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Chapter 20: Problem 9

20.9a) The maximum efficiency of a Carnot engine is \(100 \%\) since the Carnot cycle is an ideal process. b) The Carnot cycle consists of two isothermal processes and two adiabatic processes. c) The Carnot cycle consists of two isothermal processes and two isentropic processes (constant entropy). d) The efficiency of the Carnot cycle depends solely on the temperatures of the two thermal reservoirs.

Short Answer

Expert verified
Question: Evaluate the accuracy of each statement about the Carnot engine. a) Maximum efficiency of a Carnot engine is 100%. b) The Carnot cycle consists of two isothermal processes and two adiabatic processes. c) The Carnot cycle consists of two isothermal processes and two isentropic processes. d) The efficiency of the Carnot cycle depends solely on the temperatures of the two thermal reservoirs. Answer: a) False b) True c) True d) True

Step by step solution

01

Statement a: Maximum efficiency of a Carnot engine is 100%.

False. The ideal "Carnot engine" is a theoretical construct that assumes perfectly reversible processes. Its efficiency is given by the formula: Efficiency = \(1-\frac{T_{cold}}{T_{hot}}\) Where \(T_{cold}\) and \(T_{hot}\) are the cold and hot reservoir temperatures, respectively, in Kelvin. Even in this ideal case, the efficiency can never reach 100% unless the temperature of the cold reservoir is absolute zero, which is impossible.
02

Statement b: The Carnot cycle consists of two isothermal processes and two adiabatic processes.

True. A Carnot cycle comprises four distinct steps: two isothermal processes (one at the hot reservoir, one at the cold reservoir) and two adiabatic processes (one for expansion, one for compression). During isothermal processes, the temperature remains constant; during adiabatic processes, there is no transfer of heat.
03

Statement c: The Carnot cycle consists of two isothermal processes and two isentropic processes.

True. The two adiabatic processes in the Carnot cycle are also isentropic (constant entropy) processes. In an ideal Carnot cycle, the two isothermal processes are assumed to be perfectly reversible, so they are also isentropic. As a result, both statements are true: the Carnot cycle consists of two isothermal processes and two adiabatic or isentropic processes.
04

Statement d: The efficiency of the Carnot cycle depends solely on the temperatures of the two thermal reservoirs.

True. The efficiency of the Carnot cycle relies on the temperature difference between the hot and cold reservoirs. As previously mentioned, the efficiency of a Carnot engine is given by the formula: Efficiency = \(1-\frac{T_{cold}}{T_{hot}}\) Where \(T_{cold}\) and \(T_{hot}\) are the cold and hot reservoir temperatures, respectively, in Kelvin. The larger the temperature difference, the higher the Carnot engine's efficiency.

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Most popular questions from this chapter

Why might a heat pump have an advantage over a space heater that converts electrical energy directly into thermal energy?

A Carnot refrigerator is operating between thermal reservoirs with temperatures of \(27.0^{\circ} \mathrm{C}\) and \(0.00^{\circ} \mathrm{C}\) a) How much work will need to be input to extract \(10.0 \mathrm{~J}\) of heat from the colder reservoir? b) How much work will be needed if the colder reservoir is at \(-20.0^{\circ} \mathrm{C}^{2}\)

Assume that it takes \(0.0700 \mathrm{~J}\) of energy to heat a \(1.00-\mathrm{g}\) sample of mercury from \(10.000^{\circ} \mathrm{C}\) to \(10.500{ }^{\circ} \mathrm{C}\) and that the heat capacity of mercury is constant, with a negligible change in volume as a function of temperature. Find the change in entropy if this sample is heated from \(10 .{ }^{\circ} \mathrm{C}\) to \(100^{\circ} \mathrm{C}\).

An inventor claims that he has created a water-driven engine with an efficiency of 0.200 that operates between thermal reservoirs at \(4^{\circ} \mathrm{C}\) and \(20 .{ }^{\circ} \mathrm{C}\). Is this claim valid?

Explain how it is possible for a heat pump like that in Example 20.2 to operate with a power of only \(6.28 \mathrm{~kW}\) and heat a house that is losing thermal energy at a rate of \(21.98 \mathrm{~kW}\).
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