Thermodynamics: 2A.2 The Definition of Internal Energy

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What is the internal energy of a system comprised of?

The potential energy of the system only

The kinetic and potential energy of the constituents of the system (correct)

The kinetic energy arising from the motion of the system as a whole

The total kinetic energy of the system

What does the symbol ΔU represent in thermodynamics?

The change in internal energy of a system (correct)

The total internal energy of a system

The initial state of a system

The final state of a system

What is the convention used in thermodynamics to denote the change in a property of a system?

ΔX = Xf - Xi (correct)

ΔX = Xi - Xf

ΔX = Xf + Xi

ΔX = Xi / Xf

What is the characteristic of internal energy as a state function?

It depends on the current state of the system only Signup and view all the answers

What happens to the internal energy of a system when one of the state variables is changed?

It may result in a change in internal energy Signup and view all the answers

What is the unit of measurement for internal energy?

Joules Signup and view all the answers

What is the key idea behind the comparison of a system to a bank?

A system can accept energy deposits in the form of either heat or work. Signup and view all the answers

What is the significance of the First Law of thermodynamics?

It summarizes the observations that the internal energy of an isolated system remains constant. Signup and view all the answers

What is the mathematical statement of the First Law of thermodynamics?

ΔU = q + w Signup and view all the answers

What is the significance of the 'acquisitive convention' in the mathematical statement of the First Law?

It views the flow of energy from the system's perspective. Signup and view all the answers

What can be inferred about an isolated system?

Its internal energy is constant. Signup and view all the answers

Why is it impossible to build a perpetual motion machine?

Because it would violate the First Law of thermodynamics. Signup and view all the answers

What is the unit of molar internal energy?

kJmol−1 Signup and view all the answers

Which of the following is a type of motion that contributes to the internal energy of a molecule?

Translation, rotation, and vibration Signup and view all the answers

What is the equipartition theorem used to predict?

The average energy associated with each mode of motion Signup and view all the answers

What is the average value of each quadratic contribution to the energy according to the equipartition theorem?

1/2 kT Signup and view all the answers

Why is the equipartition theorem unlikely to apply to vibrational and electronic states?

The separation between the energy levels is too large Signup and view all the answers

What is the average kinetic energy of an atom in a gas according to the equipartition theorem?

3/2 kT Signup and view all the answers

What is the molar translational energy of a perfect gas?

3/2 RT Signup and view all the answers

Why is the internal energy of a perfect gas independent of the volume it occupies?

Because there are no intermolecular interactions Signup and view all the answers

What happens to the internal energy of a system as the temperature is raised?

It increases as the various modes of motion become more highly excited Signup and view all the answers

How can the internal energy of a system be changed?

Either by doing work on the system or by heating it Signup and view all the answers

What is the implication of the internal energy being a state function in terms of its independence from the system's preparation history?

It means that the internal energy is independent of how the system has been prepared, and only depends on the current state of the system. Signup and view all the answers

How does the internal energy of a system differ from the kinetic energy of the system as a whole?

The internal energy is the energy internal to the system, whereas the kinetic energy of the system as a whole refers to the energy arising from the motion of the system as a whole, such as its kinetic energy as it accompanies the Earth on its orbit round the Sun. Signup and view all the answers

What is the significance of the convention ΔX = Xf − Xi in thermodynamics, and how does it relate to the internal energy?

This convention is used to denote the change in a property of a system, and in the case of internal energy, it is used to calculate the change in internal energy (ΔU) as a system changes from an initial state to a final state. Signup and view all the answers

Why is the internal energy of a system considered an extensive property, and what are the implications of this property?

The internal energy is an extensive property because it depends on the amount of substance present, and its value increases with the size of the system. Signup and view all the answers

What is the relationship between the internal energy of a system and the variables that determine its current state?

The internal energy is a function of the variables that determine the current state of the system, such as pressure, temperature, and volume. Signup and view all the answers

What is the implication of the internal energy being independent of the system's motion as a whole?

It means that the internal energy is a property of the system's internal state, and does not depend on the system's motion or position in space. Signup and view all the answers

What is the physical significance of the quadratic contributions to the energy in the context of the equipartition theorem?

Quadratic contributions to the energy represent the kinetic energy or potential energy associated with various modes of motion, such as translation, rotation, and vibration, which are proportional to the square of the momentum or displacement from an equilibrium position. Signup and view all the answers

How does the internal energy of a system change when the temperature is raised, and what is the underlying physical explanation?

The internal energy of a system increases as the temperature is raised, and states of higher energy become more highly populated. This is because the molecules gain more energy and their modes of motion become more highly excited. Signup and view all the answers

What is the significance of the distinction between intensive and extensive properties in the context of internal energy?

The internal energy is an extensive property that depends on the amount of substance, whereas the molar internal energy is an intensive property that is independent of the amount of substance. Signup and view all the answers

How does the internal energy of a perfect gas differ from that of a system with interacting molecules?

The internal energy of a perfect gas is independent of the volume it occupies, whereas the internal energy of a system with interacting molecules has an additional contribution from the potential energy of interaction. Signup and view all the answers

What is the physical basis for the increase in internal energy of a system with increasing temperature?

The increase in internal energy is due to the greater population of higher energy states as the temperature is raised, resulting in increased energy associated with various modes of motion. Signup and view all the answers

How does the equipartition theorem relate to the concept of thermal equilibrium?

The equipartition theorem applies to systems at thermal equilibrium, where the average energy associated with each mode of motion is proportional to the temperature. Signup and view all the answers

What is the significance of the Boltzmann distribution in understanding the behavior of systems at different temperatures?

The Boltzmann distribution provides a way to calculate the average energy associated with each mode of motion of an atom or molecule in a sample at a given temperature. Signup and view all the answers

How does the internal energy of a system depend on the modes of motion of its constituent molecules?

The internal energy of a system depends on the energy associated with various modes of motion, such as translation, rotation, and vibration, which are influenced by the temperature and interactions between molecules. Signup and view all the answers

What does the 'blindness' of a system to the mode of energy transfer imply about the internal energy of the system?

It implies that the internal energy of a system is independent of the mode of energy transfer, and that both heat and work can bring about changes in internal energy. Signup and view all the answers

What is the physical significance of the separation between energy levels in the context of the equipartition theorem?

The separation between energy levels determines whether the equipartition theorem is applicable, with the theorem being applicable when the separation is small compared to kT. Signup and view all the answers

What is the fundamental idea behind the comparison of a system to a bank, and what does it suggest about the nature of internal energy?

The fundamental idea is that a system can accept 'deposits' of energy in different forms (work or heat), but stores its energy as internal energy, suggesting that internal energy is a state function that is independent of the mode of energy transfer. Signup and view all the answers

How does the concept of internal energy relate to the concept of energy in classical mechanics?

The internal energy of a system is related to the energy associated with various modes of motion, such as translation, rotation, and vibration, which are concepts from classical mechanics. Signup and view all the answers

What is the significance of the experimental evidence for the impossibility of building a perpetual motion machine, and what does it imply about the nature of energy and its transformations?

The impossibility of building a perpetual motion machine implies that energy cannot be created or destroyed, only converted from one form to another, and that the total energy of an isolated system remains constant. Signup and view all the answers

What does the mathematical statement of the First Law (ΔU = q + w) imply about the relationship between the internal energy of a system and the energy transferred to it as heat and work?

It implies that the change in internal energy of a system is equal to the total energy transferred to it as heat and work, and that the internal energy of a system is a state function that depends only on the initial and final states of the system. Signup and view all the answers

What is the implication of the 'acquisitive convention' used in the mathematical statement of the First Law, and how does it influence our understanding of energy transfer and internal energy?

The 'acquisitive convention' implies that energy transfer is viewed from the perspective of the system, and that energy transferred to the system is positive, while energy transferred from the system is negative, influencing our understanding of energy transfer and internal energy as a state function. Signup and view all the answers

What is the significance of the First Law of thermodynamics, and what does it imply about the nature of energy and its transformations in isolated systems?

The First Law implies that the total energy of an isolated system remains constant, and that energy cannot be created or destroyed, only converted from one form to another, highlighting the fundamental principle of energy conservation. Signup and view all the answers