Thermodynamics Quiz: Second Law and Entropy
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Questions and Answers

What is the entropy change for a reversible adiabatic process?

  • ΔS = 0 (correct)
  • ΔS > 0
  • ΔS = nRln(P2/P1)
  • ΔS < 0

    • For a system undergoing an isothermal change, what is the correct expression for entropy change?

  • ΔS = nC_Pln(T2/T1)
  • ΔS = nRln(V2/V1)
  • ΔS = nRln(P2/P1)
  • ΔS = nC_Vln(V2/V1) (correct)

    • What describes the relationship between the entropy changes of a system and its surroundings?

  • ΔS_universe = 0 only
  • ΔS_universe < 0 for spontaneous processes
  • ΔS_system always equals ΔS_surroundings
  • ΔS_universe = ΔS_system + ΔS_surroundings (correct)

    • What is the entropy change for a phase transition of a substance when temperature is constant?

    <p>ΔS = ΔH_trans/T_trans</p> Signup and view all the answers

    Which of the following statements is true regarding irreversible processes?

    <p>ΔS = ΔS_system + ΔS_surroundings for all processes</p> Signup and view all the answers

    What is the change in entropy for the reversible isothermal process?

    <p>-19.14 EU</p> Signup and view all the answers

    What is the value of ΔS for the surroundings in the irreversible process?

    <p>+74.9 EU</p> Signup and view all the answers

    How is the change in entropy for an irreversible process related to a reversible process?

    <p>It equals the reversible change.</p> Signup and view all the answers

    What is the change in entropy of the universe for the irreversible process described?

    <p>+55.83 EU</p> Signup and view all the answers

    For the example using argon, what is the change in entropy resulting from the expansion?

    <p>0.172 J/K</p> Signup and view all the answers

    What is the mathematical expression for the first law of thermodynamics?

    <p>dq = dE + PdV</p> Signup and view all the answers

    What happens when you substitute the second law into the first law of thermodynamics?

    <p>You form the combined expression for the laws.</p> Signup and view all the answers

    What is the temperature used in the calculation of ΔS for the surroundings during the irreversible process?

    <p>298 K</p> Signup and view all the answers

    In the equation ΔS = nR ln(V2/V1) + nC_V ln(T2/T1), what does C_V represent?

    <p>The molar heat capacity at constant volume</p> Signup and view all the answers

    What is the final value of ΔS for the irreversible process involving argon?

    <p>+55.83 EU</p> Signup and view all the answers

    What is the relationship between Helmholtz free energy and work done in a system?

    <p>The decrease in Helmholtz free energy is equivalent to maximum reversible work done isothermally.</p> Signup and view all the answers

    What is the expression for Gibbs free energy?

    <p>G = H - TS</p> Signup and view all the answers

    What happens to the Helmholtz free energy at constant temperature when there is an increase in volume?

    <p>Helmholtz free energy increases.</p> Signup and view all the answers

    According to Maxwell's relations for Helmholtz free energy, what is the derivative of A with respect to T at constant V?

    <p>It is equal to the entropy S.</p> Signup and view all the answers

    When differentiating Helmholtz free energy with respect to volume at constant temperature, what does the result yield?

    <p>Pressure P.</p> Signup and view all the answers

    Which equation relates the changes in Helmholtz free energy to infinitesimal changes in entropy and volume?

    <p>dA = -PdV - SdT</p> Signup and view all the answers

    What is indicated by the second derivative of Helmholtz free energy with respect to volume and temperature?

    <p>It reflects the change in entropy with respect to pressure.</p> Signup and view all the answers

    Why is studying the variation of entropy with volume at constant temperature experimentally challenging?

    <p>Entropy cannot be measured directly.</p> Signup and view all the answers

    What is the expression for the total differential of energy, E?

    <p>$dE = T dS - P dV$</p> Signup and view all the answers

    What is the relationship stated by the Maxwell equation (1)?

    <p>$\frac{\partial^2 E}{\partial V \partial S} = -\frac{\partial P}{\partial S}$</p> Signup and view all the answers

    Which of the following correctly describes Enthalpy (H)?

    <p>$H = E + PV$</p> Signup and view all the answers

    How is Helmholtz free energy (A) defined?

    <p>$A = E - TS$</p> Signup and view all the answers

    What denotes the change in Enthalpy with respect to entropy at constant pressure?

    <p>$\frac{\partial H}{\partial S} = T$</p> Signup and view all the answers

    Which equation represents the differential of Enthalpy (H) correctly?

    <p>$dH = TdS + VdP$</p> Signup and view all the answers

    What does the equation $\frac{\partial^2 E}{\partial S \partial V} = \frac{\partial T}{\partial P}$ indicate?

    <p>Change in temperature with pressure</p> Signup and view all the answers

    When differentiating the equation $\frac{\partial H}{\partial P} = V$ at constant entropy, what does this represent?

    <p>Volume as a function of pressure</p> Signup and view all the answers

    The integration of $dE = TdS$ gives a new expression for energy. What does this expression become?

    <p>$E = TS + C$</p> Signup and view all the answers

    What is the result when differentiating the equation $\frac{\partial^2 H}{\partial S \partial P}$?

    <p>$\frac{\partial T}{\partial S}$</p> Signup and view all the answers

    What is the expression for the change in Gibbs free energy at constant temperature?

    <p>dG = -SdT + VdP</p> Signup and view all the answers

    What does the Gibbs-Helmholtz equation relate?

    <p>Free energy change to enthalpy change</p> Signup and view all the answers

    At constant pressure, what does the derivative of Gibbs free energy with respect to temperature represent?

    <p>Entropy</p> Signup and view all the answers

    What does the Maxwell relation involving the second derivatives of G indicate?

    <p>The relationship between entropy and pressure</p> Signup and view all the answers

    In the expression for dG = -SdT + VdP, what does the term VdP represent?

    <p>Pressure-volume work</p> Signup and view all the answers

    For a system transitioning from state 1 to state 2, what is the expression used to calculate the change in Gibbs free energy?

    <p>ΔG = nRT ln(P2/P1)</p> Signup and view all the answers

    When using the equation dG = -SdT + VdP under constant temperature, what is the simplification of dT?

    <p>dT = 0</p> Signup and view all the answers

    Which variable is held constant when deriving the variation of free energy with pressure?

    <p>Temperature</p> Signup and view all the answers

    What is the equation for the change in A?

    <p>$A2 - A1 = (E2 - E1) + T \left[ \frac{A2 - A1}{V} \right]$</p> Signup and view all the answers

    What does the term 'net work' (dwnet) refer to in the context of G?

    <p>Available energy for doing work after accounting for mechanical work</p> Signup and view all the answers

    How is the change in free energy related to work at constant temperature and pressure?

    <p>$(dG)T,P = -(dw - PdV)$</p> Signup and view all the answers

    Which expression represents the differential form of G?

    <p>dG = TdS - dw + PdV + VdP - SdT - TdS</p> Signup and view all the answers

    What does the equation A2 indicate when it includes a partial derivative?

    <p>It assesses how A changes with temperature at constant volume.</p> Signup and view all the answers

    According to the equations presented, how are H and G related?

    <p>G = H - TS</p> Signup and view all the answers

    What do the terms 'dH', 'dG', and 'dE' represent in thermodynamics?

    <p>Total changes in Enthalpy, Free energy, and Internal energy</p> Signup and view all the answers

    What does the equation $(\Delta G){T,P} = -w{net}$ signify?

    <p>The change in free energy equals the net useful work output of the system.</p> Signup and view all the answers

    Study Notes

    Thermodynamics

    • Second Law of Thermodynamics: Mathematical statements are used to describe the second law of thermodynamics.

      • dS = dqrev/T
      • ΔS = nCvln(T2/T1)
      • ΔS = nCpln(T2/T1)
      • ΔS = nRln(V2/V1)
      • ΔS = nRln(P2/P1)

    • Reversible Adiabatic Changes:

      • ΔS = 0 (for reversible adiabatic changes)
      • These changes are also known as isentropic processes.

    • Entropy Change for Isolated System:

      • (dS)rev = 0, and (dS)irr > 0
      • Or (ΔS)rev = 0, and (ΔS)irr > 0

    Entropy Change on Heating or Cooling

    • ΔS = nCvln(T2/T1)
    • ΔS= nCpln (T2/T1)
    • Example of Ideal gas compression

    Combined Form of the First and Second Laws of Thermodynamics

    • dq = dE + PdV
    • TdS = dE + PdV
    • dE = TdS – PdV

    Enthalpy and Entropy

    • H = E + PV
    • dH = TdS + VdP

    Energy as a Function of S and V

    • dE = TdS − PdV
    • E = f(S,V)

    Free Energy Functions A and G

    • Entropy is a measure of unavailable energy
    • Total heat absorbed in a system(q) is equal to the entropy (TS) plus useful work (X).
      • X = q-TS
    • Free energy (X) can be expressed as either E-TS or H-TS.

    Properties of A

    • A = E – TS
    • dA = dE – TdS - SdT
      • dA = -dw – SdT

    Variation of A with T at constant V

    • A = E – TS
    • dA = dE – TdS – SdT
      • dA = -PdV – SdT
    • A = E + T(∂A/∂T)V

    Calculation of Free Energy Changes with Temperature at Constant Pressure

    • Gibbs-Helmholtz equation relates free energy change to enthalpy, rate of free energy change w.r.t. temp.
    • G = H – TS
    • (∂G/∂T)P = -ΔH/T2

    Variation of Free Energy with Pressure at Constant T

    • dG = -SdT + VdP
    • At constant temperature, dT = 0 - (dG)T = VdP
    • For a system changing from state 1 to 2, ΔG = nRTln(P2/P1)

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    Description

    Test your knowledge of the second law of thermodynamics and entropy changes with this quiz. Explore key equations and concepts related to reversible adiabatic processes and entropy changes during heating or cooling. Perfect for students studying thermodynamics in physics or engineering.

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