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A heat engine is operating in between 500 K and 400 K. If the engine absorbs 100 J heat per cycle, then which of the following is impossible amount of heat rejected by the engine per cycle?

A. 75 J
B. 85 J
C. 90 J
D. 70 J

1 Answer

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Final answer:

A heat engine is a device that converts heat energy into mechanical work. The efficiency of a heat engine depends on the amount of heat rejected and absorbed. By calculating the efficiency for each option, we can determine the impossible amount of heat rejected.

Step-by-step explanation:

A heat engine is a device that converts heat energy into mechanical work. The efficiency of a heat engine is given by the formula:

E = 1 - Qc / Qh

Where E is the efficiency of the engine, Qc is the amount of heat rejected to the low-temperature reservoir, and Qh is the amount of heat absorbed from the high-temperature reservoir.

In this case, the engine absorbs 100 J of heat per cycle. To find the impossible amount of heat rejected, we need to calculate the efficiency using the given temperatures:

  1. Calculate the efficiency using the formula E = 1 - Qc / Qh. Let's assume Qh = 100 J.
  2. Substitute the given temperatures into the formula:

E = 1 - Qc / 100

= 1 - Qc / 100

= 1 - Qc / 100

Now, let's calculate the efficiency for each option:

  • A. If Qc = 75 J, then the efficiency is calculated as E = 1 - 75 / 100 = 0.25.
  • B. If Qc = 85 J, then the efficiency is calculated as E = 1 - 85 / 100 = 0.15.
  • C. If Qc = 90 J, then the efficiency is calculated as E = 1 - 90 / 100 = 0.10.
  • D. If Qc = 70 J, then the efficiency is calculated as E = 1 - 70 / 100 = 0.30.

From the calculations, we can see that the efficiency of the engine cannot be 0.15, 0.10, or 0.30. Therefore, the impossible amount of heat rejected by the engine per cycle is 85 J (option B).

User Kyrylo Bulat
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