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Unformatted text preview: Chapter 5: Entropy and the Second and Third Laws of Thermodynamics Problem numbers in italics indicate that the solution is included in the Student’s Solutions Manual. Questions on Concepts Q5.1) Which of the following processes is spontaneous set? a) The reversible isothermal expansion of an ideal gas. b) The vaporization of superheated water at 102º C and 1 bar. c) The constant pressure melting of ice at its normal freezing point by the addition of an infinitesimal quantity of heat. d) The adiabatic expansion of a gas into a vacuum. a) is not spontaneous because the system and surroundings are in equilibrium. b) is spontaneous because the equilibrium phase under the stated conditions is a gas. c)is not spontaneous because the process is reversible. d) is spontaneous because at equilibrium, the density of a gas is uniform throughout its container. Q5.2) Why are ∆ S fusion and ∆ S vaporization always positive? This is the case because ∆ H fusion and ∆ H vaporization are always positive. In each of these transitions, attractive forces must be overcome. Q5.3) Why is the efficiency of a Carnot heat engine the upper bound to the efficiency of an internal combustion engine? This is the case because the maximum work that can be done on the surroundings in the expansion of a gas is in a reversible process. Q5.4) The amplitude of a pendulum consisting of a mass on a long wire is initially adjusted to have a very small value. The amplitude is found to decrease slowly with time. Is this process reversible? Would the process be reversible if the amplitude did not decrease with time? No, because dissipative forces are acting on the system. If the amplitude did not decrease, no dispersive forces act on the system and the oscillation is reversible in the limit of very small amplitudes. If the amplitude did not decrease with time, no dissipative forces act on the system, and because the amplitude is very small, the process is reversible. Q5.5) A process involving an ideal gas is carried out in which the temperature changes at constant volume. For a fixed value of ∆ T , the mass of the gas is doubled. The process is repeated with the same initial mass and ∆ T is doubled. For which of these processes is ∆ S greater? Why? 5-1 Chapter 5/Entropy and the Second and Third Laws of Thermodynamics ∆ S is greater if the mass is doubled, because ∆ S increases linearly with the amount of material. By contrast, ∆ S only increases as the logarithm of the temperature. This increase is much slower than a linear increase. Q5.6) Under what conditions does the equality H S T ∆ ∆ = hold? Because reversible dq S T / ∆ = , the equality holds if . reversible dq H / = ∆ This is the case for a reversible process at constant pressure....
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- Fall '09
- Thermodynamics, mol, Carnot cycle