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Chapter 8: Problem 142

Keeping the limitations imposed by the second law of thermodynamics in mind, choose the wrong statement below: (a) A heat engine cannot have a thermal efficiency of \(100 \%\) (b) For all reversible processes, the second-law efficiency is \(100 \%\) (c) The second-law efficiency of a heat engine cannot be greater than its thermal efficiency. (d) The second-law efficiency of a process is \(100 \%\) if no entropy is generated during that process. \((e)\) The coefficient of performance of a refrigerator can be greater than 1

Short Answer

Expert verified
Question: Identify any incorrect statements in the following options related to the second law of thermodynamics: (a) A heat engine cannot have a thermal efficiency of \(100\%\). (b) For all reversible processes, the second-law efficiency is \(100 \%\). (c) The second-law efficiency of a heat engine cannot be greater than its thermal efficiency. (d) The second-law efficiency of a process is \(100\%\) if no entropy is generated during that process. (e) The coefficient of performance of a refrigerator can be greater than 1. Answer: None of the given statements are incorrect. All statements are in accordance with the second law of thermodynamics.

Step by step solution

01

Understanding the Second Law of Thermodynamics

The second law of thermodynamics states that heat cannot spontaneously flow from a colder body to a hotter body. Moreover, it introduces the concept of entropy, in which any natural thermodynamic process increases the total entropy. This law helps us understand the limitations of heat engines, refrigerators, and other thermodynamic processes.
02

Evaluating Statement (a)

(a) A heat engine cannot have a thermal efficiency of \(100\%\). This statement is correct because, according to the second law of thermodynamics, some heat must be discarded to a colder reservoir for the process to be spontaneous, which means that a heat engine has limits in converting heat into work.
03

Evaluating Statement (b)

(b) For all reversible processes, the second-law efficiency is \(100 \%\). This statement is correct. In a reversible process, there is no net change in entropy, and no heat is wasted during the process. As a result, the second-law efficiency is maximum for a reversible process.
04

Evaluating Statement (c)

(c) The second-law efficiency of a heat engine cannot be greater than its thermal efficiency. This statement is correct because second-law efficiency considers the amount of available work energy used, while thermal efficiency considers the amount of heat energy converted into work. In a heat engine, the second-law efficiency is usually lower than the thermal efficiency.
05

Evaluating Statement (d)

(d) The second-law efficiency of a process is \(100\%\) if no entropy is generated during that process. This statement is correct because, as mentioned earlier, the second-law efficiency is maximized in the case of a reversible process, meaning no entropy is generated during the process.
06

Evaluating Statement (e)

(e) The coefficient of performance of a refrigerator can be greater than 1. This statement is also correct. The coefficient of performance (COP) of a refrigerator is defined as the amount of heat removed from the cold reservoir divided by the amount of work input. As a refrigerator transfers heat from a colder body to a hotter body with the help of external work, it is possible for the COP to be greater than 1, indicating that the refrigerator can remove considerably more heat energy from the colder body than the work energy it requires. All of the given statements are correct, which means there is no wrong statement among the options.

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Most popular questions from this chapter

Obtain a relation for the second-law efficiency of a heat engine that receives heat \(Q_{H}\) from a source at temperature \(T_{H}\) and rejects heat \(Q_{L}\) to a sink at \(T_{L},\) which is higher than \(T_{0}\) (the temperature of the surroundings), while producing work in the amount of \(W\)

A well-insulated \(4-m \times 4-m \times 5-m\) room initially at \(10^{\circ} \mathrm{C}\) is heated by the radiator of a steam heating system. The radiator has a volume of \(15 \mathrm{L}\) and is filled with superheated vapor at \(200 \mathrm{kPa}\) and \(200^{\circ} \mathrm{C}\). At this moment both the inlet and the exit valves to the radiator are closed. A 150 -W fan is used to distribute the air in the room. The pressure of the steam is observed to drop to \(100 \mathrm{kPa}\) after \(30 \mathrm{min}\) as a result of heat transfer to the room. Assuming constant specific heats for air at room temperature, determine ( \(a\) ) the average temperature of room air in 24 min, \((b)\) the entropy change of the steam, \((c)\) the entropy change of the air in the room, and (d) the exergy destruction for this process, in \(\mathrm{kJ}\). Assume the air pressure in the room remains constant at \(100 \mathrm{kPa}\) at all times, and take \(T_{0}=10^{\circ} \mathrm{C}\)

Air is throttled from \(50^{\circ} \mathrm{C}\) and 800 kPa to a pressure of \(200 \mathrm{kPa}\) at a rate of \(0.5 \mathrm{kg} / \mathrm{s}\) in an environment at \(25^{\circ} \mathrm{C}\) The change in kinetic energy is negligible, and no heat transfer occurs during the process. The power potential wasted during this process is \((a) 0\) (b) \(0.20 \mathrm{kW}\) \((c) 47 \mathrm{kW}\) \((d) 59 \mathrm{kW}\) \((e) 119 \mathrm{kW}\)

A refrigerator has a second-law efficiency of 28 percent, and heat is removed from the refrigerated space at a rate of \(800 \mathrm{Btu} / \mathrm{min} .\) If the space is maintained at \(25^{\circ} \mathrm{F}\) while the surrounding air temperature is \(90^{\circ} \mathrm{F}\), determine the power input to the refrigerator.

Steam is to be condensed in the condenser of a steam power plant at a temperature of \(50^{\circ} \mathrm{C}\) with cooling water from a nearby lake that enters the tubes of the condenser at \(12^{\circ} \mathrm{C}\) at a rate of \(240 \mathrm{kg} / \mathrm{s}\) and leaves at \(20^{\circ} \mathrm{C}\). Assuming the condenser to be perfectly insulated, determine (a) the rate of condensation of the steam and ( \(b\) ) the rate of energy destruction in the condenser.
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