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Questions and Answers

What does the symbol ΔS represent in thermodynamics?

  • Change in temperature
  • Change in volume
  • Change in energy
  • Change in entropy (correct)
  • What is the SI unit of entropy?

  • Joule
  • J/K (correct)
  • Calorie
  • Watt
  • What happens to entropy during a spontaneous process?

  • It decreases
  • It fluctuates randomly
  • It remains constant
  • It increases (correct)
  • How is the heat transfer (dQ) calculated during the mixing of water at different temperatures?

    <p>dQ is the mass of water multiplied by the heat capacity and temperature difference</p> Signup and view all the answers

    Which average temperature is used to calculate the gain of entropy for the cooler water in the example?

    <p>30°C</p> Signup and view all the answers

    What is the total entropy change (ΔS) during the mixing of the two water samples?

    <p>6.44 J/K</p> Signup and view all the answers

    According to the statistical mechanics definition, what does entropy measure?

    <p>Disorder or randomness</p> Signup and view all the answers

    What is the primary contribution of Clausius in thermodynamics?

    <p>Discovery of entropy</p> Signup and view all the answers

    What is the zeroth law of thermodynamics concerned with?

    <p>The relationship of temperature across systems in equilibrium</p> Signup and view all the answers

    According to the first law of thermodynamics, how is the change in internal energy ( $ ext{ΔU} $ ) calculated?

    <p>$ ext{ΔU} = ext{Q} - ext{W} $</p> Signup and view all the answers

    What does the second law of thermodynamics imply about entropy?

    <p>Entropy is always increasing in isolated systems.</p> Signup and view all the answers

    How does spontaneity relate to entropy according to thermodynamic principles?

    <p>Higher entropy indicates more spontaneous processes.</p> Signup and view all the answers

    What is stated by the third law of thermodynamics?

    <p>All processes cease as temperature approaches absolute zero.</p> Signup and view all the answers

    What does a positive total entropy change signify in thermodynamic terms?

    <p>The degree of disorder in the system is increasing.</p> Signup and view all the answers

    What is the relationship between internal energy and thermodynamic work?

    <p>Internal energy decreases with more work done by the system.</p> Signup and view all the answers

    Which of the following best describes entropy in a thermodynamic context?

    <p>Entropy is a thermodynamic state quantity influenced by temperature, pressure, and volume.</p> Signup and view all the answers

    What does W represent in Boltzmann's formula for entropy?

    <p>The number of ways atoms or molecules can be arranged</p> Signup and view all the answers

    In the first system involving three particles, how many possible states are there?

    <p>3</p> Signup and view all the answers

    What is the entropy of the second system with four particles where the total energy is zero?

    <p>$k imes ext{ln} 6$</p> Signup and view all the answers

    How is the total entropy of both systems calculated when they are combined?

    <p>$S = k imes ext{ln} 18$</p> Signup and view all the answers

    What is the combined degeneracy function W when the two systems are in thermal contact?

    <p>35</p> Signup and view all the answers

    What indicates an increase in entropy in a thermodynamic process?

    <p>The number of arrangements increases</p> Signup and view all the answers

    What does the term 'degeneracy function' refer to?

    <p>The number of distinct arrangements of particles</p> Signup and view all the answers

    Given k = $1.38065 imes 10^{-23} J/K$, what would be the units of entropy calculated using Boltzmann's formula?

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

    What is the expression for the average pressure exerted by N gas molecules?

    <p>$N\frac{mv_{x}^{2}}{V}$</p> Signup and view all the answers

    How is the momentum delivered by a gas molecule during a collision with the wall calculated?

    <p>$2mv_{x}$</p> Signup and view all the answers

    Given the equation $PV = \frac{N}{3}m \langle v^{2} \rangle$, what does $\langle v^{2} \rangle$ represent?

    <p>The average square of the speed of gas molecules</p> Signup and view all the answers

    What is the relationship between the root mean square speed ($v_{\text{rms}}$) and the temperature (T) of the gas?

    <p>$v_{\text{rms}} = \sqrt{\frac{3kT}{m}}$</p> Signup and view all the answers

    In the equation for average impulse exerted by a molecule, which variable represents the length of the container?

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

    Which physical constant is represented by $R$ in the equation $R = N_{\text{avo}} k$?

    <p>Universal gas constant</p> Signup and view all the answers

    What does the term $k$ represent in $kT = \frac{1}{3} m \langle v^{2} \rangle$?

    <p>Boltzmann's constant</p> Signup and view all the answers

    What does $v_{x}$ represent in the context of gas molecule movement?

    <p>Velocity of the gas molecule</p> Signup and view all the answers

    What does the equation ΔSuniverse > 0 represent?

    <p>The total entropy of the universe is always increasing.</p> Signup and view all the answers

    What is the freezing point of water on the Celsius scale?

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

    Which of the following conversions between temperature scales is correct?

    <p>T(F) = (9/5)(T(C)) + 32</p> Signup and view all the answers

    What does the ideal gas law equation PV = NkT represent?

    <p>It relates pressure, volume, and temperature of an ideal gas.</p> Signup and view all the answers

    What does absolute zero (0 K) signify in terms of kinetic energy?

    <p>Molecular movement and kinetic energy stop.</p> Signup and view all the answers

    What is the significance of ${1.38065 imes 10^{-23} }$ J/K in the context of the ideal gas law?

    <p>It is known as the Boltzmann constant.</p> Signup and view all the answers

    Which statement about the volume of ideal gas molecules is correct?

    <p>The volume is negligible compared to the space they occupy.</p> Signup and view all the answers

    Which of the following describes the relationship between temperature and kinetic energy?

    <p>Temperature is directly related to the average kinetic energy of particles.</p> Signup and view all the answers

    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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