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Chapter 15: Q22P (page 412)

Question:(I) A heat engine鈥檚 high temperature\({T_{\bf{H}}}\)could be ambient temperature, because liquid nitrogen at 77 K could be\({T_{\bf{L}}}\)and is cheap. What would be the efficiency of a Carnot engine that made use of heat transferred from air at room temperature (293 K) to the liquid nitrogen 鈥渇uel鈥�(Fig.15鈥�25)?

Short Answer

Expert verified

The efficiency of the Carnot engine is \(73.72\% \).

Step by step solution

01

Identification of given data

The given data can be listed below as:

  • The high temperature of the heat engine is\({T_{\rm{H}}} = 293{\rm{ K}}\).
  • The cold temperature of the liquid nitrogen is \({T_{\rm{L}}} = 77{\rm{ K}}\).
02

Understanding the transfer of heat from the air to the liquid nitrogen

The ambient temperature is considered the high temperature of the heat engine.

The liquid nitrogen temperature is considered the cold temperature reservoir.

The heat is being transferred from the ambient air to the liquid nitrogen. The Carnot engine utilizes the high temperature of the heat engine to transfer heat to the fuel.

03

Determination of the efficiency of the Carnot engine

The efficiency of the Carnot engine can be expressed as:

\(e = \left( {1 - \frac{{{T_{\rm{L}}}}}{{{T_{\rm{H}}}}}} \right)\)

Substitute the values in the above equation.

\(\begin{aligned}{c}e &= \left( {1 - \frac{{{\rm{77 K}}}}{{{\rm{293 K}}}}} \right)\\ &= 0.7372\\ &= 0.7372 \times 100\% \\ &= 73.72\% \end{aligned}\)

Thus, the efficiency of the Carnot engine is \(73.72\% \).

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Most popular questions from this chapter

Question: Entropy is often called the鈥榯ime鈥檚 arrow鈥� because it tells us the direction in which natural processes occur. If a movie is run backward, name some processes that you might see that would tell you that time is 鈥榬unning backward鈥�.

Can you warm a kitchen in winter by leaving the oven door open? Can you cool the kitchen on a hot summer day by leaving the refrigerator door open? Explain.

On a very hot day, could you cool your kitchen by leaving the refrigerator door open?

(a) Yes, but it would be very expensive.

(b) Yes, but only if the humidity is below 50%.

(c) No, the refrigerator would exhaust the same amount of heat into the room as it takes out of the room.

(d) No, the heat exhausted by the refrigerator into the room is more than the heat the refrigerator takes out of the room.

(III) A real heat engine working between heat reservoirs at 970 K and 650 K produces 550 J of work per cycle for a heat input of 2500 J.

(a) Compare the efficiency of this real engine to that of an ideal (Carnot) engine.

(b) Calculate the total entropy change of the universe per cycle of the real engine, and

(c) also if the engine is ideal (Carnot).

Question: In an isobaric compression of an ideal gas,

(a) no heat flows into the gas.

(b) the internal energy of the gas remains constant.

(c) no work is done on the gas.

(d) work is done on the gas.

(e) work is done by the gas.
See all solutions

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