Thermodynamics Quiz: Internal Energy of Gases

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Questions and Answers

What is internal energy primarily comprised of in a monatomic gas?

Rotational and vibrational energies

Only translational kinetic energy (correct)

Translational and vibrational energies

Internal potential energy and translational energy

Which of the following equations correctly represents the internal energy of a monatomic gas with N particles?

U = rac{3}{2} N $ kT $ (correct)

U = N $ mv_{rms}^2 $

U = N $ kT $

U = N $ RT $

How does the internal energy of an ideal gas relate to its temperature?

It is directly proportional to the Kelvin temperature. (correct)

It is inversely proportional to the temperature.

It is independent of the temperature.

It is proportional to the square of the temperature.

For a monatomic gas, how can the internal energy also be expressed using moles (n)?

U = rac{3}{2} n $ kT $ Signup and view all the answers

What condition is NOT applicable when using the equation U = nRT for internal energy?

When the gas is diatomic Signup and view all the answers

What does the internal energy of an ideal gas depend on?

Temperature in Kelvin Signup and view all the answers

According to the first law of thermodynamics, which equation correctly represents the relationship between internal energy, heat, and work?

ΔU = Q - W Signup and view all the answers

Which of the following accurately describes a thermodynamic system?

The object of focus that exchanges energy with its surroundings Signup and view all the answers

What is the change in internal energy when 3000 J of heat flows into a system and 1000 J of work is done by the system?

2000 J Signup and view all the answers

What conclusion can be made about the energy of diatomic gases compared to monatomic gases regarding internal energy?

Diatomic gases have a different constant of proportionality for internal energy than monatomic gases Signup and view all the answers

What does the branch of thermodynamics primarily focus on?

The relationship between heat and other forms of energy Signup and view all the answers

Which type of wall allows heat to flow through?

Diathermal walls Signup and view all the answers

Which law states that two systems in equilibrium with a third are also in thermal equilibrium with each other?

Zeroth Law of Thermodynamics Signup and view all the answers

When two systems are brought into contact and no heat flows between them, they are said to be in what?

Thermal equilibrium Signup and view all the answers

If a thermometer is used to measure the temperature of two systems, what can be concluded about the systems if they are in equilibrium with the thermometer?

They are in thermal equilibrium with each other Signup and view all the answers

In the context of the Zeroth Law, what is an indicator of thermal equilibrium?

There is no heat flow Signup and view all the answers

Which of the following best describes an adiabatic wall?

Perfectly insulates against heat transfer Signup and view all the answers

What is the main requirement for a system to be described as having a single temperature?

All parts in thermal equilibrium Signup and view all the answers

What is the relationship between temperature and heat flow when systems are in thermal contact?

Heat flows towards the cooler system Signup and view all the answers

What does the change in internal energy depend on according to the first law of thermodynamics?

Heat flow and work done Signup and view all the answers

In the context of the first law of thermodynamics, how is work defined by engineers?

As work done by the system Signup and view all the answers

If a system gains heat, what is the sign of Q in ΔU = Q - W?

Positive Signup and view all the answers

How is work treated in the sign convention used by physicists?

As positive when done on the system Signup and view all the answers

What would be the internal energy change if a system gains 1500 J of heat and 2200 J of work is done by the system?

−700 J Signup and view all the answers

What does ΔU = U f − U i = Q − W represent?

The change in internal energy due to heat flow and work Signup and view all the answers

What does work done BY the system indicate in terms of energy transfer?

Energy is lost from the system Signup and view all the answers

Which statement correctly describes the other sign convention mentioned?

Work done by the system is considered negative. Signup and view all the answers

How does an air conditioner operate in terms of heat transfer?

It transfers heat from inside the house to outside the house. Signup and view all the answers

What happens to the internal energy of a monatomic gas that absorbs heat while expanding at constant pressure and temperature?

The internal energy increases due to heat absorption. Signup and view all the answers

In an adiabatic process, what happens to the temperature of boiling water in a thermally equilibrated container?

The temperature remains constant as long as heat is not added or removed. Signup and view all the answers

What is the change in internal energy when heat is lost by a system?

It decreases by the amount of heat lost. Signup and view all the answers

What does the first law of thermodynamics imply when a system does work on its surroundings?

The internal energy decreases. Signup and view all the answers

When is heat considered positive in the context of thermodynamics?

When the system gains heat from the surroundings. Signup and view all the answers

If a physicist removes energy from a system until it reaches a temperature close to absolute zero, what is true about the internal energy?

It approaches zero as the temperature nears absolute zero. Signup and view all the answers

Which statement about the transfer of heat and work in the context of the first law of thermodynamics is accurate?

Heat transfer can change the internal energy of a system. Signup and view all the answers

Study Notes

Lecture 9 Summary

Lecture 9 covers internal energy, thermodynamic systems, the zeroth law of thermodynamics, and the first law of thermodynamics.
The reading material is from Cutnell & Johnson sections 14.3, 15.1-15.3.
Internal energy (U) is the sum of all the energies of the individual atoms or molecules of a substance. This includes translational, rotational, vibrational (kinetic and potential) energies, and potentially other energies (e.g., magnetic).
For a monatomic gas, atoms are considered point-like with mass concentrated at the point. There is no rotational, vibrational, or chemical bonding energy. Internal energy is the sum of only the translational kinetic energies.
For N particles, U = N * (1/2) * mv_rms². Using the microscopic definition of temperature, mv_rms²/2 = (3/2)kT, internal energy becomes U = N * (3/2)kT. n moles can replace N particles, so U = (3/2)*nRT.
Internal energy is proportional to Kelvin temperature for any ideal gas, although the constant of proportionality can differ based on the gas type (monatomic, diatomic, etc.)
Thermodynamics is the branch of physics dealing with heat and its relation to other energy forms and work. It looks at macroscopic properties like temperature, internal energy, pressure, and volume.
A car engine is an example of a thermodynamic system: Fuel is burned at high temperatures. Some internal energy is used to drive pistons, and excess heat is removed by the cooling system.
A thermodynamic system is the object or collection of objects of interest. Surroundings are everything else in the environment.
Heat and work may transfer between the system and the surroundings.
Walls of a system, like diathermal walls, permit heat flow, or adiabatic walls (perfectly insulating) prevent heat flow.
The zeroth law of thermodynamics states: Two systems individually in equilibrium with a third system are in thermal equilibrium with each other. This signifies a shared temperature. No heat flow occurs between objects of the same temperature in contact. Thermal equilibrium exists when there's no heat flow between two objects when brought in contact. Temperature is the indicator of this equilibrium.
The zeroth law of thermodynamics is useful conceptually in defining a temperature scale in relation to various objects and systems. For example, a thermometer is used as a third system to determine if two other systems are in thermal equilibrium with each other.
First law of thermodynamics: Forces can do work, changing the kinetic and potential energy of an object. A substance's atoms/molecules collide; exert forces on each other and surrounding walls. This gives kinetic and potential energy. Internal energy is the total sum of this energy and other molecular energies.
When heat or work occurs in a thermodynamic system, the internal energy can change as a result. The first law relates the change in internal energy to the heat transferred and the work done.
- AU = U_f – U_i = Q – W
- A system gains heat (Q), the change in internal energy (AU) is equal to the heat gained minus the work done. The sign convention is that heat is positive when the system gains heat, and negative when it loses heat. Work (W) is positive when done by the system and negative when done on the system.
The example problems illustrate how heat and work affect the change in internal energy (AU) of a system (following the first law in either scenario with heat being absorbed by the system, or work done by the system or on the system.

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Test your knowledge on the internal energy of monatomic gases in this thermodynamics quiz. Explore key concepts such as the relationship between internal energy, temperature, and thermodynamic laws. Ideal for students studying thermodynamics in physics courses.