Q.28 A Carnot engine whose hot-reserv... [FREE SOLUTION]

Chapter 21: Q.28 (page 595)

A Carnot engine whose hot-reservoir temperature is $400 掳 C$ has a thermal efficiency of $40 %$ . By how many degrees should the temperature of the cold reservoir be decreased to raise the engine's efficiency to $60 %$ $?$

Short Answer

Expert verified

The temperature decrease of the cold bath required is $135 degrees, Kelvin or Celsius .$

Step by step solution

Formula for thermal efficiency

The efficiency of a Carnot engine working between a hot bath of temperature $T_{h}$ and a cold bath of temperature T_cis given as,

$畏 = 1 - \frac{T_{c}}{T_{h}}$

Calculation for the temperature decrease of the heat bath

Initial cold bath temperature is $T_{c 1}$ and efficiency is $畏_{1}$ .

When the cold bath temperature is localid="1648646350008" $T_{c 2}$ , the efficiency is localid="1648646357282" $畏_{2}$ .

The relation between the two parameters, mentioned in the beginning, allows us to write:

localid="1649393943368" $螖畏 = 畏_{2} - 畏_{1} = (1 - \frac{T_{c 2}}{T_{h}}) - (1 - \frac{T_{c 1}}{T_{h}}) = \frac{T_{c 1} - T_{c 2}}{T_{h}} = - \frac{{螖罢}_{c}}{T_{h}}$

The temperature decrease of the heat bath ,

localid="1648646396333" $- {螖罢}_{c} = {螖畏罢}_{h}$

localid="1648646409862" $- {螖罢}_{c} = 0.2 路 (400 + 273) = 135 K$

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91影视

A Carnot engine whose hot-reservoir temperature is $400 掳 C$ has a thermal efficiency of $40 %$ . By how many degrees should the temperature of the cold reservoir be decreased to raise the engine's efficiency to $60 %$ $?$

Short Answer

Step by step solution

Formula for thermal efficiency

Calculation for the temperature decrease of the heat bath

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Most popular questions from this chapter

Recommended explanations on Physics Textbooks

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91影视

A Carnot engine whose hot-reservoir temperature is 400掳C has a thermal efficiency of 40%. By how many degrees should the temperature of the cold reservoir be decreased to raise the engine's efficiency to 60%?

Short Answer

Step by step solution

Formula for thermal efficiency

Calculation for the temperature decrease of the heat bath

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Kinematics Physics

Fundamentals of Physics

Electrostatics

Medical Physics

Fluids

Circular Motion and Gravitation

Study anywhere. Anytime. Across all devices.

A Carnot engine whose hot-reservoir temperature is $400 掳 C$ has a thermal efficiency of $40 %$ . By how many degrees should the temperature of the cold reservoir be decreased to raise the engine's efficiency to $60 %$ $?$