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Chapter 21: Q. 14 (page 594)

What are (a) $W_{out}$ and $Q_{H}$ and (b) the thermal efficiency for the heat engine shown in $FIGURE EX 21.14 ?$

Short Answer

Expert verified

a.The work done by the gas will be numerically equal to the area under the graph is $10 J$ , $Q_{h}$ is $124 J$ .

b.The efficiency for a heat engine is $8 %$ .

Step by step solution

01

Calculation work done (part a)

a.

The work done by the gas will be quantitatively equal to the area beneath the graph.

Work is,

$W_{out} = \frac{1}{2} 路 200 路 10^{3} 路 100 路 10^{- 6} = 10 J$

The heat injected into the system will be converted to mechanical energy which is equal to 10 J and heat rejected out which is equal to 114 J.

We can write it in the following way.

$Q_{H} = W_{o u t} + Q_{c}$

$Q_{H} = 10 + 114 = 124 J$

02

Calculation for efficiency of heat engine(part b)

b.

The efficiency can be calculated as,

$畏 = \frac{W_{out}}{Q_{H}}$

$畏 = \frac{10}{124} = 8 %$

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Most popular questions from this chapter

The engine that powers a crane burns fuel at a flame temperature of 2000掳C. It is cooled by 20掳C air. The crane lifts a 2000 kg steel girder 30 m upward. How much heat energy is transferred to the engine by burning fuel if the engine is 40% as efficient as a Carnot engine?

A heat engine with $50 %$ of the Carnot efficiency operates between reservoirs at $20 掳 C$ and $200 掳 C$ . The engine inputs heat energy at an average rate of $63 W$ while compressing a spring $22 c m$ in $0.50 s$ . What is the spring constant?

shows the thermodynamic cycles of two heat engines. Which heat engine has the larger thermal efficiency? Or

are they the same? Explain.

A Carnot refrigerator operates between reservoirs at $- 20 掳 C$ and $50 掳 C$ in a $25 掳 C$ room. The refrigerator is a $40 c m 脳 40 c m 脳 40 c m$ box. Five of the walls are perfect insulators, but the sixth is a $1.0 - c m -$ thick piece of stainless steel. What electric power does the refrigerator require to maintain the inside temperature at $- 20 掳 C$ ?

FIGURE P $21.60$ is the $pV$ diagram of Example $21.2$ , but now the device is operated in reverse.

a. During which processes is heat transferred into the gas?

b. Is this $Q_{H}$ , heat extracted from a hot reservoir, or $Q_{C}$ , heat extracted from a cold reservoir? Explain.

c. Determine the values of $Q_{H}$ and $Q_{C}$ .

Hint: The calculations have been done in Example $21.2$ and do not need to be repeated. Instead, you need to determine which processes now contribute to $Q_{H}$ and which to $Q_{C}$ .

d. Is the area inside the curve $W_{in}$ or $W_{out}$ ? What is its value?

e. The device is now being operated in a ccw cycle. Is it a refrigerator? Explain.

See all solutions

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