Can any ideal gas power cycle have a thermal efficiency greater than 55 percent when using thermal energy reservoirs at 627∘C at 17∘C? Explain. What is the maximum possible efficiency for such an engine?

Respuesta :

Answer:

Since the maximum thermal efficiency is higher than 55 percent, there can be a power cycle with these reservoir temperature with an efficiency higher than 55 percent.

Explanation:

The maximum thermal efficiency is determined from the given temperature

nth Carnot = 1- TL/TH

Where TL= 17+273= 290k

TH= 627*273= 900K.

nth Carnot = 1- 290/900 = 0.68

0.68*100 = 68 percent

The carnot cycle of the efficiency of thermal machines allows to find the result for whether it is possible to have machines with an efficiency of 55% is:

  • The efficiency of the 55% is easy to obtain for machines with the given bulbs.
  • The maximum efficiency is e = 68%

Given parameters.

  • Cold focus temperature Tc = 17º + 273 = 290 K
  • Hot spot temperature Th = 627 + 273 = 900K

To find.

  • It is possible to have an efficiency greater than e = 55%
  • Maximum efficiency

The efficiency of a heat engine is given by the Carnot cycle, which is the relationship between the energy obtained and the energy consumed. This efficiency is determined by the absolute temperatures between the heat and cold sources.

        [tex]e= 1 - \frac{T_c}{T_h}[/tex]

where e is the efficiency, [tex]T_c[/tex] and [tex]T_h[/tex] are the temperatures of the heat and cold source, respectively.

Let's  calculate the maximum efficiency.

       [tex]e= 1 - \frac{290}{900}[/tex]  

       e = 0.68 = 68%

As the maximum efficiency for these two bulbs is much higher than the 55% efficiency, it is easy for the thermal machines to reach this efficiency.

In conclusion, using the Carnot cycle of the efficiency of thermal machines we can find the result for whether it is possible to have machines with an efficiency of 55% is:

  • The maximum efficiency is e = 68%
  • The efficiency of the 55% is easy to obtain for machines with the given bulbs.

Learn more about the Carnot cycle here:  brainly.com/question/25819144

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