Chapter 21: Q. 27 (page 595)

A Carnot engine operating between energy reservoirs at temperatures $500 k$ and $300 k$ produces a power output of $1000 W$ . What are (a) the thermal efficiency of this engine, (b) the rate of heat input, in $W$ and (c) the rate of heat output, in $W$ ?

Short Answer

Expert verified

a.Thermal efficiency of engine is $40 %$ .

b.The rate of heat input is $2500 W$ .

c.The rate of heat output is $1500 W$ .

Step by step solution

Calculation of thermal efficiency of carnot engine (part a)

The thermal efficiency of a Carnot engine working between the temperatures $T_{h}$ of the heat bath and $T_{c}$ is given as,

$η = 1 - \frac{T_{c}}{T_{h}}$

Efficiency,

$η = 1 - \frac{300}{500} = 40 %$

Calculation of rate of heat input (part b)

The efficiency can be expressed in terms of the power as,

$η = \frac{W}{Q_{h}} = \frac{Pt}{P_{h} t} = \frac{P}{P_{h}}$

where $P$ is the useful power, W is work output.

$P_{h}$ is the heating power required.

$P_{h} = \frac{P}{η}$

$P_{h} = \frac{1000}{0.4} = 2500 W$

Calculation of rate of heat output (part c)

(c)

Using solution b,

$Q_{h} = W + Q_{c}$

Q_cis heat dumped to cold reservoir.

This might be written in terms of power as,

$P_{h} = P + P_{c}$

P is power output.

$P_{c} = P_{h} - P$

$P_{c} = 2500 - 1000 = 1500 W$

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A Carnot engine operating between energy reservoirs at temperatures $500 k$ and $300 k$ produces a power output of $1000 W$ . What are (a) the thermal efficiency of this engine, (b) the rate of heat input, in $W$ and (c) the rate of heat output, in $W$ ?

Short Answer

Step by step solution

Calculation of thermal efficiency of carnot engine (part a)

Calculation of rate of heat input (part b)

Calculation of rate of heat output (part c)

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A Carnot engine operating between energy reservoirs at temperatures 500kand 300kproduces a power output of 1000W. What are (a) the thermal efficiency of this engine, (b) the rate of heat input, in Wand (c) the rate of heat output, in W?

Short Answer

Step by step solution

Calculation of thermal efficiency of carnot engine (part a)

Calculation of rate of heat input (part b)

Calculation of rate of heat output (part c)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Turning Points in Physics

Medical Physics

Mechanics and Materials

Linear Momentum

Geometrical and Physical Optics

Electrostatics

Study anywhere. Anytime. Across all devices.

A Carnot engine operating between energy reservoirs at temperatures $500 k$ and $300 k$ produces a power output of $1000 W$ . What are (a) the thermal efficiency of this engine, (b) the rate of heat input, in $W$ and (c) the rate of heat output, in $W$ ?