MKT, thermodynamics (changes in physical quantities in processes).

1.1. Three identical vessels under equal conditions contain the same amount of hydrogen, helium and nitrogen. The distribution of helium molecules will be described by the curve numbered...

1.2. There is a mass in a closed container m= 28 g nitrogen at pressure R 1 = 100 kPa and temperature t 1 = 27°C. After heating, the pressure in the vessel increased 6 times. Determine to what temperature the gas was heated and what is the volume of the vessel?

1.3. One mole of an ideal monatomic gas is compressed first adiabatically and then isobarically (see figure). The final temperature is equal to the initial one. During the entire process 1-2-3, external forces performed work equal to 5 kJ. Determine what is the difference between the maximum and minimum gas temperatures in the cycle?

1.4. During the isobaric expansion of a diatomic gas, work was done A= 164 J. How much heat was imparted to the gas during this expansion?

1.5. A heat engine, the working fluid of which is an ideal monatomic gas, completes a cycle, the diagram of which is shown in the figure. If R 2 = 4R 1 , V 3 = 2V 1, Determine the efficiency of such a heat engine .

Idz "mkt. Thermodynamics" Option 2

2.1. The figure shows a graph of the velocity distribution function of oxygen molecules (Maxwell distribution) for temperature T= 273 K, at speed v = 380 m/s the function reaches its maximum. Here:

1) the probability that an oxygen molecule at T = 273 K has a speed equal to 380 is nonzero m/s

2) the area of ​​the shaded strip is equal to the fraction of molecules with velocities in the range from 380 m/s up to 385 m/s or the probability that the speed of a molecule has a value in this speed range

3) with decreasing temperature, the area under the curve decreases

4) when the temperature changes, the maximum position changes.

Specify at least two answer options.

2.2. The constant mass of an ideal gas is involved in the process shown in the figure. In what state will the gas volume be the smallest?

1) at point 1 2) at point 2

3) at point 3 4) the volume will be the same everywhere

2.3. Helium undergoes a circular process consisting of two isochores and two isobars (see figure). The change in the internal energy of the gas in section 1–2 is equal to ...

1) 0,5 P 1 V 1 2) 1,5 P 1 V 1 3) 2 P 1 V 1 4) 4 P 1 V 1

2.4. The graph shows a cycle with an ideal monatomic gas of constant mass with an amount of ν = 2 mol. Represent the cycle graph in coordinates R –V and determine the amount of heat received by the gas per cycle if the parameters of the gas in state 1 are equal T 1 = 300 K, and pressure R 1 = 10 5 Pa.

2.5. An ideal gas undergoes a Carnot cycle. Heater temperature T 1 =470K, cooler temperature T 2 =280 K. During isothermal expansion, the gas performs work A = 100 J. Determine the thermal efficiency η of the cycle, as well as the heat Q 2, which the gas gives to the cooler during isothermal compression.

Idz "mkt. Thermodynamics" Option 3

3.1. On ( P,V) – the diagram shows the process carried out by an ideal gas in an insulated vessel. The initial and final states will correspond to the velocity distributions shown in the figure...

3.2. In the figure, in two of the three pairs of coordinate axes P- V, P- T And V- T graphs of the same isoprocess are shown (the first coordinate is plotted along the ordinate axis). Determine what process it is.

1) Isothermal. 2) Isochoric.

3) Isobaric. 4) Adiabatic.

3.3. An ideal diatomic gas in an amount = 1 mol first expanded isothermally ( T 1 = 300 K). Then the gas was heated, increasing the pressure 3 times. What is the work done for the entire process? Present the process graph in coordinates R – V.

3.4. Monoatomic IG, taken in an amount of 2.0 mol, undergoes the 1 – 2 – 3 – 4 process shown in the figure. The amount of heat given off by the gas in process 2–3 is ... kJ.

3.5. If the efficiency of the Carnot cycle is 60%, then the temperature of the heater is greater than the temperature of the refrigerator in ....... once.

1) UNIFIED STATE EXAMINATION IN PHYSICS IS LASTING 235 min

2) STRUCTURE of CIMs - 2018 and 2019 compared to 2017. Slightly CHANGED: The exam version will consist of two parts and will include 32 tasks. Part 1 will contain 24 short-answer items, including self-report items that require a number, two numbers, or a word, as well as matching and multiple choice items that require answers to be written as a sequence of numbers. Part 2 will contain 8 tasks united by a common type of activity - problem solving. Of these, 3 tasks with a short answer (25–27) and 5 tasks (28–32), for which you need to provide a detailed answer. The work will include tasks of three difficulty levels. Basic level tasks are included in part 1 of the work (18 tasks, of which 13 tasks with the answer recorded in the form of a number, two numbers or a word, and 5 matching and multiple choice tasks). Advanced-level tasks are distributed between parts 1 and 2 of the examination paper: 5 short-answer tasks in part 1, 3 short-answer tasks and 1 long-answer task in part 2. The last four tasks of part 2 are tasks of a high level of complexity. Part 1 of the examination paper will include two blocks of tasks: the first tests the mastery of the conceptual apparatus of the school physics course, and the second tests the mastery of methodological skills. The first block includes 21 tasks, which are grouped based on thematic affiliation: 7 tasks on mechanics, 5 tasks on MCT and thermodynamics, 6 tasks on electrodynamics and 3 on quantum physics.

A new task of a basic level of complexity is the last task of the first part (position 24), timed to coincide with the return of the astronomy course to the school curriculum. The task has a characteristic of the type “choosing 2 judgments out of 5.” Task 24, like other similar tasks in the examination paper, is scored a maximum of 2 points if both elements of the answer are correct, and 1 point if an error is made in one of the elements. The order in which the numbers are written in the answer does not matter. As a rule, tasks will be contextual in nature, i.e. Some of the data required to complete the task will be presented in the form of a table, diagram or graph.

In accordance with this task, the subsection “Elements of Astrophysics” of the section “Quantum Physics and Elements of Astrophysics” was added to the codifier, including the following points:

· Solar system: terrestrial planets and giant planets, small bodies of the solar system.

· Stars: variety of stellar characteristics and their patterns. Sources of star energy.

· Modern ideas about the origin and evolution of the Sun and stars. Our galaxy. Other galaxies. Spatial scales of the observable Universe.

· Modern views on the structure and evolution of the Universe.

You can learn more about the structure of KIM-2018 by watching the webinar with the participation of M.Yu. Demidova https://www.youtube.com/watch?v=JXeB6OzLokU or in the document below.

Unified State Exam 2012. Physics. Model exam options: 32 options: grades 9-11. Ed. Demidova M.Yu.

M.: 2011. - 272 p.

For the first time the series “Unified State Exam 2011. FIPI-school" provides the opportunity for systematic, high-quality preparation for the Unified State Exam, both within the framework of school classes and independently.

The collection contains a system of thematic options for all sections of the Unified State Exam - training and final options that cover the topics covered in the school physics course (22 options in total). To consolidate knowledge and intensive training, 10 standard options for the Unified State Exam are offered.

The collection contains specifications for thematic training options and a system for assessing assignments. Answers to all options allow you to correctly assess the success of completing tasks.

Format: pdf

Size: 12.5 MB

Download: drive.google

CONTENT
Introduction 4
Specification of thematic training options 6
Reference data 7
THEMED TRAINING OPTIONS
SECTION 1. MECHANICS 9
Option 1.1. “Kinematics”, “Dynamics” 9
Option 1.2. “Kinematics”, “Dynamics” 15
Option 1.3. “Conservation laws in mechanics” 18
Option 1.4. “Conservation laws in mechanics” 24
Option 1.5. "Static" 27
Option 1.6. “Vibrations and Waves” 33
Final version 1. “Mechanics” 39
Final version 2. “Mechanics” 47
SECTION 2. MCT AND THERMODYNAMICS 55
Option 2.1. "Molecular Physics" 55
Option 2.2. "Thermodynamics" 61
Option 2.3. “MKT and thermodynamics” 68
Option 2.4. "MCT and thermodynamics". 71
Final version 3. “Mechanics”, “MKT and thermodynamics” 74
Final version 4. “Mechanics”, “MKT and thermodynamics” 83
SECTION 3. ELECTRODYNAMICS 92
Option 3.1. “Electrostatics”, “Direct Current”, “Magnetic Field” 92
Option 3.2. “Electrostatics”, “Direct Current”, “Magnetic Field” 98
Option 3.3. “Electromagnetic induction”, “Electromagnetic oscillations”, “Optics”. 101
Option 3.4. “Electromagnetic induction”, Electromagnetic oscillations”, “Optics”. 108
Final version 5. “Mechanics”, “MCT and thermodynamics”, “Electrodynamics” 111
Final version 6. “Mechanics”, “MCT and thermodynamics”, “Electrodynamics” 121
SECTION 4. QUANTUM PHYSICS 130
Option 4.1. "Quantum Physics" 130
Option 4.2. "Quantum Physics" 137
STANDARD EXAMINATION OPTIONS
Instructions for performing work 140
Option 1 143
Option 2 151
Option 3 158
Option 4 165
Option 5 172
Option 6 180
Option 7 187
Option 8 194
Option 9 201
Option 10 209
ANSWERS TO THEMATIC TRAINING OPTIONS 217
ANSWERS TO STANDARD EXAMINATION OPTIONS 246

 § 2. Molecular physics. Thermodynamics

In molecular physics, the amount of a substance is usually measured in moles.
 Molem ν is the amount of a substance that contains the same number of atoms or molecules (structural units) as there are in 12 g of carbon. This number of atoms in 12 g of carbon is called Avogadro's number:

 Molar mass M = M r 10 −3 kg/mol is the mass of one mole of a substance. The number of moles in a substance can be calculated using the formula

 The basic equation of the molecular kinetic theory of an ideal gas:

Where m 0- mass of the molecule; n- concentration of molecules; Ṽ - root mean square speed of molecules.

 2.1. Gas laws

In coordinates p−V isotherm is a hyperbola, and in coordinates V−T And p−T- straight (see Fig. 4)

 Isochoric process(Charles' law):
For a given mass of gas at a constant volume, the ratio of pressure to temperature in degrees Kelvin is a constant value (see Fig. 5).

 Isobaric process(Gay-Lussac's law):
For a given mass of gas at constant pressure, the ratio of gas volume to temperature in degrees Kelvin is a constant value (see Fig. 6).

 Dalton's law:
If there is a mixture of several gases in a vessel, then the pressure of the mixture is equal to the sum of the partial pressures, i.e. those pressures that each gas would create in the absence of the others.

 2.2. Elements of thermodynamics

 Work in thermodynamics:
work during isobaric expansion of a gas is equal to the product of the gas pressure and the change in its volume:

 Law of conservation of energy in thermal processes (first law of thermodynamics):
the change in the internal energy of a system during its transition from one state to another is equal to the sum of the work of external forces and the amount of heat transferred to the system:

Application of the first law of thermodynamics to isoprocesses:
 A) isothermal process T = const ⇒ ∆T = 0.
In this case, the change in internal energy of an ideal gas

Hence: Q = A.
All the heat transferred to the gas is spent on doing work against external forces;

 b) isochoric process V = const ⇒ ∆V = 0.
In this case, the gas work

Hence, ∆U = Q.
All heat transferred to the gas is spent on increasing its internal energy;

 V) isobaric process p = const ⇒ ∆p = 0.
In this case:

 Adiabatic is a process that occurs without heat exchange with the environment:

In this case A = −∆U, i.e. The change in the internal energy of the gas occurs due to the work done by the gas on external bodies.
When a gas expands, it does positive work. The work A performed by external bodies on a gas differs from the work done by a gas only in sign:

 The amount of heat required to warm the body in a solid or liquid state within one state of aggregation, calculated by the formula

where c is the specific heat capacity of the body, m is the mass of the body, t 1 is the initial temperature, t 2 is the final temperature.
 The amount of heat required to melt a body at the melting point, calculated by the formula

where λ is the specific heat of fusion, m is the mass of the body.
 Amount of heat required for evaporation, calculated by the formula

where r is the specific heat of vaporization, m is the body mass.

In order to convert part of this energy into mechanical energy, heat engines are most often used. Heat engine efficiency is the ratio of the work A performed by the engine to the amount of heat received from the heater:

The French engineer S. Carnot came up with an ideal heat engine with an ideal gas as a working fluid. The efficiency of such a machine

Air, which is a mixture of gases, contains water vapor along with other gases. Their content is usually characterized by the term “humidity”. A distinction is made between absolute and relative humidity.
 Absolute humidity is called the density of water vapor in the air - ρ ([ρ] = g/m3). Absolute humidity can be characterized by the partial pressure of water vapor - p([p] = mmHg; Pa).
 Relative humidity (ϕ)- the ratio of the density of water vapor present in the air to the density of the water vapor that would have to be contained in the air at this temperature for the vapor to be saturated. Relative humidity can be measured as the ratio of the partial pressure of water vapor (p) to the partial pressure (p0) that saturated vapor has at that temperature:

Option 1

1. Is it correct to say that Brownian motion is the result of the collision of particles suspended in a liquid?

A) the statement is true; B) the statement is not true; B) I don’t know.

2. The relative molecular mass of helium is 4. Express the molar mass of helium in kg/mol.
A) 0.004 kg/mol; B) 4 kg/mol; B) 4 ∙ 10 -4 kg/mol.

3. State the basic equation of MKT of gases.

A); B)
; IN)
; G)
.

4. What is absolute zero temperature, expressed on the Celsius scale?

A) 273 0 C; B) -173 0 C; B) -273 0 C.

5. Which process corresponds to the graph shown in Fig. 1?

A) isobaric;
B) isochoric;
B) isothermal;
D) adiabatic.

6. How will the pressure of an ideal gas change if, at a constant temperature, its volume decreases by 4 times?

A) will increase 4 times; B) will not change; B) will decrease by 4 times.

7. What is the ratio of the number of molecules in one mole of oxygen to the number of molecules in one mole of nitrogen?

A) ; B) ; IN) ; D) 1; D 2.

8. Find how many times the root mean square speed of hydrogen molecules is greater than the root mean square speed of oxygen molecules. Gases are at the same temperature.

A) 16; B) 8; AT 4; D) 2.

9. In Fig. Figure 2 shows a graph of gas pressure versus temperature. Is the volume of gas greater in state 1 or state 2?
A) in state 1;
B) in state 2;
B) the pressure in states 1 and 2 is the same;
D) I don’t know.

10. At constant pressure p, the volume of gas will increase by ∆V. What physical quantity is equal to the product p|∆V| in this case?
A) work done by gas; B) work done on the gas by external forces;

B) the amount of heat received by the gas; D) internal energy of the gas.

11. Work A is done on the body by external forces, and the amount of heat Q is transferred to the body. What is the change in internal energy ∆U of the body?
A) ∆U=A; B) ∆U=Q C) ∆U=A+Q; D) ∆U=A-Q; D) ∆U=Q-A.

12. What physical quantity is calculated by the formula
?

A) the amount of heat in an ideal gas; B) ideal gas pressure;
B) internal energy of a monatomic ideal gas;
D) internal energy of one mole of an ideal gas.

13. What process occurred in an ideal gas if the change in its internal energy is equal to the amount of heat supplied.

A) isobaric; B) isothermal; B) isochoric; D) adiabatic.

14. Figure 3 shows a graph of an isoprocess with an ideal gas. Write down the first law of thermodynamics for him.
A) ∆U=Q+A / ;

15. What is the change in internal energy of one mole of an ideal monatomic gas if T 1 = T, and T 2 = 2 T?
A) RT; B) 2RT; B) 3RT; D) 1.5RT.

16. What work does a gas do when expanding isobarically at a pressure of 2 ∙ 10 5 Pa from a volume V 1 = 0.1 m 3 to a volume V 2 = 0.2 m 3?
A) 2 ∙ 10 6 J; B) 200 kJ; B) 0.2 ∙ 10 5 J.

17. In the chamber, as a result of fuel combustion, energy equal to 600 J was released, and the refrigerator received energy equal to 400 J. What work was done by the engine?

A) 1000 J; B) 600 J; B) 400 J; D) 200 J.

18. What is the maximum efficiency of a heat engine that uses a heater with a temperature of 427ºC and a refrigerator with a temperature of 27ºC?

A) 40%; B) 6%; B) 93%; D) 57%.

19. There is air in the cylinder under the piston, weighing 29 kg. What work will be done by the air during isobaric expansion if its temperature increases by 100 K. Ignore the mass of the piston.
A) 831 J; B) 8.31 kJ; B) 0.83 MJ.

20. A gas undergoes a Carnot cycle. The absolute temperature of the heater is 3 times greater than the absolute temperature of the refrigerator. Determine the fraction of heat given off to the refrigerator.

A) 1/2; B) 1/3; B) 1/5; D) 2/3.

21. Three balls of equal mass - copper, steel and iron - fall onto a tiled floor from the same height. Which one will heat up to a higher temperature? Specific heat capacity of copper 400
, iron 460
and steel 500
.
A) copper; B) steel; B) iron.

22. A gas undergoes a Carnot cycle. 70% of the heat received from the heater is transferred to the refrigerator. The heater temperature is 430 K. Determine the temperature of the refrigerator.
A) 3 K; B) 301 K; B) 614 K.

A) M. Lomonosov; B) I. Newton; B) O. Stern; D) R. Paul; D) R. Brown.

24. Avogadro's constant shows:

A) the number of molecules in a substance; B) the number of molecules in carbon;

C) one mole of any substance contains a different number of molecules;

D) one mole of any substance contains the same number of molecules;

D) no answer.

25. The mass of a substance in the amount of one mole is called...

A) molecular; B) molar; C) atomic D) nuclear; D) no answer.

Correct answer keys version 1

Option 2

1. What quantity characterizes the state of thermodynamic equilibrium?
A) pressure; B) pressure and temperature; B) temperature;
D) pressure, volume and temperature; D) pressure and volume.

2. Which expression given below corresponds to the formula for the amount of a substance?
A) ; B) ; IN) ; G)
.

3. Which expression given below corresponds to the formula of the Mendeleev-Clapeyron equation?

A) ; B)
; IN)
; G.)
.

4. What defines a work ?

A) ideal gas pressure; B) absolute temperature of an ideal gas;
B) internal energy of an ideal gas;
D) average kinetic energy of an ideal gas molecule.

5. When implementing what isoprocess, an increase in the absolute temperature of an ideal gas by 2 times leads to an increase in volume also by 2 times?
A) isothermal; B) isochoric; B) adiabatic; D) isobaric.

6. How will the pressure of an ideal gas change during the transition from state 1 to state 2 (see Fig. 1)?
A) will not change;
B) will increase;
B) will decrease;
D) I don’t know.

7. How will the volume of an ideal gas change during the transition from state 1 to state 2 (see Fig. 2)?

A) will decrease;
B) will increase;
B) will not change.

8. At a constant temperature of 27 0 C and a pressure of 10 5 Pa, the gas volume is 1 m 3. At what temperature will this gas occupy a volume of 2 m 3 at the same pressure of 10 5 Pa?
A) 327ºС; B) 54ºС; B) 600 K.

9. What is the initial absolute temperature of the gas if, when it is heated isochorically by 150 K, the pressure increases by 1.5 times?
A) 30 K; B) 150 K; B) 75 K; D) 300 K.

10. Select a graph of the density of an ideal gas versus temperature during an isochoric process (see Fig. 3).

11. A closed vessel contains air and a drop of water weighing 1 g. The volume of the vessel is 75 l, the pressure in it is 12 kPa and the temperature is 290 K. What will the pressure in the vessel be if the drop evaporates?
A) the pressure will not change; B) 13.785 kPa; B) 13.107 kPa.

12. What process occurred in an ideal gas if the change in its internal energy is zero?
A) isobaric; B) isothermal; B) isochoric; D) adiabatic.

13. An amount of heat is transferred to an ideal gas in such a way that at any moment of time the transferred amount of heat Q is equal to the work A performed by the gas. What process is being carried out?

A) adiabatic; B) isobaric; B) isochoric; D) isothermal.

14. Among the formulas given below, find the one that calculates the maximum efficiency value of a heat engine.

A) ; B) ; IN) ; G) .

15. With rapid compression of the gas in the cylinder, its temperature increased. Will the internal energy of the gas change? Write the equation for the first law of thermodynamics for this case.
A) energy decreased Q=∆U+A / ; B) energy increased ∆U=-A /;

B) the energy has not changed Q=A / .

16. Determine the internal energy of two moles of a monatomic (ideal) gas taken at a temperature of 300 K.

A) 2.5 kJ; B) 2.5 J; B) 4.9 J; D) 4.9 kJ; D) 7.5 kJ.

17. An amount of heat equal to 2000 J is transferred to a thermodynamic system, and 500 J of work is done on it. Determine the change in its internal energy of this system.

A) 2500 J; B) 1500 J; B) ∆U=0.

18. When isobarically heating a certain mass of oxygen at ∆T=160 K, 8.31 J of work was done to increase its volume. Determine the mass of oxygen if M=3.2 ∙ 10 -2 kg/mol, R=8.31 ​​J/(K ∙ mol).
A) 0.2 kg; B) 2 kg; B) 0.5 kg; D) 0.2 g.

19. The temperature of the heater of an ideal heat engine is 425 K, and the temperature of the refrigerator is 300 K. The engine receives 4 ∙ 10 4 J of heat from the heater. Calculate the work done by the working fluid of the engine.
A) 1.2 ∙ 10 4 J; B) 13.7 ∙ 10 4 J; C) the work cannot be calculated.

20. An ideal gas passes from state A to state B (see Fig. 4) in three different ways. In which case was the gas work maximum?

21. Neon, which was under normal conditions in a closed vessel with a capacity of 20 liters, was cooled to 91 K. Find the change in the internal energy of the gas and the amount of heat given off by it.

A) 1 MJ; B) 0.6 kJ; B) 1.5 kJ; D) 1 kJ.

22. A gas undergoes a Carnot cycle. Temperature of the heater T 1 = 380 K, refrigerator T 2 = 280 K. How many times will the efficiency of the cycle increase if the heater temperature is increased by ∆T = 200 K.

A) 2 times; B) 3 times; B) 1.5 times; D) 2.5 times.

23. What is called thermal motion?

A) the movement of one body on the surface of another; B) random movement of molecules;

B) body movement in hot water; D) Brownian motion; D) no answer.

24. In what states of aggregation does diffusion proceed faster?

A) liquid; B) hard; B) gaseous; D) liquid and gaseous;

D) gaseous and solid.

25. What is the temperature on the Celsius scale, if on the Kelvin scale it is 273K?

A) 0°; B) 10°; B) 273°; D) 3°; D) 100°.

Correct answer keys version 2