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Questions and Answers
What does the fundamental equation apply to?
What does the fundamental equation apply to?
Which statement correctly describes U in relation to state functions?
Which statement correctly describes U in relation to state functions?
What expression represents the differential form of U?
What expression represents the differential form of U?
What condition must be satisfied for df to be an exact differential?
What condition must be satisfied for df to be an exact differential?
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How are Maxwell relations useful in thermodynamics?
How are Maxwell relations useful in thermodynamics?
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What does the symbol $T$ represent in the expression $T = rac{ iny{ rac{ ext{d}U}{ ext{d}S}}}{ ext{d}V}$?
What does the symbol $T$ represent in the expression $T = rac{ iny{ rac{ ext{d}U}{ ext{d}S}}}{ ext{d}V}$?
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What does the derivative $ rac{ iny{ rac{ ext{d}U}{ ext{d}S}}}{ ext{d}V}$ imply about the relationship between U, S, and V?
What does the derivative $ rac{ iny{ rac{ ext{d}U}{ ext{d}S}}}{ ext{d}V}$ imply about the relationship between U, S, and V?
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What does the negative sign in $- rac{ iny{ rac{ ext{d}p}{ ext{d}S}}}{ ext{d}V}$ indicate?
What does the negative sign in $- rac{ iny{ rac{ ext{d}p}{ ext{d}S}}}{ ext{d}V}$ indicate?
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What is the relationship used to determine if a spontaneous change is enthalpy driven?
What is the relationship used to determine if a spontaneous change is enthalpy driven?
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How is Gibbs energy defined mathematically?
How is Gibbs energy defined mathematically?
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What does a decrease in Gibbs energy indicate at constant temperature and pressure?
What does a decrease in Gibbs energy indicate at constant temperature and pressure?
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What is the correct equation for the Helmholtz energy?
What is the correct equation for the Helmholtz energy?
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What is true about Helmholtz energy (A) and its relation to work?
What is true about Helmholtz energy (A) and its relation to work?
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Which of the following statements about Gibbs energy is true?
Which of the following statements about Gibbs energy is true?
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What does the relationship dU = TdS - pdV represent?
What does the relationship dU = TdS - pdV represent?
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What type of work does ∆G represent at constant temperature and pressure?
What type of work does ∆G represent at constant temperature and pressure?
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What does the Clausius inequality imply for a system in thermal and mechanical contact with its surroundings?
What does the Clausius inequality imply for a system in thermal and mechanical contact with its surroundings?
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What is the Gibbs energy a measure of in a system?
What is the Gibbs energy a measure of in a system?
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In the context of the First and Second Laws of Thermodynamics, what does the Fundamental equation relate?
In the context of the First and Second Laws of Thermodynamics, what does the Fundamental equation relate?
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At constant volume, what can be said about the relationship between heat transfer and the internal energy change of a system?
At constant volume, what can be said about the relationship between heat transfer and the internal energy change of a system?
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When heat transfer occurs at constant pressure, what does the equation $dqp = dH$ imply?
When heat transfer occurs at constant pressure, what does the equation $dqp = dH$ imply?
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What condition must be met for the equation $dS_{sys} ≥ -dq_{sys}/T$ to hold true?
What condition must be met for the equation $dS_{sys} ≥ -dq_{sys}/T$ to hold true?
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What happens to the heat transfer ($dq$) if the system is isolated?
What happens to the heat transfer ($dq$) if the system is isolated?
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What can be concluded about spontaneity if the change in entropy of the system ($dS_{sys}$) is positive?
What can be concluded about spontaneity if the change in entropy of the system ($dS_{sys}$) is positive?
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Study Notes
Maximum Work and Free Energy
- Maximum work and free energy are derived from combining the first and second laws of thermodynamics.
- Maxwell relations are also involved.
Overview
- Derive the Clausius inequality, expressing it in terms of the system only.
- Define Gibbs (G) and Helmholtz (H) state functions.
- Derive that Gibbs energy measures maximum non-expansion work.
- Derive the fundamental equation by combining the first and second laws.
- Use this equation to derive Maxwell relations and discuss their importance.
The Clausius Inequality
- For a system in thermal and mechanical contact with surroundings (not necessarily in equilibrium), undergoing spontaneous change, dSsys + dSsurr ≥ 0.
- This implies dSsys ≥ -dSsurr.
- Recall dSsurr= - dqsys / T.
- Therefore, dSsys ≥ dqsys / T.
- This is the Clausius inequality.
- Consider what happens if the system is isolated.
Concentrating on the System Only
- Entropy (S) measures spontaneity, but simultaneously considering the system and surroundings can be complex.
- System-only criteria for spontaneity are needed.
- For a system in thermal equilibrium with surroundings at temperature T, consider the Clausius inequality: dS - dq/T ≥ 0.
System-Only Parameters
- When heat transfer occurs at constant volume, dU = dq, since no work is done (dw = 0).
- This implies dS ≥ dU/T, which rearranges to TdS ≥ dU.
- System-only parameters are used to describe spontaneous change.
- Consider constant U and constant S.
- For heat transfer occurring at constant pressure (dU = dH), the Clausius inequality gives TdS ≥ dH.
Gibbs and Helmholtz Functions
- Two ways to describe spontaneous change without including surroundings.
- dU - TdS ≤ 0 and dH - TdS ≤ 0
- Helmholtz energy (A) is defined as A = U - TS, with dA = dU - TdS or ΔA = ΔU - TΔS.
- Gibbs energy (G) is defined as G = H - TS, with dG = dH - TdS or ΔG = ΔH - TΔS.
- Now spontaneity can be evaluated as dA ≤ 0 or dG ≤ 0, at constant T, respectively.
Why Focus on Gibbs Energy?
- Gibbs energy (G) is more popular than Helmholtz energy (A) at constant T and P.
- Spontaneous changes and reactions occur when Gibbs energy decreases.
- Gibbs energy can be used to determine if a change is enthalpy or entropy driven.
ΔG and Maximum Non-expansion Work
- Non-expansion work is additional work.
- Examples include moving electrons or raising a mass.
- ΔG is the maximum possible non-expansion work a system can perform at constant temperature and pressure. -ΔG = Wadd, max
Justification for Maximum Non-Expansion Work
- Change in enthalpy considers conditions and dH=dq+dw+d(pV)
- Corresponding change of Gibbs energy, dG = dH-TdS.
- At constant temperature and reversible change, ΔG = Wadd,max.
- This work can occur in any process occurring reversibly at constant P and T.
- Work can include electrical work or pushing electrons through a circuit.
ΔA and Maximum Work
- The change in Helmholtz energy is equal to the maximum work in a process.
- dA = dwmax
- Helmholtz functions are sometimes referred to as maximum work functions.
Justification for Maximum Work
- To demonstrate that maximum work = the change in Helmholtz energy, combine Clausius inequality (TdS ≥ dq) and first law (dU = dq + dw).
- dU ≤ TdS + dw.
- dw ≥ dU - TdS.
- Maximum work = the most negative value of dw = dU - TdS, or dwmax = dA for constant T.
Combining First and Second Laws
- First law states dU = dq + dw.
- Second law states dqrev = TdS.
- Also, dwrev = -pdV.
- Combining these gives dU = TdS - pdV.
Maxwell Relations
- The fundamental equation applies to enclosed systems with constant composition that do no additional work.
- Since U is a state function, dU is an exact differential, thus dU= (∂U/∂S)V dS + (∂U/∂V)S dV.
- This implies T = (∂U/∂S)V and -p = (∂U/∂V)S .
- Maxwell relations allow to derive relationships between quantities that might not seem related allowing for changes in the system in convenient paths.
- Maxwell relations can be derived for H, G and A.
- Table 3.5 includes derived Maxwell relations.
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Description
This quiz covers the concepts of maximum work and free energy in thermodynamics, integrating the first and second laws. You will explore the Clausius inequality, Gibbs and Helmholtz state functions, and derive Maxwell relations, highlighting their significance in thermodynamic processes.
