to overcome the forces of interaction between molecules without increasing the average speed of their movement
4) to increase the average speed of movement of molecules and to increase the forces of interaction between molecules
Decision.
When boiling, the temperature of the liquid does not change, but the process of transition to another state of aggregation occurs. The formation of another state of aggregation occurs with overcoming the forces of interaction between molecules. The constancy of temperature also means the constancy of the average velocity of the molecules.
Answer: 3
Source: GIA in Physics. main wave. Option 1313.
An open vessel with water is placed in a laboratory, which maintains a certain temperature and humidity. The rate of evaporation will be equal to the rate of condensation of water in the vessel
1) only if the temperature in the laboratory is more than 25 °C
2) only under the condition that the humidity in the laboratory is 100%
3) only on condition that the temperature in the laboratory is less than 25 ° C, and the air humidity is less than 100%
4) at any temperature and humidity in the laboratory
Decision.
The rate of evaporation will be equal to the rate of condensation of water in the vessel only if the humidity in the laboratory is 100%, regardless of temperature. In this case, dynamic equilibrium will be observed: how many molecules evaporated, the same number condensed.
The correct answer is numbered 2.
Answer: 2
Source: GIA in Physics. main wave. Option 1326.
1) to heat 1 kg of steel by 1 °C, it is necessary to spend 500 J of energy
2) to heat 500 kg of steel by 1 °C, it is necessary to expend 1 J of energy
3) to heat 1 kg of steel by 500 °C, it is necessary to expend 1 J of energy
4) to heat 500 kg of steel by 1 °C, it is necessary to spend 500 J of energy
Decision.
Specific heat capacity characterizes the amount of energy that must be imparted to one kilogram of a substance for the one of which the body consists, in order to heat it by one degree Celsius. Thus, to heat 1 kg of steel by 1 °C, it is necessary to expend 500 J of energy.
The correct answer is numbered 1.
Answer: 1
Source: GIA in Physics. main wave. Far East. Option 1327.
The specific heat capacity of steel is 500 J/kg °C. What does this mean?
1) when 1 kg of steel is cooled by 1 ° C, energy of 500 J is released
2) when 500 kg of steel is cooled by 1 ° C, energy of 1 J is released
3) when cooling 1 kg of steel at 500 ° C, energy of 1 J is released
4) when cooling 500 kg of steel, 500 J of energy is released by 1 ° C
Decision.
Specific heat capacity characterizes the amount of energy that must be imparted to one kilogram of a substance in order to heat it by one degree Celsius. Thus, to heat 1 kg of steel by 1 °C, it is necessary to expend 500 J of energy.
The correct answer is numbered 1.
Answer: 1
Source: GIA in Physics. main wave. Far East. Option 1328.
Regina Magadeeva 09.04.2016 18:54
In the textbook of the eighth grade, my definition of specific heat capacity looks like this: a physical quantity numerically equal to the amount of heat that must be transferred to a body with a mass of 1 kg in order for its temperature! to change! by 1 degree. The solution says that the specific heat capacity is needed in order to heat up by 1 degree.
1. Plot temperature (t i) (for example t 2) versus heating time (t, min). Verify that steady state is reached.
3. Calculate the values of and lnA only for the stationary mode, enter the results of the calculations in the table.
4. Construct a graph of the dependence on x i , taking the position of the first thermocouple x 1 = 0 as the origin (the coordinates of the thermocouples are indicated on the installation). Draw a straight line through the given points.
5. Determine the average tangent of the slope or
6. Using formula (10), taking into account (11), calculate the thermal conductivity of the metal and determine the measurement error.
7. Using a reference book, determine the metal from which the rod is made.
test questions
1. What phenomenon is called thermal conductivity? Write down his equation. What characterizes the temperature gradient?
2. What is the carrier of thermal energy in metals?
3. What mode is called stationary? Get equation (5) describing this mode.
4. Derive formula (10) for the thermal conductivity coefficient.
5. What is a thermocouple? How can it be used to measure the temperature at a certain point on the rod?
6. What is the method for measuring thermal conductivity in this work?
Lab #11
Fabrication and calibration of a temperature sensor based on a thermocouple
Objective: familiarization with the method of manufacturing a thermocouple; manufacturing and calibration of a temperature sensor based on a thermocouple; using a temperature probe 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, the temperature is proportional to the average kinetic energy of the thermal motion of body particles. The range of temperatures at which physical, chemical and other processes take place is extremely wide: from absolute zero to 10 11 K and above.
Temperature cannot be measured directly; its value is determined by the temperature change of some physical property of the substance that is convenient for measuring. Such thermometric properties can be: gas pressure, electrical resistance, thermal expansion of a liquid, sound propagation speed.
When constructing a temperature scale, the temperature value t 1 and t 2 is assigned to two fixed temperature points (the value of the measured physical parameter) x \u003d x 1 and x \u003d 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 of temperature with the values of the measured thermometric property. An unlimited number of temperature scales is possible, differing in thermometric property, accepted dependence t(x) and temperatures of fixed points. For example, there are scales of Celsius, Réaumur, Fahrenheit, and others. The fundamental disadvantage of empirical temperature scales is their dependence on the thermometric substance. This shortcoming is absent in the thermodynamic temperature scale based on the second law of thermodynamics. For equilibrium processes, the equality is true:
where: Q 1 - the amount of heat received by the system from the heater at temperature T 1; and Q 2 - the amount of heat given to the refrigerator at a temperature of T 2. The ratios do not depend on the properties of the working fluid and make it possible to determine the thermodynamic temperature from the values Q 1 and Q 2 available for measurements. It is customary to consider T 1 \u003d 0 K - at absolute zero temperatures and T 2 \u003d 273.16 K at the triple point of water. The temperature on the thermodynamic scale is expressed in degrees Kelvin (0 K). The introduction of 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 an ideal gas, the laws of black body radiation, etc. Over a wide range of temperatures, roughly from the boiling point of helium to the solidification point of gold, the most accurate thermodynamic temperature measurements are provided by a gas thermometer.
In practice, measuring temperature on a thermodynamic scale is difficult. The value of this temperature is usually marked on a convenient secondary thermometer, which is more stable and sensitive than instruments reproducing the thermodynamic scale. Secondary thermometers are calibrated according to highly stable reference points, the temperatures of which, according to the thermodynamic scale, are found in advance by extremely accurate measurements.
In this paper, a thermocouple (the contact of two different metals) is used as a secondary thermometer, and the melting and boiling temperatures 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 the electric current due to the thermoelectromotive force will flow in the circuit. The value of thermoelectromotive force e is proportional to the temperature difference:
where k is 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. Thermocouple manufacturing
Study of the rate of cooling of water in a vessel
under various conditions
Executed the command:
Team number:
Yaroslavl, 2013
Brief description of study parameters
Temperature
The concept of body temperature seems at first glance simple and understandable. Everyone knows from everyday experience that there are hot and cold bodies.
Experiments and observations show that when two bodies come into contact, of which we perceive one as hot and the other as cold, changes in the physical parameters of both the first and second bodies occur. “The 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 under study, we see various kinds of changes: a “column” of liquid moves, the volume of gas changes, etc. But soon thermodynamic equilibrium necessarily sets in between the thermometer and the body - a state in which all quantities characterizing these bodies: their masses, volumes, pressures, and so on. From this point 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 with a liquid thermometer. Here, the property of liquids to expand when heated is used to measure temperature. To measure the temperature of a body, a thermometer is brought into contact with it, a heat transfer process is carried out between the body and the thermometer until thermal equilibrium is established. In order for the measurement process not to 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 a change in temperature. The phenomena of heat transfer accompany all our daily life.
At the end of the 17th century, the famous English physicist Isaac Newton hypothesized: “The rate of heat transfer between two bodies is the greater, the more their temperatures differ (by the rate of heat transfer 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 one. We are convinced of this by numerous observations, even at the household level (a spoon in a glass of tea heats up, and the tea cools down). When the temperature of the bodies equalizes, the heat transfer process stops, i.e., thermal equilibrium sets in.
A simple and understandable statement that heat independently transfers 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 various conditions
Hypothesis: We assume that the rate of cooling of water in a vessel depends on the layer of liquid (oil, milk) poured onto the surface of the water.
Target: Determine whether the surface layer of butter and the surface layer of milk affect the rate of cooling of water.
Tasks:
1. Study the phenomenon of water cooling.
2. Determine the dependence of the cooling temperature of water with the surface layer of oil on time, write the results in a table.
3. Determine the dependence of the cooling temperature of water with a surface layer of milk on time, write the results in a table.
4. Build dependency graphs, analyze the results.
5. Make a conclusion about which surface layer on the water has a greater influence on the rate of cooling of water.
Equipment: laboratory glass, stopwatch, thermometer.
Experiment plan:
1. Determination of the division value of the thermometer scale.
2. Measure the water temperature during cooling every 2 minutes.
3. Measure the temperature when the water with the surface layer of oil cools every 2 minutes.
4. Measure the temperature when the water with the surface layer of milk cools down every 2 minutes.
5. Record the measurement results in a table.
6. According to the table, draw graphs of the dependences of the water temperature on time.
8. Analyze the results and give their rationale.
9. Make 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 spread over the surface of the water, forming an even layer. Vegetable oil is a product extracted from vegetable raw materials and consisting of fatty acids and related substances. Milk 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 it was made from a dry product, and in both cases the physical properties of the milk change. Natural milk undiluted with water in water is collected in a clot and does not dissolve for some time. To determine the cooling time of liquids, we fixed the cooling temperature every 2 minutes.
Table. Study of the 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 shown more clearly in the graph.
In the coordinate plane with the axes temperature and time marked points displaying the relationship between these quantities. Averaging the values, draw a line. The graph shows a linear dependence of the cooling temperature of water on the cooling time under various conditions.
Calculate the rate of cooling 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 with oil cooled the slowest. This is due to the fact that the oil layer does not allow water to intensively exchange heat with air. This means that the heat exchange of water with air slows down, the rate of cooling of water 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 highest cooling rate, which means it will cool faster.
Conclusion: thus, we have experimentally verified that the surface layer of oil has a greater effect on the rate of cooling of water, the rate of cooling decreases and the water cools more slowly.
(the amount of heat transferred to the liquid when heated)
1. The system of actions for obtaining and processing the results of measuring the time of heating the liquid to a certain temperature and changing the temperature of the liquid:
1) check if an amendment needs to be introduced; if so, introduce an amendment;
2) determine how many measurements of a given quantity need to be made;
3) prepare a table for recording and processing the results of observations;
4) to make the specified number of measurements of a given quantity; record the results of observations 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 reserve figure rule:
6) calculate the modules of absolute deviations of the results of individual measurements from the average:
7) find a random error;
8) find the instrumental error;
9) find the reading error;
10) find the calculation error;
11) find the total absolute error;
12) record the result indicating the total absolute error.
2. The system of actions for plotting the dependency graph Δ t = f(Δ τ ):
1) draw coordinate axes; denote the abscissa axis Δ τ , with, and the y-axis is Δ t, 0 С;
2) select the scales for each of the axes and apply scales on the axes;
3) depict the intervals of values Δ τ and Δ t for every experience;
4) draw a smooth line so that it runs inside the intervals.
3. OI No. 1 - water weighing 100 g at an initial temperature of 18 0 С:
1) to measure the temperature, we will use a thermometer with a scale of up to 100 0 С; to measure the heating time, we will use a sixty-second mechanical stopwatch. These instruments do not require any adjustments;
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 the calculations, this will triple the random error). When measuring the temperature, no random errors were found. 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 value 2 0 C (Table 3);
3) make a table for recording and processing the measurement results:
| experience number | |||||||
| 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 | |
| t2, 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 | |
| t4, s | 27,0 | 89,0 | 143,0 | 202,0 | 272,0 | 330,0 | |
| t5, s | 26,0 | 87,0 | 149,0 | 207,0 | 269,0 | 329,0 | |
| tav, s | 27,4 | 86,2 | 146,8 | 206,8 | 269,0 | 328,2 |
4) the results of the measurements carried out are entered in the table;
5) arithmetic mean of each measurement τ calculated and indicated in the last line of the table;
for temperature 25 0 C:
7) find a random measurement error:
8) the instrumental error of the stopwatch in each case is found 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) the error of reading a mechanical stopwatch is taken equal to one division of the scale: Δ t about= 1.0 s;
10) the calculation error in this case is zero;
11) calculate the total absolute error:
Δ t = Δ tC + Δ t and + Δ t0 + Δ t B= 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) we calculate the modules of absolute deviations of the results of individual observations from the mean for temperature 40 0 С:
Δ t and= 2.0 s;
t about= 1.0 s;
Δ t = Δ tC + Δ t and + Δ t0 + Δ t B= 8.88 + 2.0 + 1.0 + 0 = 11.88 s ≈ 11.9 s;
t= (86.2 ± 11.9) s
for temperature 55 0 С:
Δ t and= 3.5 s;
t about= 1.0 s;
Δ t = Δ tC + Δ t and + Δ t0 + Δ t B= 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 about= 1.0 s;
Δ t= Δ tC + Δ t and + Δ t0 + Δ t B= 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 С:
Δ t and= 6.4 s;
9 d) mechanical stopwatch reading error Δt о = 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 about= 1.0 s;
10 e) the calculation error in this case is zero;
Δ t = Δ tC + Δ t and + Δ t0 + Δ t B= 5.28 + 8.0 + 1.0 + 0 = 14.28 s ≈ 14.3 s;
t= (328.2 ± 14.3) s.
The results of the calculations are presented in the form of a table, which shows the differences in the final and initial temperatures in each experiment and the time of heating the water.
4. Let's build a graph of the dependence of the change in water temperature on the amount of heat (heating time) (Fig. 14). When plotting, in all cases, the interval of time measurement error is indicated. The line thickness corresponds to the temperature measurement error.
Rice. 14. Graph of the dependence of the change in water temperature on the time of its heating
5. We establish that the graph we received is similar to the graph of direct proportionality y=kx. Coefficient value k in this case, it is easy to determine from the graph. Therefore, we can finally write Δ t= 0.25Δ τ . From the constructed graph, we can conclude that the water temperature is directly proportional to the amount of heat.
6. Repeat all measurements for OI No. 2 - sunflower oil.
In the table, in the last row, the average results are given.
| t, 0C | 18±2 | 25±2 | 40±2 | 55±2 | 70±2 | 85±2 | 100±2 |
| t1, c | 10,0 | 38,0 | 60,0 | 88,0 | 110,0 | 136,0 | |
| t2, c | 11,0 | 36,0 | 63,0 | 89,0 | 115,0 | 134,0 | |
| t3, c | 10,0 | 37,0 | 62,0 | 85,0 | 112,0 | 140,0 | |
| t4, c | 9,0 | 38,0 | 63,0 | 87,0 | 112,0 | 140,0 | |
| t5, c | 12,0 | 35,0 | 60,0 | 87,0 | 114,0 | 139,0 | |
| t cf, 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 С:
1) find a random measurement error:
2) the instrumental error of the stopwatch in each case is found in the same way as in the first series of experiments. In the first experiment Δ t and= 0.3 s;
3) the error of reading a mechanical stopwatch is taken equal to one division of the scale: Δ t about= 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 t0 + Δ t B= 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 modules of absolute deviations of the results of individual observations from the mean for temperature 40 0 С:
7 a) we find a random measurement error:
8 a) instrumental error of the stopwatch in the second experiment
Δ t and= 0.8 s;
9 a) mechanical stopwatch reading error Δ t about= 1.0 s;
10 a) the calculation error in this case is zero;
11 a) we calculate the total absolute error:
Δ t = Δ tC + Δ t and + Δ t0 + Δ t B= 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) we calculate the modules of absolute deviations of the results of individual observations from the mean for temperature 55 0 С:
7 b) we find a random measurement error:
8 b) instrumental error of the stopwatch in this experiment
Δ t and= 1.5 s;
9 b) mechanical stopwatch reading error Δ t about= 1.0 s;
10 b) the calculation error in this case is zero;
11 b) we calculate the total absolute error:
Δ t = Δ tC + Δ t and + Δ t0 + Δ t B= 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) we calculate the modules of absolute deviations of the results of individual observations from the mean for temperature 70 0 C:
7 c) we find a random measurement error:
8 c) instrumental error of the stopwatch in this experiment
Δ t and= 2.1 s;
9 c) mechanical stopwatch reading error Δ t about= 1.0 s;
10 c) the calculation error in this case is zero;
11 c) we calculate the total absolute error:
Δ t = Δ tC + Δ t and + Δ t0 + Δ t B= 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 modules of absolute deviations of the results of individual observations from the mean for temperature 85 0 С:
7 d) we find a random measurement error:
8 d) instrumental error of the stopwatch in this experiment
Δ t and= 2.7 s;
9 d) mechanical stopwatch reading error Δ t about= 1.0 s;
10 d) the calculation error in this case is zero;
11 d) we calculate the total absolute error:
Δ t = Δ tC + Δ t and + Δ t0 + Δ t B= 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 modules of absolute deviations of the results of individual observations from the mean for temperature 100 0 C:
7 e) we find a random measurement error:
8 e) instrumental error of the stopwatch in this experiment
Δ t and= 3.4 s;
9 e) mechanical stopwatch reading error Δ t about= 1.0 s;
10 e) the calculation error in this case is zero.
11 e) we calculate the total absolute error:
Δ t = Δ tC + Δ t and + Δ t0 + Δ t B= 5.28 + 3.4 + 1.0 + 0 = 9.68 s ≈ 9.7 s;
12 e) write down the measurement result: t= (137.8 ± 9.7) s.
The results of the calculations are presented in the form of a table, which shows the differences in the final and initial temperatures in each experiment and the heating time of sunflower oil.
7. Let's build a graph of the dependence of the change in oil temperature on the heating time (Fig. 15). When plotting, in all cases, the interval of time measurement error is indicated. The line thickness corresponds to the temperature measurement error.
Rice. 15. Graph of the dependence of the change in water temperature on the time of its heating
8. The constructed graph is similar to a graph of a direct proportional relationship y=kx. Coefficient value k in this case, it is easy to find from the graph. Therefore, we can finally write Δ t= 0.6Δ τ .
From the constructed 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 PZ: 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 on an experimental setup, the schematic diagram of which is shown in Fig. 16).
To solve this problem, you need to perform the following steps.
1. Draw up a system of actions for obtaining and processing the results of measuring the equivalent resistance of a circuit section and voltage at the load R n(See Section 2.2.8 or Section 2.2.9).
2. Draw up a system of actions for plotting the dependence of the output voltage (on a resistor R n) from the equivalent resistance of the circuit section AB.
3. Select ROI No. 1 - a section with a certain value R n1 and perform all the actions planned in paragraphs 1 and 2.
4. Choose a functional dependence known in mathematics, the graph of which is similar to the experimental curve.
5. Write down mathematically this functional dependence for the load R n1 and formulate for her the answer to the cognitive task.
6. Select ROI No. 2 - a segment of the aircraft with a different resistance value R H2 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 mathematically this functional dependence for resistance R H2 and formulate for him the answer to the cognitive task.
9. Formulate a functional relationship between the quantities in a generalized form.
Report on the identification of 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 abridged 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 the limit of 1000 ohms, that is, the measurement accuracy is equal to the price of the least significant digit, which corresponds to ±1 ohm.
The dependent variable was the value of the output voltage taken at the load resistance (points B and C). A digital voltmeter with a minimum discharge of hundredths of a volt was used as a measuring device.
Rice. 16. Scheme of the experimental setup for studying the type of dependence of the output voltage on the value of the equivalent resistance of the circuit
The equivalent resistance was changed using keys Q 1 , Q 2 and Q 3 . For convenience, the switched on state of the key will be denoted by “1”, and the switched off state by “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, AT | |||||
| U 1,AT | U 2, AT | U 3, AT | U 4, AT | U 5, AT | ||||
| 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 shown in the following table:
| № | Q 3 Q 2 Q 1 | R E, Ohm | U Wed, AT | U cf. env. , AT | Δ U Wed, AT | Δ U and, AT | Δ U about, AT | Δ U in, AT | Δ U, AT | U, AT |
| 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 build a graph of the dependence of the output voltage on the value of the equivalent resistance U = f(R E).
When constructing 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 line thickness corresponds to the measurement error of the equivalent resistance. The resulting graph is shown in Fig. 17.
Rice. 17. Graph of the dependence of the output voltage
from the value of the equivalent resistance in section AB
The graph resembles an inverse proportional graph. In order to verify this, we plot the dependence of the output voltage on the reciprocal value of the equivalent resistance U = f(1/R E), that is, from the conductivity σ chains. For convenience, the data for this graph will be presented in the form of the following table:
The resulting graph (Fig. 18) confirms the above assumption: 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 choose another object of study: RI No. 2 - another value of the load resistance R H2, and perform the same steps. We get a similar result, but with a different coefficient k.
We formulate the answer to the PZ: the output voltage at the load resistance R n inversely proportional to the value of the equivalent resistance of a circuit section consisting of three conductors connected in parallel, which can be included in one of eight combinations.
Rice. 18. Graph of the dependence of the output voltage on the conductivity of the circuit section AB
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 task No. 4
Experimental determination of a specific value of a specific physical quantity (solution of 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 execution of which will allow obtaining a specific value of a specific quantity in a specific situation. Common to both situations is the expression of the required quantity in terms of other quantities, the value of which can be found by direct measurement. It is said that in this case the person makes an indirect measurement.
Quantity values obtained by indirect measurement are inaccurate. This is understandable: they are based on the results of direct measurements, which are always inaccurate. In this regard, the system of actions for solving cognitive task No. 4 must necessarily include actions for calculating errors.
To find the errors of indirect measurements, two methods have been developed: the method of error limits and the method of limits. Consider the content of each of which.
Error Bound Method
The error bound 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 y.
Usually Δ x1<< Х 1, Δ X 2<< Х 2 , …, Δ X N<< Х n , Δ y<< у. Therefore, we can go to infinitesimal values, that is, replace Δ X 1,Δ X 2 , …,Δ XN,Δ y their differentials dX 1, dX 2, ..., dX N, dy respectively. Then the relative error
the relative error of a function is equal to the differential of its natural logarithm.
In the right side of the equality, instead of differentials of variables, their absolute errors are substituted, and instead of the quantities themselves, their average values. In order to determine the upper limit of the error, the algebraic summation of errors is replaced by arithmetic.
Knowing the relative error, find the absolute error
Δ at= ε u ּu,
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 off according to general rules. The answer is written as
Y = Y meas± Δ At; ε y \u003d ...
Expressions for relative and absolute errors depend on the type of function y. The main formulas that are often encountered in laboratory work are presented in Table 5.
For this task, you can get 2 points on the exam in 2020
Task 11 of the USE in physics is devoted to the basics of thermodynamics and molecular kinetic theory. The general theme of this ticket is the explanation of various phenomena.
Task 11 of the Unified State Examination in physics is always built in the same way: the student will be offered a graph or a description of any dependence (the release of thermal energy when a body is heated, a change in gas pressure depending on its temperature or density, any processes in an ideal gas). After that, five statements are given, directly or indirectly related to the topic of the ticket and representing a textual description of thermodynamic laws. Of these, the student must select two statements that he considers true, corresponding to the condition.
Task 11 of the Unified State Examination in Physics usually scares students, because it contains a lot of digital data, tables, and graphs. In fact, it is theoretical, and the student will not have to calculate anything when answering the question. Therefore, in fact, this question usually does not cause any special difficulties. However, the student must adequately assess his abilities and it is not recommended to “stay up” on the eleventh task, because the time to complete the entire test is limited to a certain number of minutes.
