Chapter 21: Q. 30 (page 595)

A heat engine operating between energy reservoirs at $20 ° C$ and $600 ° C$ has $30 %$ of the maximum possible efficiency. How much energy must this engine extract from the hot reservoir to do $1000 J$ of work?

Short Answer

Expert verified

The energy extract from the hot reservoir is $5020 W$ .

Step by step solution

Formula for the energy extract from the hot reservoir

The energy extracted from the hot reservoir can be calculated using the following heat engine efficiency expression:

$η = \frac{W}{Q_{in}}$

where:

$W$ is the work done;

$Q_{in}$ is the energy extracted from the hot reservoir.

Calculation for energy extraction

Using,

$Q_{in} = \frac{W}{η}$

The maximum efficiency,

$η_{\max} = 1 - \frac{T_{C}}{T_{H}}$

$η_{\max} = 1 - \frac{20 + 273}{600 + 273} = 0.664$

Note that the temperatures must be in $K$ .

The efficiency of the heat engine is:

$η = 0.3 \times 0.664 = 0.1992$

Substitute all values,

$Q_{in} = \frac{1000}{0.1992}$

$Q_{in} = 5020 W$

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A heat engine operating between energy reservoirs at $20 ° C$ and $600 ° C$ has $30 %$ of the maximum possible efficiency. How much energy must this engine extract from the hot reservoir to do $1000 J$ of work?

Short Answer

Step by step solution

Formula for the energy extract from the hot reservoir

Calculation for energy extraction

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A heat engine operating between energy reservoirs at20°Cand 600°Chas 30%of the maximum possible efficiency. How much energy must this engine extract from the hot reservoir to do 1000Jof work?

Short Answer

Step by step solution

Formula for the energy extract from the hot reservoir

Calculation for energy extraction

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Conservation of Energy and Momentum

Rotational Dynamics

Magnetism and Electromagnetic Induction

Torque and Rotational Motion

Famous Physicists

Atoms and Radioactivity

Study anywhere. Anytime. Across all devices.

A heat engine operating between energy reservoirs at $20 ° C$ and $600 ° C$ has $30 %$ of the maximum possible efficiency. How much energy must this engine extract from the hot reservoir to do $1000 J$ of work?