66 Questions
What is the internal energy of a system comprised of?
The kinetic and potential energy of the constituents of the system
What does the symbol ΔU represent in thermodynamics?
The change in internal energy of a system
What is the convention used in thermodynamics to denote the change in a property of a system?
ΔX = Xf - Xi
What is the characteristic of internal energy as a state function?
It depends on the current state of the system only
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
What is the unit of measurement for internal energy?
Joules
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.
What is the significance of the First Law of thermodynamics?
It summarizes the observations that the internal energy of an isolated system remains constant.
What is the mathematical statement of the First Law of thermodynamics?
ΔU = q + w
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.
What can be inferred about an isolated system?
Its internal energy is constant.
Why is it impossible to build a perpetual motion machine?
Because it would violate the First Law of thermodynamics.
What is the unit of molar internal energy?
kJmol−1
Which of the following is a type of motion that contributes to the internal energy of a molecule?
Translation, rotation, and vibration
What is the equipartition theorem used to predict?
The average energy associated with each mode of motion
What is the average value of each quadratic contribution to the energy according to the equipartition theorem?
1/2 kT
Why is the equipartition theorem unlikely to apply to vibrational and electronic states?
The separation between the energy levels is too large
What is the average kinetic energy of an atom in a gas according to the equipartition theorem?
3/2 kT
What is the molar translational energy of a perfect gas?
3/2 RT
Why is the internal energy of a perfect gas independent of the volume it occupies?
Because there are no intermolecular interactions
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
How can the internal energy of a system be changed?
Either by doing work on the system or by heating it
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
The change in internal energy ΔU is independent of the path by which the change occurs.
True
The internal energy of a system includes the kinetic energy of the system as a whole.
False
The internal energy is an intensive property of a system, meaning its value is independent of the amount of substance present.
False
The unit of internal energy is typically measured in joules per kilogram.
False
The change in internal energy ΔU can be either positive, negative, or zero.
True
The internal energy of a system is a measurable quantity, meaning it can be directly measured in experiments.
False
If a system is isolated from its surroundings, its internal energy can be changed by doing work or transferring heat.
False
The First Law of thermodynamics states that the internal energy of a closed system is equal to the energy transferred as heat or work.
True
The 'acquisitive convention' used in the mathematical statement of the First Law implies that energy is always transferred from the system to the surroundings.
False
A system can do work without consuming fuel or using some other source of energy, but only in ideal conditions.
False
The internal energy of a system is a function of the mode of energy transfer, whether it is heat or work.
False
The First Law of thermodynamics is a statement about the conservation of energy in a system.
True
The internal energy of a perfect gas is dependent on the volume it occupies.
False
The equipartition theorem can be used to predict the contributions of each mode of motion of a molecule to the total energy of an interacting system.
False
The molar internal energy is an intensive property.
True
The internal energy of a system increases as the temperature is lowered.
False
The Boltzmann distribution can be used to calculate the average energy associated with each mode of motion of a molecule at a given temperature.
True
The internal energy of a system is a function of the system's motion as a whole.
False
The molar translational energy of a perfect gas is 1 2 kT.
False
The internal energy of a system can be changed only by doing work on the system.
False
The equipartition theorem is a conclusion from quantum mechanics.
False
The internal energy of a system is a function of the volume occupied by the molecules.
False
Learn about the internal energy of a system, its constituents, and the change in internal energy denoted by ΔU. Understand the kinetic and potential energy of atoms, ions, or molecules and how it differs from the kinetic energy of the system as a whole.
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