Thermodynamics Chapter T2

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Questions and Answers

How does statistical mechanics extend the study of thermodynamics?

Statistical mechanics provides a statistical treatment of the underlying complex systems to explain how thermodynamic properties emerge.

In the context of thermodynamics, what distinguishes a reversible process from an irreversible process?

A reversible process is one where a video of the process could play forwards or backwards and still appear physically plausible; an irreversible process only looks plausible in one direction.

Why is friction considered an irreversible process at the macroscopic level, even though it conserves energy?

Although energy is conserved, the reverse process requires precise coordination of individual molecules, which is never observed.

How is the internal energy ($U$) of a stationary macroscopic object defined, and what factors can cause it to change?

<p>Internal energy is the sum of the kinetic and potential energies of the object's constituent particles. It can change with temperature, phase, chemical composition, or nuclear composition.</p> Signup and view all the answers

Differentiate between heat, work, and energy transfer in the context of thermodynamics.

<p>Heat ($Q$) is energy flow solely due to temperature difference, work ($W$) is energy flow due to an external force, and energy transfer ($E$) encompasses other forms of energy crossing the system boundary.</p> Signup and view all the answers

Explain why the classification of energy exchange as heat, work, or energy transfer depends on the system boundary.

<p>The classification depends on whether the energy crosses the boundary due to a temperature difference (heat), an external force (work), or another mechanism (energy transfer) within the defined system.</p> Signup and view all the answers

State the first law of thermodynamics and explain its significance.

<p>The first law states that the change in internal energy ($\Delta U$) of a system equals the heat added ($Q$) plus the work done on the system ($W$) plus any other form of energy transfer ($E$): $\Delta U = Q + W + E$. It's a statement of energy conservation.</p> Signup and view all the answers

Describe the paradigmatic thermal process and why it is considered irreversible.

<p>It involves placing two objects at different temperatures in contact until they reach thermal equilibrium. It's irreversible because heat spontaneously flows from hot to cold, not vice versa.</p> Signup and view all the answers

In thermodynamics, how is temperature defined operationally?

<p>Temperature is defined in terms of a process for measuring it, often using a thermoscope, which is a device that measures a property dependent on temperature.</p> Signup and view all the answers

Explain the zeroth law of thermodynamics and its importance in defining temperature.

<p>The zeroth law states that if two objects are each in thermal equilibrium with a third object, then they are in thermal equilibrium with each other. This allows for a consistent definition of temperature, ensuring that objects in equilibrium have the same temperature reading on any valid thermoscope.</p> Signup and view all the answers

What is a thermoscope, and how does it differ from a thermometer?

<p>A thermoscope is a device that measures a property of a system dependent on temperature, while a thermometer is a thermoscope with a defined scale for measuring temperature.</p> Signup and view all the answers

Why did early thermometers based on different liquids lead to questioning the idea of a unique true temperature?

<p>Thermometers using different liquids disagreed in their readings, indicating that temperature measurements were device-dependent.</p> Signup and view all the answers

What key concept regarding thermal energy is implied by Kelvin's definition of temperature, and what value is assigned to it?

<p>Kelvin's definition implies the existence of absolute zero, the lowest possible temperature, at which a gas would have zero thermal energy. This is approximately -273.15°C.</p> Signup and view all the answers

How are the Celsius and Fahrenheit scales defined in terms of the Kelvin scale today?

<p>The Kelvin scale is the SI unit of temperature, and the Celsius and Fahrenheit scales are defined relative to it using specific conversion formulas: $T_{[C]} = (T - 273.15 \text{ K}) \cdot \frac{{}^{\circ}\text{C}}{\text{K}}$ and $T_{[F]} = \frac{9}{5}{}^{\circ}\text{C} \cdot T_{[C]} + 32 {}^{\circ}\text{F}$</p> Signup and view all the answers

Explain the relationship between temperature and thermal energy for small temperature changes.

<p>For small temperature changes, the relationship between temperature and thermal energy is approximately linear, described by the equation $dU = mc dT$, where $dU$ is the change in thermal energy, $m$ is the mass, $c$ is the specific heat, and $dT$ is the change in temperature.</p> Signup and view all the answers

Define specific heat and explain its significance in determining temperature changes.

<p>Specific heat ($c$) is the amount of energy required to raise the temperature of a unit mass of a substance by one degree. It relates temperature changes to the amount of thermal energy added or removed.</p> Signup and view all the answers

Describe the difference between internal and thermal energy.

<p>Internal energy is the total energy of a system's constituent particles, including kinetic and potential energies. Thermal energy is that portion of the internal energy that changes with temperature.</p> Signup and view all the answers

Explain what an irreversible process is. Give an example.

<p>An irreversible process is a process in which the system and its surroundings cannot return to their original states. An example is the sliding of a box on the floor due to friction.</p> Signup and view all the answers

Explain why heat is identified with the symbol Q, work is identified with the symbol W, and energy transfer is identified with the symbol [E].

<p>Heat is identified with the symbol <em>Q</em>, work is identified with the symbol <em>W</em>, and energy transfer is identified with the symbol <em>[E]</em> because those are the symbols that are used for them.</p> Signup and view all the answers

Does the sign of work, heat, and energy transfer change, and what does that indicate?

<p>Yes heat, work, and energy transfer can be positive or negative. Positive indicates energy transferred <em>into</em> the system, and negative indicates energy transferred <em>out of</em> the system.</p> Signup and view all the answers

What is the difference between thermodynamics and statistical mechanics?

<p>Thermodynamics studies the relationships between bulk properties of a system. Statistical mechanics seeks to relates the bulk properties to the motion of individual molecules.</p> Signup and view all the answers

With respect to the first law of thermodynamics, is it possible to ignore one of AU, Q, W, or E?

<p>Sometimes it is possible to ignore one or more of the terms on the right side of the first law of thermodynamics. Most frequently the energy transfer term [E] is ignored.</p> Signup and view all the answers

What is the name and value of the constant represented by $k_B$?

<p>It's Boltzmann's constant, and the value is $1.38 \times 10^{-23} \frac{J}{K}$</p> Signup and view all the answers

How is specific heat defined in equation form?

<p>Specific heat is defined as $c = \frac{1}{m} \frac{dU}{dT}$</p> Signup and view all the answers

What is another way to write change in internal energy besides $dU = mc dT$?

<p>Another way to write change in internal energy is $dU ≈ (\frac{n}{2} k_B) N dT$</p> Signup and view all the answers

Is heat a property of a system?

<p>No, heat is not a property of a system. It is a process by which energy is transferred.</p> Signup and view all the answers

In which direction does heat flow?

<p>Heat spontaneously flows from a hotter object to a colder object.</p> Signup and view all the answers

What might a 'thermoscope' measure?

<p>It measures a property of a system that is known to be dependent on temperature.</p> Signup and view all the answers

What important statement does the zeroeth law of thermodynamics make about temperature?

<p>It states that temperature exists such that two objects in thermal contact will be in thermal equilibrium if and only if both have the same temperature.</p> Signup and view all the answers

What are the freezing and boiling points of water in Celsius?

<p>0 degrees Celsius and 100 degrees Celsius</p> Signup and view all the answers

What temperature has zero thermal energy?

<p>Absolute zero</p> Signup and view all the answers

Suppose electromagnetic waves enter a system. By what symbol is that represented?

<p>[E]</p> Signup and view all the answers

Why is putting a hot metal block into an ice bath an example of a "paradigmatic thermal process?"

<p>The process illustrates basic example that illustrates main ideas.</p> Signup and view all the answers

What are examples of changes in a system that would change the internal energy?

<p>The internal energy can change with temperature, phase (solid, liquid, or gas), chemical composition, and nuclear composition.</p> Signup and view all the answers

If the temperature range is small, how does the specific heat typically change?

<p>It typically changes very slowly.</p> Signup and view all the answers

What 18th century device was used as a kind of thermoscope?

<p>A mercury thermometer</p> Signup and view all the answers

Before there was a device-independent definition of temperature, how was temperature defined?

<p>Temperature was simply defined as the reading on some specific kind of thermoscope.</p> Signup and view all the answers

State the formula relating Celsius to Fahrenheit using $T_{[C]}$ and $T_{[F]}$

<p>$T_{[F]} = \frac{9}{5} {^{\circ}C} T_{[C]} + 32 {^{\circ}F}$</p> Signup and view all the answers

How do the temperature differences compare between a temperature difference of 1 Kelvin and a temperature difference of 1 degree Celsius?

<p>They are the same</p> Signup and view all the answers

What 1840's thermoscope was thought to yield consistent results but was later found to be spoiled by changing the density of the gas?

<p>Thermometers based on measuring the pressure of a gas at a fixed volume.</p> Signup and view all the answers

In statistical mechanics, how will temperature be defined?

<p>It will be defined in terms of the motions of constituent molecules of the system.</p> Signup and view all the answers

In thermodynamics, why is focusing on the bulk properties like pressure and temperature more practical than tracking individual particles in a complex system like a gas?

<p>Tracking individual particles is virtually impossible due to their vast number. Bulk properties offer a manageable and statistically relevant way to understand the system's behavior.</p> Signup and view all the answers

Explain why friction is considered an irreversible process at the macroscopic level, even though the laws of physics are consistent with both forward and reverse scenarios.

<p>Friction converts macroscopic motion into disordered internal motions at the atomic level. The reverse process requires precise coordination of individual molecules, an event that is never observed.</p> Signup and view all the answers

How does the concept of internal energy differ for a stationary object versus a moving object, and why is this distinction important in thermodynamic analysis?

<p>For a stationary object, internal energy is the total kinetic and potential energy of its constituent particles. For a moving object, the kinetic energy of the center of mass is subtracted. This is important to isolate thermal effects from the object's overall motion.</p> Signup and view all the answers

Differentiate between heat and work as energy transfer mechanisms in thermodynamics, emphasizing the primary factor that distinguishes the two.

<p>Heat is a flow of energy across a system boundary due solely to a temperature difference. Work is a flow of energy across a boundary due to an external force acting on the system.</p> Signup and view all the answers

Why is it crucial in thermodynamics to first define the system boundary before analyzing energy exchanges, using the example of electrical energy transfer versus heat?

<p>The classification of energy exchange (heat, work, or energy transfer) depends on where the system boundary is defined. For example, inside a battery, it is electrical energy transfer, but outside it can be heat.</p> Signup and view all the answers

According to the first law of thermodynamics, $\Delta U = Q + W + [E]$. If a system is perfectly insulated and no external forces act on it, what can you conclude about the change in its internal energy?

<p>If the system is perfectly insulated (Q = 0), no external forces act on it (W = 0), and there are no other energy transfers ([E] = 0), the change in internal energy ($\Delta U$) is zero.</p> Signup and view all the answers

Describe the key characteristics of a 'paradigmatic thermal process', and why is achieving thermal equilibrium considered irreversible?

<p>It involves placing two objects at different temperatures in contact and waiting for their temperatures to equalize. The process is irreversible because heat spontaneously flows from hot to cold, not vice versa.</p> Signup and view all the answers

Explain the concept of an 'operational definition' in the context of temperature, and why is this approach necessary in thermodynamics?

<p>An operational definition defines temperature in terms of a process for measuring it. This is necessary in thermodynamics because temperature must be defined through empirically observed relationships before statistical mechanics provides a molecular explanation.</p> Signup and view all the answers

What is a 'thermoscope', and why are they useful for measuring temperature even if the relationship to temperature is complicated?

<p>A thermoscope is a device that measures a property of a system dependent on temperature, like resistance. Even if the relationship is complex, the thermoscope provides a measurable indicator of temperature changes.</p> Signup and view all the answers

State the Zeroth Law of Thermodynamics and explain its significance in defining and measuring temperature.

<p>If two objects are each in thermal equilibrium with a third object, then they are in thermal equilibrium with each other. This law allows for a consistent definition of temperature, ensuring that all objects in equilibrium have the same temperature.</p> Signup and view all the answers

Explain why thermometers based on different materials (e.g., mercury, gas) showed disagreements in the early days of thermometry and how Kelvin addressed this issue.

<p>Different materials expand differently with temperature, leading to discrepancies. Kelvin proposed a thermodynamic temperature scale based on statistical mechanics, independent of any specific material properties.</p> Signup and view all the answers

What is 'absolute zero', and how does it relate to Kelvin's temperature scale?

<p>Absolute zero is the lowest possible temperature, where a gas would have zero thermal energy and pressure. It corresponds to 0 K on the Kelvin scale, which is equivalent to -273.15°C.</p> Signup and view all the answers

Describe the relationship between temperature and thermal energy. Also, write the formula relating the change in thermal energy to temperature.

<p>Increasing the temperature of a system usually increases its thermal energy. The relationship is approximately linear: $dU = mc dT$, where $dU$ is the change in thermal energy, $m$ is mass, $c$ is specific heat, and $dT$ is the change in temperature.</p> Signup and view all the answers

A container has $N$ molecules of monatomic gas $A$ and a separate container has $2N$ molecules of monatomic gas $B$. Both gases start at the same temperature. If you add the same amount of heat to each gas, which one will end up being hotter, and why?

<p>Gas A will be hotter. Since the amount of heat added is the same, and gas A has fewer molecules, each molecule in gas A will gain more energy than each molecule in gas B. Since temperature is related to energy per molecule, gas A will be hotter.</p> Signup and view all the answers

Explain the significance of Boltzmann's constant ($k_B$) in relating the microscopic properties of a system to its macroscopic properties, especially in the context of specific heat.

<p>Boltzmann's constant relates the average kinetic energy of molecules in a gas to its temperature. For example, the specific heat can be expressed as $c \approx \frac{nNk_B}{m2}$, connecting molecular behavior to the system's thermal properties.</p> Signup and view all the answers

Flashcards

Thermodynamics

The study of complex systems consisting of a large number of parts, like a gas, focusing on bulk properties such as pressure and temperature.

Statistical Mechanics

The study of how bulk properties emerge from the statistical behavior of underlying complex systems.

Irreversible Process

A process that cannot be reversed; watching the video in reverse shows implausible physics.

Internal Energy (U)

The sum total of the kinetic energies of a stationary macroscopic object's constituent particles and the potential energies of interaction between the particles.

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Thermal Energy

Changes in internal energy that only affect the temperature of the system.

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Heat (Q)

Flow of energy across a system boundary due entirely to a temperature difference.

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Work (W)

Flow of energy across a boundary due to an external force acting on the system.

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Energy Transfer (E)

Any other form of energy crossing the boundary of a system that is not heat or work.

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Positive Energy Transfer

The energy flowing into the system.

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Negative Energy Transfer

The energy flowing out of the system.

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First Law of Thermodynamics

Change in internal energy (ΔU) is due to a flow of energy across the boundary.

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Thermal Process

Any process where the thermal energy of a system changes due to energy exchange with its environment.

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Paradigmatic Thermal Process

Placing two objects with different temperatures in contact until their temperatures equalize.

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Thermal Equilibrium

The state where two objects in contact have reached the same temperature, and there is no net flow of heat.

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Temperature

A measure of how hot an object is.

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Thermoscope

A device measuring a property of a system that is temperature-dependent.

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Zeroth Law of Thermodynamics

If systems A and B are separately in thermal equilibrium with system C, then A and B are in thermal equilibrium with each other.

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Thermometer

A device that measures temperature.

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Absolute Zero

The lowest possible temperature where a gas would have zero thermal energy and pressure.

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Celsius to Kelvin Conversion

Temperature in Celsius is equal to Temperature in Kelvin minus 273.15.

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Specific Heat (c)

The amount of heat required to raise the temperature of 1 gram of a substance by 1 degree Celsius.

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Boltzmann's constant (kB)

A new physical constant that is equal to 1.38 × 10-23 J/K

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Study Notes

Class Announcements

Thermodynamics and Statistical Mechanics

  • This unit focuses on complex systems with numerous parts, such as gases
  • Studying bulk properties is key, as tracking individual parts is impossible
  • Pressure, volume, temperature, entropy, and magnetization are some of the bulk properties of interest
  • Thermodynamics studies the relationships between these bulk properties
  • Statistical mechanics explores how these properties emerge from a statistical analysis of the complex underlying systems

Reversible and Irreversible Processes

  • Simple, isolated systems behave reversibly
  • It is impossible to determine if a video of reversible processes is being played forwards or backwards
  • Macroscopic systems typically behave irreversibly
  • The reverse direction of a video of irreversible processes does not appear physically plausible

Friction Example

  • Boxes and floors are composed of numerous interacting molecules
  • Friction converts the box's macroscopic motion into random internal atomic motions
  • The reverse of this process aligns with physics laws but isn't noticed as it needs accurate synchronization from the individual molecules
  • In the 1870s Boltzmann clarified links between bulk properties of things and the movement of specific molecules

Internal Energy

  • Internal energy, denoted as U, of a stationary macroscopic object, is the total kinetic energies of its constituent particles, also the potential energies from interacting particles
  • Subtract the kinetic energy of motion of the center of mass when considering moving objects
  • Changes in internal energy are related to changes in:
    • Temperature
    • Phase (solid, liquid, or gas)
    • Chemical composition
    • Nuclear composition

Thermal Energy

  • This unit studies changes in internal energy impacting the temperature of a system, known as thermal energy
  • 'Internal' and 'thermal' energy will be used interchangeably, denoted U
  • Thermodynamics is concerned with how an object's internal energy changes, necessitating energy flow across the system boundary

Heat, Work, and Energy Transfer

  • Heat (Q) signifies energy flow over a system's boundary, driven exclusively by a temperature difference
  • Work (W) signifies energy flow over the boundary, caused by force on system
    • Gas being compressed by a piston is one example
  • Any other form of energy that crosses a system's boundaries is known as energy transfer [E]
    • Electromagnetic and mechanical waves (sound) act as examples

Sign Convention

  • Heat, work, and energy transfers are positive when energy flows into the system, and are negative when energy flows out
  • Sign conventions vary across textbooks

System Dependence

  • Classifying energy exchange as heat, work, or energy transfer relies on the system boundary definition
    • Boundary A: electrical energy transfer
    • Boundary B: heat
  • Correctly identifying the system is important in problem-solving

The First Law of Thermodynamics

  • A change in internal energy (ΔU) arises from energy flow across system boundaries, as stated in the first law of thermodynamics
  • Expressed as: ΔU = Q + W + [E]
  • This is a statement of energy conservation
  • Energy transfers other than work and heat are often ignored, simplifying the equation to ΔU = Q + W
  • The first law was initially interpreted to mean heat is a form of energy transfer

The Paradigmatic Thermal Process

  • A thermal process involves changing a system's thermal energy because of energy exchange with surroundings
  • Paradigmatic means a basic example illustrating main ideas
  • This process explains placing two objects at different temperatures together, and waiting until equal
    • Thermal equilibrium describes equal temperatures
    • Achieving this is irreversible
    • Heat moves spontaneously from warm to cool objects
    • Heat cannot spontaneously flow between objects at the same temperature

Questions About the Thermal Process

  • What is temperature and how does it relate to thermal energy and other properties?
  • What is heat? How is it related to temperature and thermal energy? Why does heat spontaneously flow from a hotter to a colder object?
  • What is thermal equilibrium? Why does energy flow between two systems eventually stop? How is this related to temperature?
  • Why is the paradigmatic process irreversible? Why does heat spontaneously flow from a hotter object to a colder object but not vice versa?

Temperature

  • Temperature measures how hot an object is
  • Statistical mechanics defines temperature using molecule movement, but it is not yet covered in thermodynamics
  • Empirically observed relationships between bulk properties are key
  • Thermodynamics defines temperature via measurement processes, termed “operational definition”

Thermoscopes

  • A thermoscope measures properties of a system known to depend on temperature
  • Measuring a conductor or semiconductor's resistance works as an example
  • Even with complicated relationships, insight relating to temperature is gained

The Zeroth Law of Thermodynamics

  • A thermoscope in contact with a system reaches a fixed value on reaching equilibrium
  • Systems A and B are in thermal equilibrium if all possible thermoscopes the same value when each system comes into equilibrium
  • Key points:
    • Temperature exists as a well-defined quantity where objects in contact reach thermal equilibrium if, and only if, both share the same temperature

Thermometers

  • A thermometer measures temperature
  • Temperature was initially defined by a specific thermoscope reading
  • Mercury thermometers were historically used in the 18th century

Thermoscopes to Thermometers

  • In the late 18th century, thermometers based on different liquids showed expansion disagreed with mercury ones, questioning whether unique temperatures actually exist
  • In the 1840s, measuring gas pressure at a constant volume yielded consistent results, which was spoiled by changing gas density
  • In 1848, Kelvin suggested a definition of temperature derived from statistical mechanics that's separate from any thermoscope, called non-operational definition
  • Low-density monatomic gases in gas thermoscopes and mercury thermometers at everyday temperatures track Kelvin's temperature well

Kelvin and Absolute Zero

  • Kelvin's definition leads to a minimum temperature or absolute zero, where a gas would have zero thermal energy leading to zero pressure
  • Experiments determine this occurs at −273.15°C
  • Kelvin's temperature scale sets 0 K to −273.15°C
  • A temp difference of 1 K is equal to 1°C

Temperature Conversion

  • The SI unit for temperature is Kelvin (K). Celsius and Fahrenheit are defined by it
  • Formulas to convert are:
    • 𝑇[𝐶] = (𝑇 − 273.15 K) °𝐶/𝐾
    • 𝑇[𝐹] = (9/5) °𝐶𝑇[𝐶] + 32 °F

Relationship between Temperature and Thermal Energy

  • Increasing temperature in a system raises its thermal energy
  • If changes are fairly small, then the relationship is approximately linear, or dU = mcdT
    • c ≡ 1/m * dU/dT
    • c represents the specific heat
  • Changing thermal energy is related to the mass, and so, doubling the amount of molecules increases average energy by same amount to get equal distribution across all points

Specific Heat

  • "c" symbolizes specific heat, with the latter equation showing its definition
  • However, useful "c" values fluctuate slower alongside gradual temperature changes, otherwise based on the system structure

Example Problem - Lead Pipe

  • Find the thermal energy increase of a 100g lead pipe when temperature rises from 25°C to 37°C
    • Lead's specific heat is consistent at 0.128 J g-1 K-1 throughout temperature range
  • Formula: ΔU = mcΔT
  • Calculation:
  • ΔU = (100 g) * (0.128 J g-1 K-1) * [(37 - 25) K]
  • = 12.8 J K-1 × 12 K
  • = 153.6 J.
  • Use kelvin for T, however, difference is same in Celsius

Formula for The Specific Heat

  • Specific heat must be empirically determined, there are ways of calculating this via statistical mechanics
    • Result is: 𝑐 ≈ (nN kB) / m
      • kB = 1.38 × 10−23 J ⋅ K −1
      • This is Boltzmann’s constant
      • N = constituent molecules of the system
      • m = mass of the system
      • n = integer based on system
        • Most monatomic solids, n ≈ 6 at room temperature
        • Low density monatomic gas, n ≈ 3 at room temperature

Other Formulas

  • Formula 1: dU = mcdT. From it, get: 𝑐 ≡ 1/m * dU/dT
  • Formula 2: c ≈ (nN kB) / m
  • Then simpler to work with, so:
    • 𝑑𝑈 ≈ (𝑛 / 2)*𝑘𝐵𝑁 dT
    • d𝑈 / d𝑇 ≈ 𝑛𝑁 (∗𝑘𝐵 / 2)
    • Simpler than going via specific heat

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