1. The vessel contains helium at a pressure of 100 kPa. The concentration of helium was increased by 2 times, and the average kinetic energy of its molecules was reduced by 4 times. Determine the steady-state gas pressure.
2. The helium temperature increased from 27 °C to 177 °C. How many times has the average kinetic energy of its molecules increased?
3. The vessel contains argon, the absolute temperature of which is 300 K. The concentration of argon was reduced by 2 times, while its pressure increased by 1.5 times. Determine the steady-state absolute temperature of the gas.
4. The figure shows a graph of process 1-2, in which helium is involved. The volume occupied by gas in state 1 is 2 liters. Determine the volume of helium in state 2 if the amount of helium substance does not change in process 1-2.
5. The figure shows a graph of process 1-2, in which neon is involved. The absolute temperature of the gas in state 1 is 150 K. Determine the absolute temperature of neon in state 2 if the amount of gas substance does not change in process 1-2.
6. The figure shows a graph of process 1-2, in which helium is involved. The absolute temperature of the gas in state 1 is 600 K. Determine the absolute temperature of helium in state 2 if the amount of gas substance does not change in process 1-2.
7. With an increase in absolute temperature by 600 K, the root-mean-square speed of thermal motion of helium molecules increased by 2 times. What is the final temperature of the gas?
8. The temperature of the gas in the vessel is 2 °C. What is the temperature of the gas on the absolute temperature scale?
9. The gas in the cylinder is transferred from state A to state B, and its mass does not change. The parameters that determine the state of an ideal gas are given in the table:
What number should be entered in the empty cell of the table?10. A vessel with a monatomic ideal gas was compressed, increasing the concentration of gas molecules by 5 times. At the same time, the average energy of thermal motion of gas molecules was increased by 2 times. How many times did the gas pressure in the vessel increase as a result?
11. 1 mole of an ideal gas is cooled isochorically by 200 K, and its pressure decreases by a factor of 2. What is the initial absolute temperature of the gas?
12.. The volume of 1 mole of hydrogen in a vessel at temperature T and pressure p is equal to V1. The volume of 2 moles of hydrogen at the same pressure and temperature 3T is equal to V2. What is the ratio V2/V1? (Hydrogen is considered an ideal gas.)
13. The vessel contains a constant amount of an ideal gas substance. How many times will the temperature of the gas decrease if it goes from state 1 to state 2 (see figure)?
14. The vessel contains an ideal gas. The process of isochoric change in the state of a gas is shown in the diagram (see figure). The gas mass changed during the process. At which point on the diagram does the gas mass have the greatest value?
15. The figure shows the change in the state of constant mass of rarefied argon. The gas temperature in state 2 is 627 °C. What temperature corresponds to state 1?
16. During the experiment, the pressure of the rarefied gas in the vessel increased by 2 times, and the average energy of thermal motion of its molecules increased by 6 times. How many times did the concentration of gas molecules in the vessel decrease?
Answers
1.Answer: 50. 2.Answer: 1,5. 3.Answer: 900. 4.Answer: 6. 5. Answer: 750.
6. Answer: 200. 7. Answer: 800. 8. Answer: 275. 9. Answer: 4. 10. Answer: 10.
11. Answer: 400. 12. Answer: 6. 13. Answer: 6. 14. Answer: 1. 15. Answer: 300.
16. Answer: 3.
The answer to tasks 5–7, 11, 12, 16–18, 21 and 23 is
sequence of two numbers. Write your answer in the answer field in the text
work, and then transfer according to the example below without spaces,
commas and other additional symbols in answer form No. 1.
The answer to task 13 is a word. Write your answer in the answer field in
text of the work, and then transfer it according to the example below into the form
answers number 1.
The answer to tasks 19 and 22 are two numbers. Write your answer in the answer field in the text of the work, and then transfer it according to the example below, without separating the numbers with a space, into answer form No. 1.
The answer to tasks 27–31 includes a detailed description of the entire progress of the task. In answer form No. 2, indicate the task number and
write down its complete solution.
When performing calculations, it is allowed to use a non-programmable
calculator.
All Unified State Exam forms are filled out in bright black ink. You can use a gel or capillary or fountain pen.
When completing assignments, you can use a draft. Posts
in the draft are not taken into account when evaluating work.
The points you receive for completed tasks are summed up.
Try to complete as many tasks as possible and score the highest
number of points.
We wish you success!
Below is reference information that you may need when performing the work.
Decimal prefixes
| Name | Designation | Factor | Name | Designation | Factor |
| giga | G | centi | With | ||
| mega | M | Milli | m | ||
| kilo | To | micro | mk | ||
| hecto | G | nano | n | ||
| deci | d | pico | P |
| Constants number acceleration of free fall on Earth gravitational constant universal gas constant R = 8.31 J/(mol K) Boltzmann's constant Avogadro's constant speed of light in a vacuum proportionality coefficient in Coulomb's law modulus of electron charge (elementary electric charge) Planck's constant |
Part 1
1) At the moment of time 10 s, the static friction force is equal to 2 N. 2) During the first 10 s, the block has moved 20 m. 3) At the moment of time 10 s, the sliding friction force is equal to 2 N. 4) In the time interval from 12 to 20 s the block moved with constant acceleration. 5) In the time interval from 12 to 20 s, the block moved at a constant speed. Answer:
. In this process, the gas performs work equal to 3 kJ. Based on your analysis of the graph, select two true statements. 1) In process 1−2, the volume of gas decreases. 2) The amount of heat received by the gas is 1 kJ. 3) In process 1−2, the volume of gas increases. 4) The amount of heat received by the gas is 3 kJ. 5) The work of gas in process 1−2 is negative. Answer:The metal surface is illuminated with light whose wavelength is less than the wavelength λ corresponding to the red limit of the photoelectric effect for a given substance. With increasing light intensity
1) photoelectric effect will not occur at any light intensity
2) the number of photoelectrons will increase
3) the maximum energy of photoelectrons will increase
4) both the maximum energy and the number of photoelectrons will increase
5) the photoelectric effect will occur at any light intensity
Choose two true statements.
C1-1. On the floor of a stationary elevator there is a heat-insulated vessel, open at the top. In a vessel under a heavy moving piston there is a monatomic ideal gas. The piston is in equilibrium. The elevator begins to descend with uniform acceleration. Based on the laws of mechanics and molecular physics, explain where the piston will move relative to the vessel after the elevator starts moving and how the temperature of the gas in the vessel will change. Neglect friction between the piston and the walls of the vessel, as well as gas leakage from the vessel.
S3-17. A monatomic ideal gas is contained in a horizontal cylindrical vessel closed by a piston. Initial gas pressure R 1 = 4 · 10 5 Pa . The distance from the bottom of the vessel to the piston is L . Piston cross-sectional area S = 25 cm 2. As a result of slow heating, the gas received an amount of heat Q = 1.65 kJ , and the piston has moved a distance x = 10 cm . When the piston moves, a frictional force of magnitude acts on it from the side of the vessel walls F tp = 3 · 10 3 N . Find L . Assume that the vessel is in a vacuum.
S3-21. 1 mole ideal monatomic gas. Initial gas temperature 27° C
S3-22. The figure shows the change in state 1 mole
not she. Initial gas temperature 0°C
. How much heat is imparted to the gas in this process?
S3-23. 1
in a state 3
?
S3-24. The diagram shows the changes in pressure and volume of an ideal monatomic gas. How much heat was received or given off by the gas during the transition from the state 1
in a state 3
?
S3-25. The diagram (see figure) shows changes in pressure and volume of an ideal monatomic gas. How much heat was received or given off by the gas during the transition from the state 1
in a state 3
?
S3-26. A monatomic ideal gas of constant mass undergoes the cyclic process shown in the figure. During a cycle, the gas receives an amount of heat from the heater Q n = 8 kJ . What is the work done by the gas per cycle?
S3-27. With a monatomic ideal gas of constant mass, a cyclic process occurs, shown in the figure. During a cycle, the gas does work A
ts
= 5 kJ
. How much heat does the gas receive from the heater per cycle?
S3-28. Two experiments were carried out with rarefied nitrogen, which is in a vessel with a piston. In the first experiment, the gas was informed, by securing the piston, the amount of heat Q 1 = 742 J , as a result of which its temperature changed by a certain amount ΔT . In the second experiment, having given nitrogen the opportunity to expand isobarically, they told it the amount of heat Q 2 = 1039 J , as a result of which its temperature also changed by ΔT . What was the temperature change ΔT in experiments? Mass of nitrogen m = 1 kg .
S3-29. T 1 = 600 K and pressure p 1 = 4.10 5 Pa , expands and simultaneously cools so that its pressure during expansion is inversely proportional to the square of the volume. The final volume of gas is twice the initial volume. How much heat did the gas give up during expansion if it did work? A = 2493 J ?
S3-30. One mole of argon contained in a cylinder at a temperature T 1 = 600 K and pressure p 1 = 4.10 5 Pa p 2 = 10 5 Pa . How much heat did the gas give up during expansion if it did work? A = 2493 J ?
S3-31. One mole of a monatomic ideal gas is converted from the state 1 in a state 2 in such a way that during the process the gas pressure increases in direct proportion to its volume. As a result, the gas density decreases by α = 2 times. Gas receives heat during the process Q = 20 kJ . What is the temperature of the gas in the state 1 ?
S3-32. One mole of argon contained in a cylinder at a temperature T 1 = 600 K and pressure p 1 =4.10 5 Pa , expands and simultaneously cools so that its pressure during expansion is inversely proportional to the square of the volume. Final gas pressure R 2 = 10 5 Pa . What work was done by the gas during expansion if it gave the amount of heat to the refrigerator Q = 1247 J ?
S3-33. In a vessel with a volume V = 0.02 m 3 with rigid walls there is a monatomic gas at atmospheric pressure. There is a hole in the lid of the vessel with an area s , plugged with a cork. Maximum static friction force F plugs on the edges of the hole is equal to 100 N . The plug pops out if the amount of heat transferred to the gas is not less than 15 kJ. Determine the value of s, assuming the gas is ideal.
S3-34. A cyclic process shown in the figure is carried out over a monatomic ideal gas. Location on 1-2
gas does work A
12
= 1000 J
. On the adiabatic 3-1
external forces compress the gas, doing work |A
31
| = 370 J
. The amount of gas substance does not change during the process. Find the amount of heat |Q
hall
|, given off by gas per cycle to the refrigerator.
Solution:
Since the process is isochoric, therefore V = const.
Mendeleev-Clapeyron equation pV = vRT or (vR)\V = p\T, if v = const, then p/T is also const. This means that the relation / = / is satisfied, from here we express (which is what we need to find)
= (*) / or ((27 + 273)*3*) /1* (we changed the Celsius scale to the Kelvin scale by adding 273), from here we reduced the degrees and 300*3 = 900K
Answer: 900
Demonstration version of the Unified State Exam 2016 - task No. 8
Four metal bars having different temperatures were placed close to each other, as shown in the figure. The arrows indicate the direction of heat transfer from block to block. Select the correct statement about the temperature(s) of the bars.
1) Bar C has the lowest temperature.
2) The temperature of block C is higher than that of block B.
3) Bar D has the lowest temperature.
4) The temperature of block A is higher than that of block B.
Solution:
From the law of thermodynamics, we know that heat is transferred from more heated bodies to less heated ones. From the figure it can be seen that block C only receives heat, therefore, it is the coldest body of the four.
Answer: 1
Early version of the Unified State Exam 2016 – task No. 8
A certain vessel contains nitrogen and oxygen.
Thermodynamic equilibrium of these gases will occur only when these gases become identical
1) temperature
2) partial pressures
3) particle concentrations
4) density
Solution:
In thermodynamic equilibrium, all parts of the system have the same temperature.
Fromvet: 1
Unified State Exam in Physics 06/06/2013. Main wave. Far East. Option 1
Diffusion in a liquid occurs faster as the temperature increases because as the temperature increases
1) the interaction forces between molecules increase
2) the speed of thermal movement of molecules increases
3) liquids expand
4) the interaction forces between molecules decrease
Solution:
Diffusion is the process of mutual penetration of molecules of one substance between the molecules of another, leading to spontaneous equalization of their concentrations throughout the occupied volume. It occurs due to the continuous chaotic movement of molecules. As is known, an increase in temperature leads to an increase in the rate of thermal movement.
Fromvet: 2
The answers to tasks 1–24 are a word, a number, or a sequence of digits or numbers. Write your answer in the appropriate field on the right. Write each character without spaces. There is no need to write units of measurement of physical quantities.
1
The figure shows a graph of the cyclist's path S as a function of time t. Find the speed of the cyclist in the time interval from 50 to 70 s.
Answer: _____ m/c
2
Determine the force under which a spring with a stiffness of 200 N/m will lengthen by 5 cm.
Answer: _____ N.
3
In an inertial frame of reference, a body with a mass of 2 kg moves in a straight line in one direction under the influence of a constant force equal to 3 N. How much will the momentum of the body increase in 5 s of movement?
Answer: _____ kg m/s.
4
A vessel 20 cm high is filled with water, the level of which is 2 cm below the edge of the vessel. What is the force of water pressure on the bottom of the vessel if the bottom area is 0.01 m2? Do not take into account atmospheric pressure.
Answer: _____ N.
5
A block of mass 1 kg rests on a rough surface. A horizontal force \overrightarrow F begins to act on it, directed along the surface and depending on time as shown in the graph on the left. The dependence of the work of this force on time is presented in the graph on the right. Select two true statements based on your analysis of the graphs presented.
1. For the first 10 s, the block moved at a constant speed.
2. During the first 10 s, the block moved 20 m.
3. The sliding friction force is 2 N.
4. In the time interval from 12 to 20 s, the block moved with constant acceleration.
5. In the time interval from 12 to 20 s, the block moved at a constant speed.
6
The flight altitude of the artificial satellite above the Earth increased from 400 to 500 km. How did the speed of the satellite and its potential energy change as a result of this?
For each quantity, determine the corresponding nature of the change:
1. increased
2. decreased
3. has not changed
7
On a smooth horizontal table, a block of mass M, attached to a vertical wall by a spring of stiffness k, performs harmonic oscillations with amplitude A (see figure). Establish a correspondence between physical quantities and formulas by which they can be calculated. For each position in the first column, select the corresponding position from the second column and write down the selected numbers in the table under the corresponding letters.
PHYSICAL QUANTITIES
A) period of oscillation of the load
B) load velocity amplitude
1) 2\mathrm\pi\sqrt(\frac(\mathrm M)(\mathrm k))
2) \mathrm A\sqrt(\frac(\mathrm M)(\mathrm k))
3) 2\mathrm\pi\sqrt(\frac(\mathrm k)(\mathrm M))
4) \mathrm A\sqrt(\frac(\mathrm k)(\mathrm M))
8
The figure shows the change in the state of constant mass of rarefied argon. The gas temperature in state 1 is 27 °C. What temperature corresponds to state 2?
Answer: _____ K.
9
In a certain process, the gas released an amount of heat equal to 10 kJ to the environment. At the same time, the internal energy of the gas increased by 30 kJ. Determine the work done by external forces by compressing the gas.
Answer: _____ kJ.
10
What work is done by an ideal gas during the transition from state 1 to state 2?
Answer: _____ kJ.
11
The figure shows the dependence of gas pressure p on its density ρ in a cyclic process performed by 2 moles of an ideal gas in an ideal heat engine. The cycle consists of two straight segments and a quarter circle. Based on your analysis of this cyclical process, select two true statements.
1. In process 1−2, the gas temperature decreases.
2. In state 3, the gas temperature is maximum.
3. In process 2−3, the volume of gas decreases.
4. The ratio of the maximum temperature to the minimum temperature in the cycle is 8.
5. The work of gas in process 3−1 is positive.
12
There is gas in a cylindrical vessel under a massive piston. The piston is not fixed and can move in the vessel without friction (see figure). The same amount of gas is pumped into the vessel at a constant temperature. How will the pressure of the gas and the concentration of its molecules change as a result? For each quantity, determine the corresponding nature of the change:
1. will increase
2. will decrease
3. will not change
Write down your chosen numbers for each physical quantity. The numbers in the answer may be repeated.
13
An electrical circuit consisting of four straight horizontal conductors (1–2, 2–3, 3–4, 4–1) and a direct current source is located in a uniform magnetic field directed vertically downwards (see figure, top view). How is the Ampere force caused by this field directed relative to the figure (to the right, left, up, down, towards the observer, away from the observer), acting on conductor 2–3? Write your answer in word(s).
Answer: _____
14
With what force do two small charged balls, located at a distance of 4 m from each other, interact in a vacuum? The charge of each ball is 8 10 -8 C.
Answer: _____ µN.
15
The figure shows a graph of current versus time in an electrical circuit whose inductance is 1 mH. Determine the self-induction EMF module in the time interval from 15 to 20 s.
Answer: _____ µV.
16
A point light source is located in a container with liquid and descends vertically down from the surface of the liquid. In this case, a spot appears on the surface of the liquid, within which rays of light from the source exit the liquid into the air. The immersion depth of the source (the distance from the surface of the liquid to the light source), measured at regular intervals, as well as the corresponding bright spot radius are presented in the table. The error in measuring the immersion depth and spot radius was 1 cm. Select two correct statements based on the data given in the table.
1. The formation of the mentioned spot on the surface is due to the dispersion of light in the liquid.
2. The limiting angle of total internal reflection is less than 45°.
3. The refractive index of the liquid is less than 1.5.
4. The formation of a spot on the surface is due to the phenomenon of total internal reflection.
5. The spot boundary moves with acceleration.
17
An unbranched DC electrical circuit consists of a current source and an external resistor connected to its terminals. How will the current in the circuit and the emf of the source change when the resistance of the resistor decreases? For each quantity, determine the corresponding nature of the change:
1. will increase
2. will decrease
3. will not change
18
A charged particle of mass m, carrying a positive charge q, moves perpendicular to the induction lines of a uniform magnetic field \overrightarrow B along a circle of radius R. Neglect the effect of gravity. Establish a correspondence between physical quantities and formulas by which they can be calculated. For each position in the first column, select the corresponding position from the second column and write down the selected numbers under the corresponding letters.
PHYSICAL QUANTITIES
A) modulus of particle momentum
B) the period of revolution of a particle in a circle
1)\frac(mq)(RB)
2)\frac m(qB)
3) \frac(2\mathrm\pi m)(qB)
4) qBR
19
How many protons and how many neutrons are there in the ()_(27)^(60)Co nucleus?
20
A graph is given of the dependence of the number of undecayed erbium nuclei ()_(68)^(172)Er on time. What is the half-life of this erbium isotope?
Answer: _____
21
How do the number of neutrons in the nucleus and the number of electrons in the electron shell of the corresponding neutral atom change with a decrease in the mass number of isotopes of the same element? For each quantity, determine the corresponding nature of the change:
1. increases
2. decreases
3. does not change
Write down the selected numbers for each physical quantity in the table. The numbers in the answer may be repeated.
22
What is the voltage across the light bulb (see figure) if the error in direct voltage measurement is half the voltmeter division?
Answer: (_______ ± _______) B.
23
It is necessary to experimentally study the dependence of the acceleration of a block sliding on a rough inclined plane on its mass (in all the figures below, m is the mass of the block, α is the angle of inclination of the plane to the horizon, μ is the coefficient of friction between the block and the plane). Which two settings should be used to conduct such a study?
24
Consider the table containing information about bright stars.
Choose two statements that match the characteristics of stars.
1) The surface temperature and radius of Betelgeuse indicate that this star is a red supergiant.
2) The temperature on the surface of Procyon is 2 times lower than on the surface of the Sun.
3) The stars Castor and Capella are at the same distance from the Earth and, therefore, belong to the same constellation.
4) The Vega star belongs to the white stars of spectral class A.
5) Since the masses of the Vega and Capella stars are the same, they belong to the same spectral class.
25
The block moves along a horizontal plane in a straight line with a constant acceleration of 1 m/s 2 under the influence of a force \overrightarrow F directed downward at an angle of 30° to the horizon (see figure). What is the mass of the block if the coefficient of friction of the block on the plane is 0.2 and F = 2.7 N? Round your answer to tenths.
Answer: _____ kg.
26
Along parallel conductors bc and ad, located in a magnetic field with induction B = 0.4 T, a conducting rod MN slides, which is in contact with the conductors (see figure). The distance between the conductors is L = 20 cm. On the left, the conductors are closed by a resistor with a resistance of R = 2 Ohms. The resistance of the rod and conductors is negligible. When the rod moves, a current I = 40 mA flows through resistor R. At what speed is the conductor moving? Assume that the vector \overrightarrow B is perpendicular to the drawing plane.
Answer: _____ m/s.
27
The threshold sensitivity of the retina of the human eye to visible light is 1.65·10 –18 W, while 5 photons hit the retina every second. Determine what wavelength this corresponds to.
Answer: _____ nm.
Part 2.
A complete correct solution to each of problems 28-32 must contain laws and formulas, the use of which is necessary and sufficient to solve the problem, as well as mathematical transformations, calculations with a numerical answer and, if necessary, a drawing explaining the solution.
A constant amount of monatomic ideal gas participates in the process, the graph of which is shown in the figure in coordinates p – n, where p is the gas pressure, n is its concentration. Determine whether the gas receives heat or releases it in processes 1–2 and 2–3. Explain your answer based on the laws of molecular physics and thermodynamics.
Answer: _____
Show answer
1. According to the first law of thermodynamics, the amount of heat that a gas receives is equal to the sum of the change in its internal energy ΔU and the work of gas A: Q = ΔU + A. Concentration of gas molecules n=\frac NV, where N is the number of gas molecules, V is its volume. For an ideal monatomic gas, the internal energy is U=\frac32vRT (where ν is the number of moles of gas). According to the conditions of the problem, N = const.
2. Since in section 1–2 the gas concentration does not change, its volume is constant (isochoric process), which means that the gas work A = 0. In this process, the gas pressure increases, according to Charles’s law, the gas temperature also increases, i.e. its internal energy increases: ΔU > 0. This means Q > 0, and the gas receives heat.
3. In section 2–3, the gas concentration decreases, which means its volume increases, and the gas work is positive: A > 0. The gas pressure is constant (isobaric process), according to Gay-Lussac’s law, the gas temperature also increases. Therefore ΔU > 0. According to the first law of thermodynamics, Q > 0.
In this process, the gas receives heat.
Answer: the gas receives a positive amount of heat in processes 1–2 and 2–3
A small ball with a mass m = 0.3 kg is suspended on a light inextensible thread with a length of l = 0.9 m, which breaks under a tension force T 0 = 6 N. The ball is removed from the equilibrium position (shown in the figure by the dotted line) and released. When the ball passes the equilibrium position, the thread breaks, and the ball immediately collides absolutely inelastically with a block of mass M = 1.5 kg, lying motionless on a smooth horizontal surface of the table. What is the speed u of the block after the impact? Assume that the block moves forward after the impact.
Show answer
1. Immediately before the thread breaks, at the moment of passing the equilibrium position, the ball moves in a circle of radius l with a speed \overrightarrow\nu. At this moment, the force of gravity m\overrightarrow g and the tension force of the thread \overrightarrow(T_0) acting on the ball are directed vertically and cause centripetal acceleration of the ball (see figure). Let's write Newton's second law in projections onto the Oy axis of the inertial reference frame Oxy associated with the Earth:
\frac(mv^2)l=T_0-mg, from where: v=\sqrt(\left(\frac(T_0)m-g\right)l)
2. When passing the equilibrium position, the thread breaks, and the ball, moving horizontally with speed, absolutely inelastically collides with the resting block. During a collision, the momentum of the “ball + block” system is conserved. In projections onto the Ox axis we obtain: mv = (M + m), where u is the projection of the velocity of the block with the ball after impact on this axis.
u=\frac m(M+m)v=\frac m(M+m)\sqrt(\left(\frac(T_0)m-g\right)l)=\frac(0.3)(1.5+ 0.3)\sqrt(\left(\frac6(0.3)-10\right)\times0.9)=\frac16\times3=0.5 m/s
Answer: u = 0.5 m/s
Two identical thermally insulated vessels are connected by a short tube with a tap. The volume of each vessel is V = 1 m3. The first vessel contains ν 1 = 1 mol of helium at a temperature T = 400 K; in the second – ν 2 = 3 mol of argon at temperature T 2 . The tap is opened. After establishing an equilibrium state, the pressure in the vessels is p = 5.4 kPa. Determine the initial temperature of argon T 2.
Show answer
1. Since in this process the gas does not do work and the system is thermally insulated, then, in accordance with the first law of thermodynamics, the total internal energy of gases is conserved:
\frac32v_1RT_1+\frac32v_2RT_2=\frac32(v_1+v_2)RT
where T is the temperature in the combined vessel in an equilibrium state after opening the tap.
2. As a result of recharging, the same voltages are established on the capacitors, since the current in the circuit stops and the voltage across the resistor R becomes zero. Therefore, the capacitors can be considered connected in parallel. Then their total capacity is C 0 =C 1 +C 2
3. According to the law of conservation of charge, the total charge of the capacitors will be equal to C 1 U.
4. According to the law of conservation of energy, the amount of heat released in the circuit is equal to the difference in the energy values of the capacitors in the initial and final states:
Q=\frac(C_1U^2)2-\frac((C_1U)^2)(2(C_1+C_2))
Where do we get:
Q=\frac(C_1C_2U^2)(2(C_1+C_2))=\frac(10^(-6)\times2\times10^(-6)\times300^2)(2(10^(-6) +2\times10^(-6)))=0.03 J.
Answer: Q = 30 mJ
A thin rod AB with a length of l = 10 cm is located parallel to the main optical axis of a thin collecting lens at a distance of h = 15 cm from it (see figure). End A of the stick is located at a distance a = 40 cm from the lens. Construct an image of the rod in the lens and determine its length L. The focal length of the lens is F = 20 cm.