S 3 We know that Entropy S is a mathematical quantity that gives us information on the direction ofpossible thermodynamic processes.You can use the following assumptions and facts without proving:I.Entropy is an increasing function of temperatureII.Second Law of ThermodynamicsIII.There exist adiabatic processes that had the sole effect of increasing the temperatureof the system. In other words, if T < T', the process (T, X) → (T', X) is possible.Planck's Principle: For any extensive variables X and temperatures T < T', adiabaticprocesses (T,X) → (T'', X) that do not change X is irreversible.Now, show that for any adiabatic operation (T, X) → (T',X') to be possible, we must ensure thecondition S(T, X) ≤ S(T', X'), where T is the temperature and X is the set of extensive variables.IV.

I. Entropy is an increasing function of temperature II. Second Law of Thermodynamics III. There…

Answered: Now, show that for any adiabatic…

Now, show that for any adiabatic operation (T, X) → (T', X') to be possible, we must ensure the condition S(T, X) ≤ S(T', X'), where T is the temperature and X is the set of extensive variables.

Principles of Modern Chemistry

8th Edition

ISBN:9781305079113

Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Publisher:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Chapter13: Spontaneous Processes And Thermodynamic Equilibrium

Section: Chapter Questions

Problem 20P

See similar textbooks

Similar questions

Explain why the statement No process is 100 efficient is not the best statement of the second law of thermodynamics.
For the process A(l) A(g), which direction is favored by changes in energy probability? Positional probability? Explain your answers. If you wanted to favor the process as written, would you raise or lower the temperature of the system? Explain.
The standard molar entropy of methanol vapor, CH3OH(g), is 239.8 J K1 mol-1. (a) Calculate the entropy change for the vaporization of 1 mol methanol (use data from Table 16.1 or Appendix J). (b) Calculate the enthalpy of vaporization of methanol, assuming that rS doesnt depend on temperature and taking the boiling point of methanol to be 64.6C.
A key component in many chemical engineering designs is the separation of mixtures of chemicals. (a) What happens to the entropy of the system when a chemical mixture is separated? (b) Are designs for chemical separation more likely to rely on spontaneous or nonspontaneous processes?
Explain why absolute entropies can be measured.
In the thermodynamic definition of a spontaneous process, why is it important that the phrase “continuous intervention” be used rather than just “intervention?”
The synthesis of glucose directly from CO2 and H2O and the synthesis of proteins directly from amino acids are both non-spontaneous processes under standard conditions. Yet it is necessary for these to occur for life to exist. In light of the second law of thermodynamics, how can life exist?
Calculate the entropy change for the vaporization of liquid methane and liquid hexane using the following data. Boilling point (1atm) Hvap Methane 112K 8.20 KJ/mol Hexane 342K 28.9 KJ/mol Compare the molar volume of gaseous methane at 112 K with that of gaseous hexane at 342 K. How do the differences in molar volume affect the values of Svap for these liquids?
Under what conditions is the entropy of a substance equal to zero?
The standard molar entropy of iodine vapor, I2(g), is 260.7 J Kl mol-1 and the standard molar enthalpy of formation is 62.4 kJ/mol. a) Calculate the entropy change for vaporization of 1 mol of solid iodine (use data from Table 16.1 or Appendix J). b) Calculate the enthalpy change for sublimation of iodine. c) Assuming that rSdoes not change with temperature, estimate the temperature at which iodine would sublime (change directly from solid to gas).
10.69 If a sample of air were separated into nitrogen and oxygen molecules (ignoring other gases present), what would be the sign of for this process? Explain your answer. The next four questions relate to the following paragraph [Frank L. Lambert, Journal of Chemical Education, 76(10), 1999, 1385]. "The movement of macro objects from one location to another by an external agent involves no change in the objects' physical (thermodynamic) entropy. The agent of movement undergoes a thermodynamic entropy increase in the process."
A 2.50-mol sample of gas is compressed isothermally from 20.0 L to 5.00 L under a constant external pressure of 10.0 atm. Calculate w, q, U, and H for the process.