Importance of teaching physics at school. The mass of gas is constant Topic: Internal energy

Lesson Objectives:

Educational:

Introduce the concept of internal energy,
To reveal the scientific ideological significance of the internal energy of the body as the sum of the kinetic energy of the movement of molecules and the potential energy of their interaction.
Introduce students to two ways to change internal energy,
Learn to solve quality problems

Developing:

Develop:

Ability to apply knowledge of theory in practice
Observation and independence
Thinking of students through logical learning activities

Educational:

Continue the formation of ideas about the unity and interconnection of natural phenomena

Lesson plan:

Molecular-kinetic interpretation of the concept of internal energy of the body.
Derivation of the formula for the internal energy of an ideal gas
Ways to change the internal and increase work

Formulate hypotheses and draw conclusions, solve qualitative problems

Lesson type:

Learning new material.

Lesson form: combined.

Complex methodological support, multimedia projector, computer, screen.

Teaching methods.

Verbal.
Visual.
Practical.

During the classes

Topic: Internal energy

1. Organizational moment.

2. Learning new material.

Internal energy. Internal energy of an ideal gas.

From the 8th grade, we know that internal energy is the energy of movement and interaction of particles (molecules) that make up the body.

At the same time, we exclude from consideration the mechanical energy of the body as a single whole (we assume that the body is motionless in a given frame of reference and the potential energy of its interaction with other bodies is equal to 0).

Thus, we are only interested in the energy of the chaotic motion of molecules and their interaction with each other. Internal energy is a function of the state of the body, i.e. depends on temperature and other parameters of the system.

Internal energy is denoted - U.

Internal energy of an ideal gas.

Let's try to calculate the internal energy of an ideal gas. An ideal gas is a model of a very rarefied gas in which the interaction of molecules can be neglected, i.e. the internal energy of an ideal gas consists only of the kinetic energy of molecular motion, which is easy to calculate through the average kinetic energy of motion:

We already know the average kinetic energy of molecular motion:

This formula is true only for a monatomic gas.

If the gas molecules are diatomic (the molecule looks like a dumbbell), then the formula will be different:

Why the energy has become larger is easily explained, if the fact is that a diatomic molecule can not only move forward, but also rotate. Rotation, it turns out, also makes a contribution to the average kinetic energy of the molecule.

How to take into account the contribution to the energy of rotation of molecules?

It turns out that it is possible to prove the theorem on the equipartition of energy over degrees of freedom, which states that for each degree of freedom of motion of molecules, on average, there is 1/2 kT of energy.

What are degrees of freedom?

Kind of molecule	What movements of a molecule are possible	number of degrees of freedom
monatomic gas	Any movement can be represented as the sum of movements in three independent directions: x, y, z, we do not take into account the rotation, so we consider the molecule to be mat. dot.	3 degrees of freedom
diatomic gas	In addition to translational motion, a molecule can also rotate around two axes (any rotation can be represented as the sum of rotations around two axes). We do not take into account the rotation about the axis passing along the molecule, so the molecules consider the mat. dots. We believe that vibrations of atoms in a molecule do not arise.	3+2=5 degrees of freedom
There are three or more atoms in a gas molecule.	There is translational motion (3 degrees of freedom) and rotations around three axes are possible (3 more degrees of freedom). There are no vibrations of atoms.	3+3=6 degrees of freedom.

3. Solving qualitative problems

Solving quality problems (control)

1. Molecular oxygen is at a pressure of 805 Pa in a vessel with a volume of 0.8 m3.

With isochoric cooling, the internal energy of the gas will decrease by 100 kJ.

What is the final pressure of oxygen.

O2
P1 \u003d 105 Pa
V = const
V = 0.8 m3
U = -100J
P2 - ?

Pressure dropped, P2 = P1 - P
i = 5 – number of degrees of freedom
U1 = 5/2 (p1V) ; U2 = 5/2 (p2V)
U \u003d U1 - U2 \u003d 5/2 (V?p) \u003d\u003e
p=2U/5V
p2= p1- (2U/5V)
p2 = 105 Pa - (2 105J/5 0.8 m3) = 105 Pa - 0.5 105 Pa = 0.5 105 Pa = 5 104 Pa

Answer: p2 \u003d 5 104 Pa.

2. Determine what air pressure will be established in two rooms with volumes V 1 and V2 if a door opens between them.

U= 1.25 x106J.

When solving problems for the application of the Clapeyron-Mendeleev equation, one should not forget that this equation describes the state of an ideal gas. In addition, it must be remembered that all the physical quantities used in this section are of a statistical nature. It is useful, when starting to solve problems, to draw a sketch diagram of the process, with suitable variables along the coordinate axes.

Basic laws and formulas

Amount of substance	or
Clapeyron-Mendeleev equation (ideal gas equation of state)
Dalton's law
Molecule concentration
The equation of the molecular kinetic theory of gases
Average kinetic energy of one ideal gas molecule (internal energy)
Internal energy of ideal gas mass
Mayer equation
Molar heat capacity and its relationship with specific
First law of thermodynamics
The work of expansion of gases in the processes:
adiabatic
isothermal
isobaric
Poisson's equation relating gas parameters in an adiabatic process	;
entropy change
Thermal efficiency Carnot cycle

Examples of problem solving

Example 4 Oxygen mass 320g. heated at constant pressure from 300K before 310K. Determine the amount of heat absorbed by the gas, the change in internal energy and the work of expansion of the gas.

Given: m=320g=0.32kg; T 1 =300 K; T 2 =310 K

To find: Q, ΔU, A

Solution: The amount of heat required to heat the gas at constant pressure is determined using the I law of thermodynamics:

substituting numerical values and taking into account that , we obtain

The work of gas expansion in an isobaric process:

(5)

and then subtracting term by term (5) from (4), we get:

and substituting into (3), we find:

Examination: Q= ∆U+A; 2910J= (2080 +830) J

Answer: Q = 2910J; Δ U = 2080J; A = 830J

Example 5. Find the average kinetic energy of the rotational motion of one oxygen molecule at a temperature T=350K, as well as the kinetic energy of the rotational motion of all oxygen molecules with a mass 4g.

Given: T=350K; m = 4g = 4 10 -3 kg; M = 32kg/kmol

To find: b ε vrñ 0 ; E square

Solution: For each degree of freedom of a gas molecule, there is the same average energy, where k- Boltzmann's constant; T is the absolute temperature of the gas. Since the rotational motion of a diatomic molecule O2 corresponds to two degrees of freedom, then the average energy of the rotational motion of an oxygen molecule will be

where N A- Avogadro's number; v = m/M- amount of substance.

Substituting this into (3), we get N = N A m/M.

Now we substitute this into (2):

E qr = N á ε vrñ 0 = N A (m/M)á ε vrñ 0 .

Substitute the numerical values, we get:

E KVR \u003d 6.02 10 -23 mol -1 4.83 10 -21 J 4 10 -3 kg / (32 10 -3 kg / mol) \u003d 364J.

Answer:á ε vrñ 0 = 4.83 10 -21 J; E qr \u003d 364J

Example 6 How will entropy change? 2g hydrogen occupying volume 40l at a temperature 270K if the pressure is doubled at constant temperature, and then the temperature is raised to 320K at a constant volume.

Given: m=2g=2 10 -3 kg; M=2kg/kmol; V \u003d 40l \u003d 4 10 -2 m 3.

T 1 =270K; T2=320K; P 2 \u003d 2P 1

To find: Δ S

Solution: The change in entropy is determined by the formula:

where dQ is the amount of heat generated in the process.

The change in entropy according to the condition occurs due to two processes:

1) isothermal and 2) isochoric. Then:

Quantity of heat dQ 1 And dQ 2 we find from the 1st law of thermodynamics for these processes:

1) dQ 1 =PdV(because dT=0 for T=const)

P we find from the Clapeyron-Mendeleev equation:

Then And

because at T=const, P 1 V 1 \u003d P 2 V 2

2) (because dV=0 And dA=0 at V=const)

And

;

Substituting numerical values, we get:

Answer: Δ S = -2.27 J/K

Tasks for independent solution

51. In a container with a capacity 10l there is compressed air at a temperature of 27°C. After some of the air was released, the pressure dropped by 2 10 5 Pa. Determine the mass of released air. The process is considered isothermal.

52. What volume does the mixture take under normal conditions 4kg helium and 4kg nitrogen?

53. In a vessel having the shape of a sphere, the radius of which 0.2m, be 80g nitrogen. To what temperature can a vessel be heated if its walls can withstand pressure 7 10 5 Pa.

54. At 27°C and pressure 12 10 5 Pa density of a mixture of hydrogen and nitrogen 10 g/dm 3. Determine the molar mass of the mixture.

55. In a container with a capacity 5l be 2kg hydrogen and 1 kg oxygen. Determine the mixture pressure if the ambient temperature is 7°C.

56. Ideal gas pressure 2MPa, concentration of molecules 2 10 3 cm -3. Determine the average kinetic energy of the translational motion of one molecule and the temperature of the gas.

57. Determine the average kinetic energy of the rotational motion of one molecule of a diatomic gas if the total kinetic energy of the molecules in 1kmole this gas 6.02 J.

58. Find the average kinetic energy of the rotational motion of all molecules contained in 0.25g hydrogen at 27°C.

59. Determine the concentration of ideal gas molecules at temperature 350K and pressure 1.0MPa.

60. Determine the temperature of an ideal gas if the average kinetic energy of the translational motion of its molecules 2.8 10 -19 J.

61. Find the increase in internal energy and the work of expansion 30g hydrogen at constant pressure if its volume has increased five times. Initial temperature 270K.

62. Nitrogen mass 1 kg, which is at a temperature 300K compress: a) isothermally; b) adiabatically, increasing the pressure tenfold. Determine the work spent on compression in both cases. How much heat should be reported 1mol oxygen to do the work 10J: a) in an isothermal process; b) with isobaric?

63. Determine how much heat must be imparted to carbon dioxide with a mass 440g to heat it up 10K: a) isochoric, b) isobaric.

64. When heated 0.5kmol nitrogen has been transferred 1000J warmth. Determine the work of expansion at constant pressure.

65. Gas occupying a volume 10l under pressure 0.5MPa, was isobarically heated from 323K before 473K. Find the work of expanding the gas.

66. Gas occupying a volume 12l under pressure 0.2MPa. Determine the work done by the gas if it is heated isobarically from 300K before 348K.

67. Find the work and change in internal energy with an adiabatic expansion of 0.5 kg air if its volume is increased five times. Initial temperature 17°C.

68. Determine the amount of heat reported 14g nitrogen if it was heated isobarically from 37°C before 187°C.. What work will he do and how will his internal energy change?

69. How many times will the volume increase 2mol hydrogen during isothermal expansion at a temperature 27°C, if the heat was spent 8kJ.

70. Determine the molar mass of the gas, if during isochoric heating by 10°С 20g gas will be required 680J heat, and at isobaric 1050J.

71. What is the change in entropy 10g air during isochoric heating from 250K before 800K?

72. With the isobaric expansion of hydrogen with a mass 20g its volume has tripled. Determine the change in the entropy of hydrogen during this process.

73. With isochoric heating 480g oxygen pressure increased 5 once. Find the change in entropy in this process.

74. Volume of helium, mass 1 kg, increased in 4 times: a) isothermally b) adiabatically. What is the entropy change in these processes?

75. Find the change in entropy when heated 1 kg water from 0°С before 100°C and then turning it into steam at the same temperature.

76. How will entropy change during isothermal expansion 0.1kg oxygen, if the volume changes from 5l before 10l?

77. Determine the change in entropy during isobaric heating 0.1kg nitrogen from 17 °С before 97°C .

78. Ice at a temperature -30°С, turns into steam. Determine the change in entropy in this process.

79. What is the change in entropy 10g air during isobaric expansion from 3l before 8l.

What is the change in entropy 20g air during isobaric cooling from 300K before 250K?

Qualitative tasks

81. The volume of gas was reduced in 3 times, and the temperature was increased by 2 times. By how much did the pressure of the gas increase? Consider the gas to be ideal.

82. A compressed spring was dissolved in acid. What was the potential energy of elastic deformation of the spring?

83. We offer two options for explaining the lift force of a balloon filled with hydrogen. According to the first - lifting force - the force of Archimedes. According to the second, the lifting force arises due to the difference in pressure on the upper and lower parts of the ball. How do these explanations differ?

84. Explain why isothermal expansion of a gas is possible only when an amount of heat is supplied to it?

85. Is there a process in which all the heat transferred to the working fluid from the heater turns into useful work?

86. Can all the internal energy of a gas be converted into mechanical work?

87. Why does the efficiency of an internal combustion engine drop sharply during the explosive combustion of a combustible mixture?

88. How will the temperature in the room change if the door of a working refrigerator is left open?

89. When a diatomic gas is heated, its heat capacity at high temperatures has a sharp increase with a subsequent decline. A similar dependence is also observed for polyatomic gases. How can this be explained?

90. A certain gas passes from state I to II, first along the isochore, and then along the isobar. In another case, first along the isobar, then along the isochore. Will the same work be done in both cases?

91. Why does the pump heat up when inflating a car wheel tire?

92. Why do metal and wood of the same temperature feel differently heated to the touch?

93. Can you boil water in a paper cup?

94. Why do drops of water on a hot stove "live" longer than on just a hot one?

95. Why does the water in the kettle "make noise" before boiling?

96. Why does water boil faster in a vessel with a lid than without a lid?

97. Can a balloon in the Earth's atmosphere rise to an unlimited height?

98. A piece of ice floats in a vessel filled to the brim with water. Will the water overflow if the ice melts?

99. Why does a wooden pencil float horizontally in water? Explain why it will float vertically if a weight is attached to one of its ends?

100. Identical lead balls are lowered into vessels of equal volume with water. In one vessel, the temperature of the water 5°C, and in the other 50°C. In which vessel will the ball reach the bottom the fastest?

test questions

21. What is an atom, molecule, ion?

22. What is called a thermodynamic system?

23. What are state parameters?

24. What state of a thermodynamic system is called equilibrium, non-equilibrium?

25. What is an ideal gas?

26. What characterizes the equation of state?

27. Give the definition of Maxwell's distribution law.

28. What is the Boltzmann distribution law?

29. What characterizes the most probable speed?

30. What is the arithmetic average speed?

31. What is heat?

32. Define the first law of thermodynamics.

33. What isoprocesses do you know?

34. What is an isothermal process?

35. How to calculate the gas work of isochoric and isobaric processes?

36. Give the definition of an adiabatic process.

37. What physical parameters are connected by Mayer's equation?

38. What is the heat capacity of a body, specific and molar heat capacities?

39. What does the second law of thermodynamics say?

40. How to increase the efficiency of a heat engine?

9.5 Heat capacity

1) In a room measuring 6 * 5 * 3 m, the air temperature is 27 0 C at a pressure of 101 kPa. Find how much heat must be removed from this air in order to lower its temperature to 17 0 C at the same pressure.

The average specific heat capacity of air is 1.004 kJ/(kg·K). The mass of air in the room is assumed to be constant. Answer: 1.06 MJ.

2) 17000 kJ of heat is removed from the nitrogen contained in the cylinder. At the same time, its temperature drops from 800 to 200 0 C. Find the mass of nitrogen contained in the balloon. Answer: 34.6 kg.

3) In a tubular air heater, the air is heated at a constant pressure from 10 to 90 0 C. Find the mass flow rate of air passing through the air heater if it is supplied with 210 MJ / h of heat.

Answer: 2610 kg/h.

4) Find the amount of heat required to heat at a constant volume of 10 kg of nitrogen from 200 0 C to 800 0 C. Answer: 4.91 MJ.

5) Find the average isobaric and isochoric molar heat capacities of the fuel combustion products when they are cooled from 1100 to 300 0 C. The molar fractions of the components of these combustion products are as follows: ; ; ; .

Answer: J / (mol K); J / (mol K).

6) Find the average specific heat capacity of oxygen at constant pressure as the temperature rises from 600 0 C to 2000 0 C.

Answer: 1.1476 kJ/(kg K).

7) Find the average molar isobaric heat capacity of carbon dioxide as its temperature rises from 200 0 С to 1000 0 С.

Answer: 52.89 kJ / mol.

8) The air contained in a cylinder with a capacity of 12.5 m 3 at a temperature of 20 0 C and a pressure of 1 MPa is heated to a temperature of 180 0 C. Find the heat supplied. Answer: 17.0 MJ.

9) Find the average specific isochoric and isobaric heat capacities of oxygen in the temperature range 1200 ... 1800 0 С.

Answer: 0.90 kJ / (kg K); 1.16 kJ/(kg K).

10) Find the average molar isochoric heat capacity of oxygen when it is heated from 0 to 1000 0 C. Answer: 25.3 kJ / (kg K).

11) The temperature of a mixture consisting of nitrogen weighing 3 kg and oxygen weighing 2 kg as a result of the supply of heat to it at a constant volume rises from 100 to 1100 0 C. Determine the amount of heat supplied. Answer: 4.1 MJ.

12) The composition of the combustion products of gasoline in the engine cylinder in moles is as follows: \u003d 71.25; =21.5; =488.3; =72.5. The temperature of these gases is 800 0 C, the environment is 0 0 C. Determine the proportion of heat losses with exhaust gases if the calorific value of gasoline is 43950 kJ / kg.

13) The gas mixture consists of 2 kg of carbon dioxide, 1 kg of nitrogen, 0.5 kg of oxygen. Find the average molar isobaric heat capacity of the mixture in the temperature range 200 ... 800 0 C. Answer: 42.86 J / (mol K).

14) Find the average isobaric and isothermal molar heat capacities of the fuel combustion products when they are cooled from 1100 to 300 0 C. The molar fractions of the components of these combustion products are as follows: = 0.09; =0.083; =0.069; =0.758. Answer: 32.3 J / (mol K); 27.0 J/(mol K).

15) The composition of the exhaust gases of the internal combustion engine in moles is as follows: \u003d 74.8; =68; =119; =853. Find the amount of heat released by these gases when their temperature is lowered from 380 to 20 0 C.

9.6 Thermodynamic processes of gases

1) What amount of heat must be imparted to carbon dioxide contained in a cylinder with a capacity of 0.8 m 3 to increase the pressure from 0.1 to 0.5 MPa, assuming = 838 J / (kg·K). Answer: 1.42 MJ.

2) Air in a cylinder with a capacity of 100 liters at a pressure of 0.3 MPa and a temperature of 15 0 C is supplied with heat in the amount of 148.8 kJ. Find the final temperature and air pressure in the balloon if the specific heat capacity = 752 J/(kg·K). Answer: 560 0 С; 0.87 MPa.

3) Air under initial conditions V 1 \u003d 0.05 m 3, T 1 \u003d 850 K and p\u003d 3 MPa expands at constant pressure to a volume of V 2 \u003d 0.1 m 3. Find the final temperature, the supplied heat of change in internal energy, and the work done to change the volume. Answer: 1700 K; 619 kJ; 150 kJ; 469 kJ.

Build process charts

Build process charts, occurring with an ideal gas, in the coordinates p, T and V, T. The mass of the gas is constant.

Build process charts, occurring with an ideal gas, in the coordinates p, T and p, V. The mass of the gas is constant.

Build process charts, occurring with an ideal gas, in the coordinates V, T and p, V. The mass of the gas is constant.

Build process charts

Build process charts, occurring with an ideal gas, in the coordinates p, V and p, T. The mass of the gas is constant.

Build process charts
Build process charts, occurring with an ideal gas, in the coordinates p, T and V, T. The mass of the gas is constant.

Build process charts, occurring with an ideal gas, in the coordinates p, V and T, V. The mass of the gas is constant.

Plot graphs of the process that occurs with an ideal gas in the coordinates p, T and V, T. The mass of the gas is constant.

Determine the temperature of an ideal gas in state 2 if states 2 and 4 lie on the same isotherm. The temperatures T1 and T3 in states 1 and 3 are known.

[µ §]
The ideal gas was sequentially transferred from state 1 with temperature T1 to state 2 with temperature T2, and then to state 3 with temperature T3 and returned to state 1. Find the temperature T3 if the state change processes occurred as shown in the figure, and T1 and T2 are known.

A mole of an ideal gas is involved in the thermal process 1 ЁC 2 ЁC 3 ЁC 4 ЁC 1, depicted in p-V coordinates. Continuations of line segments 1 ЁC 2 and 3 ЁC 4 pass through the origin, and curves 1 ЁC 4 and 2 ЁC 3 are isotherms. Draw this process in V-T coordinates and find volume V3 if volumes V1 and V2 = V4 are known.

[µ §]
one mole ideal gas, are transferred from state 1 to state 2. Determine the maximum temperature Tmax of the gas during this process.

20 g of helium enclosed in a cylinder under the piston are infinitely slowly transferred from a state with a volume of 32 liters and a pressure of 4 105 Pa to a state with a volume of 9 liters and a pressure of 15.5 105 Pa. What is the highest temperature gas in this process, if on the graph of the dependence of gas pressure on the volume of the process is depicted by a straight line?

[µ §]
The change in the standing of an ideal gas of constant mass is shown in the figure. At point 1, the gas temperature T0. Determine the gas temperature at points 2, 3, 4.

[T2=3T0; Т3=6Т0; Т4=2Т0]
The p-V diagram shows a graph of the gas expansion process, in which the gas passes from state 1 with pressure p0 and volume V0 to state 2 with pressure p0/2 and volume 2V0. draw the corresponding process graph on the p-T and V-T diagrams.

2. Fundamentals of thermodynamics
a) internal energy of a monatomic gas

µ § U ЁC internal energy (J)

B) work in thermodynamics

µ § A ЁC work (J)

µ § µ § - volume change

µ § - temperature change

B) the first law of thermodynamics

µ § ДU ЁC change in internal energy

µ § Q ЁC amount of heat

µ § - work of external forces on gas

µ § - gas work against external forces

D) efficiency of a heat engine

µ § h ЁC coefficient of performance (COP)

A ЁC the work done by the engine

Q1 EC quantity of heat received from the heater

µ § Q2 ЁC quantity of heat transferred to the refrigerator

µ § T1 ЁC heater temperature

Т2 ЁC refrigerator temperature

D) the amount of heat

µ § Q ЁC amount of heat (J)

µ § Heat balance equation

Q1 EC quantity of heat given by a more heated body;

Q2 ЁC is the amount of heat received by a colder body.

What volume is occupied by a monatomic ideal gas if at normal atmospheric pressure its internal energy is 600 J?

Find the concentration of ideal gas molecules in a vessel with a capacity of 2 liters at a temperature of 27 ° C, if its internal energy is 300 J.

What mass of hydrogen is under the piston in a cylindrical vessel if, when heated from 250 to 680 K at a constant pressure on the piston, the gas performed work equal to 400 J?

With isochoric cooling, the internal energy decreased by 350 J. What work did the gas do in this case? How much heat was transferred by the gas to the surrounding bodies?

What work did a monatomic ideal gas do and how did its internal energy change during isobaric heating of the gas in an amount of 2 mol per 50 K? How much heat was received by the gas in the process of heat exchange?

With isobaric cooling by 100 K, the internal energy of a monatomic ideal gas decreased by 1662 kJ. What work was done by the gas and how much heat was transferred by it to the surrounding bodies?

[-1108 kJ; -2770 J]
During adiabatic compression of the gas, work of 200 J was performed. How and how much did the internal energy of the gas change in this case?

During the adiabatic process, 150 J of work was done by the gas. How and how much did its internal energy change?

[-150 J]
What work will be done by oxygen with a mass of 320 g under isobaric heating of 10 K?

Calculate the increase in the internal energy of hydrogen with a mass of 2 kg with an increase in its temperature by 10 K: 1) isochoric; 2) isobaric.

The volume of oxygen weighing 160 g, the temperature of which is 27 ° C, doubled during isobaric heating. Find the work of the gas during expansion, the amount of heat that went into heating oxygen, the change in internal energy.

For isobaric heating of a gas in an amount of 800 mol per 500 K, he was given an amount of heat of 9.4 MJ. Determine the work of the gas and the increment of its internal energy.

A cylinder with a capacity of 1 liter contains oxygen at a pressure of 107 Pa and at a temperature of 300 K. An amount of heat of 8.35 kJ is supplied to the gas. Determine the temperature and pressure of the gas after heating.

When an amount of heat of 125 kJ is applied to an ideal gas, the gas does work of 50 kJ against external forces. What is the final internal energy of the gas if its energy before adding the amount of heat was equal to 220 kJ?

Oxygen weighing 32 g is in a closed vessel under a pressure of 0.1 MPa at a temperature of 17 0C. After heating, the pressure in the vessel doubled. Find: 1) the volume of the vessel; 2) the temperature to which the gas is heated; 3) the amount of heat imparted to the gas.

What amount of heat is required for an isobaric increase in the volume of molecular nitrogen weighing 14 g, having a temperature of 27 0C before heating, by 2 times?

With the adiabatic expansion of air, 500 J of work was done. What is the change in the internal energy of air?

[-500 J]
With an adiabatic air compression of 8 mol of helium in the compressor cylinder, work of 1 kJ was performed. Determine the change in gas temperature.

With the adiabatic expansion of 64 g of oxygen O2, which is under normal conditions, the temperature of the gas increased by a factor of 2. Find: change in internal energy; gas expansion work.

[-11.3 kJ; 11.3 kJ]
The temperature of nitrogen weighing 1.4 kg as a result of adiabatic expansion dropped by 20 0C. What is the work done by the gas during expansion?

Molecular oxygen occupies a volume of 2 m3 under normal conditions. When gas is compressed without heat exchange with the environment, work of 50.5 kJ is performed. What is the final temperature of oxygen?

[T1 (1+ 2A / 5p1V1) = 300.3 K]

Air weighing 87 kg is heated from 10 0C to 30 0C. Determine the change in the internal energy of air. The molar mass of air should be taken equal to 2.910 -2 kg / mol, and air should be considered a diatomic (ideal) gas.

Find the change in the internal energy of helium during the isobaric expansion of the gas from an initial volume of 10 liters to a final volume of 15 liters. Gas pressure 104 Pa.

Molecular oxygen is under pressure of 105 Pa in a vessel with a volume of 0.8 m 3. With isochoric cooling, the internal energy of the gas decreases by 100 kJ. What is the final pressure of oxygen?

When two spacecraft dock, their compartments are interconnected. The volume of the first compartment is 12 m 3, the second one is 20 m 3. The pressure and air temperature in the compartments are respectively 0.98105 Pa and 1.02105 Pa, 17 oC and 27 oC. What air pressure will be established in the combined module? What will be the air temperature in it?

What is the internal energy of 10 moles of a monatomic gas at 27°C?

How much does the internal energy of helium weighing 200 g change with an increase in temperature by 20 ° C?

[at 12.5 kJ]
What is the internal energy of helium filling a balloon with a volume of 60 m3 at a pressure of 100 kPa?

Two moles of an ideal gas are compressed isothermally at 300 K to half their original volume. What work is done by the gas? Depict qualitatively the considered process on the diagram p, V.

[-3.46 kJ]
In some process, the gas has done work equal to 5 MJ, and its internal energy has decreased by 2 MJ. How much heat is transferred to the gas in this process?

When transferring 300 J of heat to the gas, its internal energy decreased by 100 J. What work did the gas do?

0 moles of a monatomic ideal gas are heated to 50°C. The process is isobaric. How much heat is received by the gas?

A monatomic ideal gas received 2 kJ of thermal energy from the heater. How much has his internal energy changed? The process is isobaric.

[at 1200 J]
200 J of heat is transferred to the gas and the gas does 200 J of work against external forces. What is the change in the internal energy of the gas?

[per 50 kJ]
How much has the internal energy of the gas changed, which did the work of 100 kJ, receiving the amount of heat 135 kJ?

[at 35 kJ]

Work done on the gas was 25 kJ. Did the gas receive or give off heat in this process? What exactly is the amount of heat?

[-50 kJ]
Nitrogen weighing 280 g was heated at a constant pressure to 1000 C. Determine the work of expansion.

Determine the work of expansion of 20 liters of gas during isobaric heating from 300 K to 393 K. The gas pressure is 80 kPa.

With isobaric heating at 159 K by a gas whose mass is 3.47 kg, work was done 144 k J. Find the molar mass of the gas? What is this gas?

There is oxygen in the cylinder below the piston. Define its mass, if it is known that the work done when oxygen is heated from 273 K to 473 K is 16 kJ. Ignore friction.

By how much did the internal energy of the gas change if it was given an amount of heat of 20 kJ and 30 kJ of work was done on it?

[per 50 kJ]
The work done on the gas was 75 kJ, while its internal energy increased by 25 kJ. Did the gas receive or give off heat in this process? What exactly is the amount of heat?

How much heat must be transferred to the gas so that its internal energy increases by 45 kJ and the gas does work of 65 kJ.

For isobaric heating of a gas with an amount of substance of 800 mol per 500 K, he was given an amount of heat of 9.4 MJ. Determine the work of the gas and the increase in its internal energy.

There is 1.25 kg of air in the cylinder under the piston. To heat it by 40 C at constant pressure, 5 kJ of heat was expended. Determine the change in the internal energy of air (M = 0.029 kg / mol).

What work will be done by the gas, expanding at a constant pressure of 3 atm. from a volume of 3 l to a volume of 18 l? What work will be done by 6 kg of air expanding under isobaric heating from 5 to 150 C?

A balloon at a constant pressure of 1.2 105 Pa was inflated from a volume of 1 liter to a volume of 3 liters. What was the work done?

With an adiabatic compression of 5 g of helium, work of 249.3 J is performed. What was the temperature of helium if the initial temperature was 293 K? The molar mass of helium is 4 10 ЁC3kg / mol.

Piston loaded, whose mass is 50 kg, and the base area is 0.01 m2, is located in a cylinder in which the gas is heated. The piston slowly rises, and the volume of gas increases by 2 liters. Calculate the work done by the gas.

For the isobaric heating of 800 moles of gas at 500 K, he was told the amount of heat was 9.4 MJ. Determine the change in the internal energy of the gas.

The energy of 60 J was spent on heating the gas, accompanied by its expansion at a constant pressure of 3 x 104 Pa. The volume of the gas increased by 1.5 liters during heating. How has the internal energy of the gas changed?

One mole of an ideal gas is isochorically transferred from state 1 to state 2, while the pressure decreased by 1.5 times. Then the gas was heated isobarically to the initial temperature of 300 K. What work was done by the gas as a result of the transitions made?

One mole of an ideal gas completes a closed process consisting of two isochores and two isobars. The temperature at point 1 is equal to T1, at point 3 it is equal to C T3. Determine the work done by the gas per cycle if points 2 and 4 lie on the same isotherm.

One mole of ideal gas is in the cylinder under the piston at temperature T1. The gas at constant pressure is heated to a temperature T3. Next, the gas is cooled at constant pressure so that its volume is reduced to its original value. Finally, at a constant volume, the gas is returned to its original state. What is the work done by the gas in this process?

The figure shows two closed processes that occur with an ideal gas: 1 ЁC 2 ЁC 3 ЁC 1 and 3 ЁC 2 ЁC 4 ЁC 3. In which of them does the gas do work?

[in progress 3 Q 2 Q 4 - 3]
Mass m ideal gas, which is at a temperature, is cooled isochorically so that the pressure drops n times. The gas then expands at constant pressure. In the final state, its temperature is equal to the initial one. Determine the work done by the gas. Molar mass of gas M.

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Four moles of an ideal gas complete the process shown in the figure. In which area is the work of gas the maximum? What is this job?

One mole of an ideal gas completes the process shown in the figure. Find the work done by the gas per cycle.

Determine the temperature of water established after mixing 39 liters of water at 20 °C and 21 liters of water at 60 °C.

How many liters of water at 95 °C must be added to 30 liters of water at 25 °C to obtain water with a temperature of 67 °C?

A piece of tin heated to 507 K is released into a vessel containing 2.35 kg of water at 20 °C; the temperature of the water in the vessel increased by 15 K. Calculate the mass of tin. Ignore the evaporation of water.

A steel drill weighing 0.090 kg, heated during hardening to 840 °C, is lowered into a vessel containing machine oil at 20 °C. Which amount of oil to take so that its final temperature does not exceed 70 °C?