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- (b) Without further information, can you conclude whether the amount of heat transferred to the system as it goes from state 1 to state 2 is the same or different compared to that upon going from state 2 back to state 1?
Problem 18
Problem 18c
A system goes from state 1 to state 2 and back to state 1. (c) Suppose the changes in state are reversible processes. Is the work done by the system upon going from state 1 to state 2 the same or different as compared to that upon going from state 2 back to state 1?
- Consider a system consisting of an ice cube. (a) Under what conditions can the ice cube melt reversibly?
Problem 19
Problem 21d
Indicate whether each statement is true or false. (a) ΔS is a state function. (b) If a system undergoes a reversible change, the entropy of the universe increases. (c) If a system undergoes a reversible process, the change in entropy of the system is exactly matched by an equal and opposite change in the entropy of the surroundings. (d) If a system undergoes a reversible process, the entropy change of the system must be zero.
- Indicate whether each statement is true or false. (a) The entropy of the universe increases for any spontaneous process. (b) The entropy change of the system is equal and opposite that of the surroundings for any irreversible process. (c) The entropy of the system must increase in any spontaneous process. (d) The entropy change for an isothermal process depends on both the absolute temperature and the amount of heat reversibly transferred.
Problem 22
Problem 23a
The normal boiling point of Br2(l) is 58.8 °C, and its molar enthalpy of vaporization is ΔHvap = 29.6 kJ/mol. (a) When Br2(l) boils at its normal boiling point, does its entropy increase or decrease?
Problem 23b
The normal boiling point of Br2(𝑙) is 58.8 °C, and its molar enthalpy of vaporization is Δ𝐻vap=29.6 kJ/mol. (b) Calculate the value of Δ𝑆 when 1.00 mol of Br2(𝑙) is vaporized at 58.8 °C.
Problem 24a
The element gallium (Ga) freezes at 29.8 °C, and its molar enthalpy of fusion is ΔHfus = 5.59 kJ/mol. (a) When molten gallium solidifies to Ga(s) at its normal melting point, is ΔS positive or negative?
Problem 24b
The element gallium (Ga) freezes at 29.8 °C, and its molar enthalpy of fusion is ΔHfus = 5.59 kJ/mol. (b) Calculate the value of ΔS when 60.0 g of Ga(l) solidifies at 29.8 °C.
Problem 25c
Indicate whether each statement is true or false. (c) In a certain spontaneous process the system undergoes an entropy change of 4.2 J/K; therefore, the entropy change of the surroundings must be -4.2 J/K.
Problem 26a
(a) Does the entropy of the surroundings increase for spontaneous processes?
Problem 26b
(b) In a particular spontaneous process the entropy of the system decreases. What can you conclude about the sign and magnitude of ΔSsurr?
Problem 26c
(c) During a certain reversible process, the surroundings undergo an entropy change, ΔSsurr = -78 J/K. What is the entropy change of the system for this process?
- (a) What sign for ΔS do you expect when the volume of 0.200 mol of an ideal gas at 27 °C is increased isothermally from an initial volume of 10.0 L? (b) If the final volume is 18.5 L, calculate the entropy change for the process. (c) Do you need to specify the temperature to calculate the entropy change?
Problem 27
- (a) What sign for ΔS do you expect when the pressure on 0.600 mol of an ideal gas at 350 K is increased isothermally from an initial pressure of 0.750 atm? (b) If the final pressure on the gas is 1.20 atm, calculate the entropy change for the process. (c) Do you need to specify the temperature to calculate the entropy change?
Problem 28
- For the isothermal expansion of a gas into a vacuum, ΔE = 0, q = 0, and w = 0. (c) What is the “driving force” for the expansion of the gas: enthalpy or entropy?
Problem 29
Problem 29b
For the isothermal expansion of a gas into a vacuum, ΔE = 0, q = 0, and w = 0. (b) Explain why no work is done by the system during this process.
Problem 30a
(a) What is the difference between a state and a microstate of a system?
Problem 30b
(b) As a system goes from state A to state B, its entropy decreases. What can you say about the number of microstates corresponding to each state?
Problem 30c
(c) In a particular spontaneous process, the number of microstates available to the system decreases. What can you conclude about the sign of ΔSsurr?
- Would each of the following changes increase, decrease, or have no effect on the number of microstates available to a system: (a) increase in temperature, (b) change of state from liquid to gas?
Problem 31
Problem 31b
Would each of the following changes increase, decrease, or have no effect on the number of microstates available to a system: (b) decrease in volume
- (a) Using the heat of vaporization in Appendix B, calculate the entropy change for the vaporization of water at 25 °C and at 100 °C. (b) From your knowledge of microstates and the structure of liquid water, explain the difference in these two values.
Problem 32
- (a) What do you expect for the sign of ΔS in a chemical reaction in which 2 mol of gaseous reactants are converted to 3 mol of gaseous products? (b) For which of the processes in Exercise 19.11 does the entropy of the system increase?
Problem 33
Problem 34a
(a) In a chemical reaction, two gases combine to form a solid. What do you expect for the sign of ΔS?
Problem 34b
(b) How does the entropy of the system change in the processes described in Exercise 19.12?
- Does the entropy of the system increase, decrease, or stay the same when (a) a solid melts, (b) a gas liquefies, or (c) a solid sublimes?
Problem 35
- Does the entropy of the system increase, decrease, or stay the same when (a) the temperature of the system increases, (b) the volume of a gas increases, and (c) equal volumes of ethanol and water are mixed to form a solution?
Problem 36
- Indicate whether each statement is true or false. (a) The third law of thermodynamics says that the entropy of a perfect, pure crystal at absolute zero increases with the mass of the crystal. (b) “Translational motion” of molecules refers to their change in spatial location as a function of time. (c) “Rotational” and “vibrational” motions contribute to the entropy in atomic gases like He and Xe. (d) The larger the number of atoms in a molecule, the more degrees of freedom of rotational and vibrational motion it likely has.
Problem 37
Problem 38
Indicate whether each statement is true or false. (a) Unlike enthalpy, where we can only ever know changes in H, we can know absolute values of S. (b) If you heat a gas such as CO2, you will increase its degrees of translational, rotational and vibrational motions. (c) CO2(g) and Ar(g) have nearly the same molar mass. At a given temperature, they will have the same number of microstates.