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Questions and Answers
What does the symbol ΔS represent in thermodynamics?
What does the symbol ΔS represent in thermodynamics?
What is the SI unit of entropy?
What is the SI unit of entropy?
What happens to entropy during a spontaneous process?
What happens to entropy during a spontaneous process?
How is the heat transfer (dQ) calculated during the mixing of water at different temperatures?
How is the heat transfer (dQ) calculated during the mixing of water at different temperatures?
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Which average temperature is used to calculate the gain of entropy for the cooler water in the example?
Which average temperature is used to calculate the gain of entropy for the cooler water in the example?
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What is the total entropy change (ΔS) during the mixing of the two water samples?
What is the total entropy change (ΔS) during the mixing of the two water samples?
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According to the statistical mechanics definition, what does entropy measure?
According to the statistical mechanics definition, what does entropy measure?
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What is the primary contribution of Clausius in thermodynamics?
What is the primary contribution of Clausius in thermodynamics?
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What is the zeroth law of thermodynamics concerned with?
What is the zeroth law of thermodynamics concerned with?
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According to the first law of thermodynamics, how is the change in internal energy (
$
ext{ΔU}
$
) calculated?
According to the first law of thermodynamics, how is the change in internal energy ( $ ext{ΔU} $ ) calculated?
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What does the second law of thermodynamics imply about entropy?
What does the second law of thermodynamics imply about entropy?
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How does spontaneity relate to entropy according to thermodynamic principles?
How does spontaneity relate to entropy according to thermodynamic principles?
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What is stated by the third law of thermodynamics?
What is stated by the third law of thermodynamics?
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What does a positive total entropy change signify in thermodynamic terms?
What does a positive total entropy change signify in thermodynamic terms?
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What is the relationship between internal energy and thermodynamic work?
What is the relationship between internal energy and thermodynamic work?
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Which of the following best describes entropy in a thermodynamic context?
Which of the following best describes entropy in a thermodynamic context?
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What does W represent in Boltzmann's formula for entropy?
What does W represent in Boltzmann's formula for entropy?
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In the first system involving three particles, how many possible states are there?
In the first system involving three particles, how many possible states are there?
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What is the entropy of the second system with four particles where the total energy is zero?
What is the entropy of the second system with four particles where the total energy is zero?
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How is the total entropy of both systems calculated when they are combined?
How is the total entropy of both systems calculated when they are combined?
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What is the combined degeneracy function W when the two systems are in thermal contact?
What is the combined degeneracy function W when the two systems are in thermal contact?
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What indicates an increase in entropy in a thermodynamic process?
What indicates an increase in entropy in a thermodynamic process?
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What does the term 'degeneracy function' refer to?
What does the term 'degeneracy function' refer to?
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Given k = $1.38065 imes 10^{-23} J/K$, what would be the units of entropy calculated using Boltzmann's formula?
Given k = $1.38065 imes 10^{-23} J/K$, what would be the units of entropy calculated using Boltzmann's formula?
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What is the expression for the average pressure exerted by N gas molecules?
What is the expression for the average pressure exerted by N gas molecules?
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How is the momentum delivered by a gas molecule during a collision with the wall calculated?
How is the momentum delivered by a gas molecule during a collision with the wall calculated?
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Given the equation $PV = \frac{N}{3}m \langle v^{2} \rangle$, what does $\langle v^{2} \rangle$ represent?
Given the equation $PV = \frac{N}{3}m \langle v^{2} \rangle$, what does $\langle v^{2} \rangle$ represent?
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What is the relationship between the root mean square speed ($v_{\text{rms}}$) and the temperature (T) of the gas?
What is the relationship between the root mean square speed ($v_{\text{rms}}$) and the temperature (T) of the gas?
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In the equation for average impulse exerted by a molecule, which variable represents the length of the container?
In the equation for average impulse exerted by a molecule, which variable represents the length of the container?
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Which physical constant is represented by $R$ in the equation $R = N_{\text{avo}} k$?
Which physical constant is represented by $R$ in the equation $R = N_{\text{avo}} k$?
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What does the term $k$ represent in $kT = \frac{1}{3} m \langle v^{2} \rangle$?
What does the term $k$ represent in $kT = \frac{1}{3} m \langle v^{2} \rangle$?
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What does $v_{x}$ represent in the context of gas molecule movement?
What does $v_{x}$ represent in the context of gas molecule movement?
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What does the equation ΔSuniverse > 0 represent?
What does the equation ΔSuniverse > 0 represent?
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What is the freezing point of water on the Celsius scale?
What is the freezing point of water on the Celsius scale?
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Which of the following conversions between temperature scales is correct?
Which of the following conversions between temperature scales is correct?
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What does the ideal gas law equation PV = NkT represent?
What does the ideal gas law equation PV = NkT represent?
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What does absolute zero (0 K) signify in terms of kinetic energy?
What does absolute zero (0 K) signify in terms of kinetic energy?
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What is the significance of ${1.38065 imes 10^{-23} }$ J/K in the context of the ideal gas law?
What is the significance of ${1.38065 imes 10^{-23} }$ J/K in the context of the ideal gas law?
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Which statement about the volume of ideal gas molecules is correct?
Which statement about the volume of ideal gas molecules is correct?
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Which of the following describes the relationship between temperature and kinetic energy?
Which of the following describes the relationship between temperature and kinetic energy?
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Study Notes
Thermodynamics and Entropy
- The second law of thermodynamics, though seemingly obvious, is a fundamental principle of the universe.
- The zeroth law states that if two systems are each in thermal equilibrium with a third, they are also in thermal equilibrium with each other.
- The first law of thermodynamics states that the change in internal energy (∆U) of a system is equal to the heat gained (Q) minus the work done by the system (W). ∆U = Q - W.
- The second law of thermodynamics states total entropy change associated with thermal contact between systems is always positive. Heat does not spontaneously flow from a colder to a hotter body (increase in entropy, entropy equals degree of disorder).
- The third law of thermodynamics states that as the temperature of a system approaches absolute zero, all processes cease and the entropy approaches a minimum value.
Entropy Change in Thermodynamic Processes
- Entropy is associated with the second law of thermodynamics.
- Entropy of an isolated system (eventually the whole universe) always increases.
- Higher spontaneity in a process equates to higher entropy.
- Entropy is a thermodynamic state quantity (function of temperature, pressure, and volume).
- Entropy change in chemical reactions results from rearrangement of atoms and molecules.
- Entropy change (ΔS) can be calculated using the formula ΔS = dq/T, where dq is heat transferred and T is absolute temperature. SI unit of entropy is [J/K] or [J/mol/K].
- Spontaneous processes have an increase in entropy (ΔS > 0).
Example: Entropy Change Calculation
- Mixing a 100-gram sample of water at 10°C with a 100-gram sample of water at 90°C will result in 200 grams of water at 50°C.
- Calculating the gain of entropy for cool water (average temp. 30°C) is approximately 55.234 J/K.
- Calculating the loss of entropy for hot water (average temp. 70°C) is approximately -48.793 J/K.
- The total entropy change during mixing is +6.44 J/K (in practice a slightly different value as stated).
Definition of Entropy from Statistical Mechanics
- Entropy is a measure of disorder/randomness.
- Boltzmann's formula for entropy: S = k ln W, where W is the number of possible arrangements for molecules and k is the Boltzmann constant (1.38065 × 10⁻²³ J/K).
Temperature Scales
- Common temperature scales include Celsius, Fahrenheit, and Kelvin.
- Zero degrees Celsius is the freezing point of water, and 100 degrees Celsius is the boiling point of water.
- Zero degrees Kelvin corresponds to the complete stop of molecular motion or zero kinetic energy.
Ideal Gas Law
- PV = NkT = nRT, where P is pressure, V is volume, T is temperature, N is number of particles, k is Boltzmann's constant, R is the ideal gas constant, and n is the number of moles.
- Ideal gases have negligible volume and behave according to ideal gas law.
- Average speed of oxygen molecules can be calculated using the ideal gas law formulas.
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