What Is the Maximum Work a Heat Engine Can Perform in a Cycle?

In summary, the maximum possible work done by the engine in each cycle is 1200 J, as it operates in a reversible Carnot cycle with an efficiency of 42.857%. This is calculated by using the equations e = |W|/|Qh| and Qc/Qh = Tc/Th, and plugging in the given values of 2800 J for Qh, 700 K for Th, and 400 K for Tc. This results in an efficiency of 42.857% and a maximum work of 1200 J. The answer is A.
  • #1
GreenPrint
1,196
0

Homework Statement



21. A heat engine operates in a cycle between temperatures 700 K and 400 K. The heat input to the engine during each cycle is 2800 J. What is the maximum possible work done by the engine in each cycle?

(A) 1200 J
(B) 1600 J
(C) 2100 J
(D) 2800 J
(E) 4400 J

I believe that the answer is E. I just don't know how to prove it. If you could show that would be great. I know that



Homework Equations



e = |W|/|Qh|

|Qh| = |W| + |Ql|

e = 1 - |Ql|/|Qh|

The Attempt at a Solution



I'm lost...

e = |W|/|Qh|

|Qh| = |W| + |Ql|

e = 1 - |Ql|/|Qh|

I don't remember how to do this type of problem...
 
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  • #2
Wait the answer is A... but why?
 
  • #3
GreenPrint said:
Wait the answer is A... but why?
The maximum possible efficiency is in a reversible (Carnot) cycle. In a reversible cycle, [itex]\Delta S = 0[/itex], so [itex]\Delta S = \Delta S_h + \Delta S_c = -Q_h/T_h + Q_c/T_c = 0[/itex]. This means that [itex]Q_c/Q_h = T_c/T_h[/itex]

So [itex]\eta = W/Q_h = (Q_h-Q_c)/Q_h = 1 - Q_c/Q_h = 1 - T_c/T_h[/itex]

Plugging in the numbers: [itex]\eta = 1 - 400/700 = .42857[/itex].

Since [itex]W = \eta * Q_h[/itex], the maximum Work is 1200 J. (.42857 * 2800).

AM
 

Related to What Is the Maximum Work a Heat Engine Can Perform in a Cycle?

1. What is a heat engine cycle?

A heat engine cycle refers to the process of converting heat energy into mechanical work. It involves a series of steps or processes that result in the transfer of heat from a high-temperature source to a low-temperature sink, while producing useful work. Examples of heat engine cycles include the Carnot cycle, Otto cycle, and Rankine cycle.

2. How does a heat engine cycle work?

A heat engine cycle works by utilizing the principles of thermodynamics to convert heat energy into mechanical work. The cycle typically involves four stages: intake, compression, power, and exhaust. During these stages, the working fluid undergoes changes in temperature, pressure, and volume, resulting in the production of work by the engine.

3. What is the efficiency of a heat engine cycle?

The efficiency of a heat engine cycle is defined as the ratio of the work output to the heat input. It is dependent on the specific type of cycle and the operating conditions of the engine. The maximum theoretical efficiency of a heat engine cycle is given by the Carnot efficiency, which is based on the temperature of the source and sink.

4. What are some real-world applications of heat engine cycles?

Heat engine cycles are used in a variety of real-world applications. For example, the Otto cycle is used in most gasoline-powered engines, while the Rankine cycle is used in steam power plants. Heat engine cycles are also used in refrigeration and air conditioning systems, as well as in industrial processes for generating electricity or powering machinery.

5. What are the limitations of heat engine cycles?

Heat engine cycles have several limitations, including the second law of thermodynamics, which states that no engine can have 100% efficiency. This means that a certain amount of heat energy will always be lost during the conversion process. Additionally, heat engine cycles are limited by the materials and technology used to construct them, and may be affected by factors such as friction and inefficiencies in the combustion process.

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