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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

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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

One of your friends begins to talk about how unfortunate the Second Law of Thermodynamics is, how sad it is that entropy must always increase, leading to the irreversible degradation of useful energy into heat and the decay of all things. Is there any counterargument you could give that would suggest that the Second Law is in fact a blessing?

Suppose a Brayton engine (see Problem 20.26 ) is run as a refrigerator. In this case, the cycle begins at temperature \(T_{1}\), and the gas is isobarically expanded until it reaches temperature \(T_{4}\). Then the gas is adiabatically compressed, until its temperature is \(T_{3}\). It is then isobarically compressed, and the temperature changes to \(T_{2}\). Finally, it is adiabatically expanded until it returns to temperature \(T_{1}\) - a) Sketch this cycle on a \(p V\) -diagram. b) Show that the coefficient of performance of the engine is given by \(K=\left(T_{4}-T_{1}\right) /\left(T_{3}-T_{2}-T_{4}+T_{1}\right) .\)

A certain refrigerator is rated as being \(32.0 \%\) as ef ficient as a Carnot refrigerator. To remove \(100 .\) J of heat from the interior at \(0^{\circ} \mathrm{C}\) and eject it to the outside at \(22^{\circ} \mathrm{C}\), how much work must the refrigerator motor do?

What is the minimum amount of work that must be done to extract \(500.0 \mathrm{~J}\) of heat from a massive object at a temperature of \(27.0^{\circ} \mathrm{C}\) while releasing heat to a high temperature reservoir with a temperature of \(100.0^{\circ} \mathrm{C} ?\)

What capacity must a heat pump with a coefficient of performance of 3 have to heat a home that loses heat energy at a rate of \(12 \mathrm{~kW}\) on the coldest day of the year? a) \(3 \mathrm{~kW}\) c) \(10 \mathrm{~kW}\) e) \(40 \mathrm{~kW}\) b) \(4 \mathrm{~kW}\) d) \(30 \mathrm{~kW}\)
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