Universe
Universe
11th Edition
ISBN: 9781319039448
Author: Robert Geller, Roger Freedman, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 5, Problem 25Q

(a)

To determine

The wavelength of maximum emission of the volcano at a temperature of 320°C.

(a)

Expert Solution
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Answer to Problem 25Q

Solution:

4.89 μm

Explanation of Solution

Given data:

The temperature of the volcano named Pele on Jupiter’s moon, Io, is 320°C.

Formula used:

The conversion of the unit of temperature from Celsius to kelvin is done as follows:

TK=T°C+273

Here, TK is the temperature in kelvin and T°C is the temperature in Celsius.

The expression for Wien’s law is:

λmax=0.0029 mKT

Here, T is the temperature of the object and λmax is the wavelength of maximum emission of the object.

Explanation:

The conversion of the unit of temperature from Celsius to kelvin is done as follows:

TK=T°C+273

Substitute 320°C for T°C.

K=320°C+273=593 K

The expression for Wien’s law is:

λmax=0.0029 mKT

Substitute 593 K for T.

λmax=0.0029 mK593 K=4.89×106 m(106 μm1 m)=4.89 μm

Conclusion:

The wavelength of maximum emission of the volcano is 4.89 μm.

(b)

To determine

The energy emitted by a square meter of the surface of Pele compared to that by a square meter of the surface of the moon, Io, if the temperature of Io’s surface is 150°C.

(b)

Expert Solution
Check Mark

Answer to Problem 25Q

Solution:

A square meter of the surface of Pele emits 540.3 times more energy than a square meter of the surface of Io.

Explanation of Solution

Given data:

The average temperature of the surface of Io is 150°C.

Formula used:

The conversion of the unit of temperature from Celsius to kelvin is done as follows:

TK=T°C+273

Here, TK is the temperature in kelvin and T°C is the temperature in Celsius.

The expression for Stefan Boltzmann law is:

F=σT4

Here, T is the temperature of the object, F is the energy flux per square unit per second and σ is the Stefan constant (5.67×108 Wm2K4).

Explanation:

The conversion of the unit of temperature from Celsius to kelvin is done as follows:

TK=T°C+273

Substitute 150°C for T°C.

K=150°C+273=123 K

The expression for Stefan Boltzmann law is:

F=σT4

Here, the energy per square unit per second will be same as the flux.

Use this relation to find the ratio of energy per square unit per second.

FpeleFIo=Tpele4TIo4

Substitute 123 K for TIo and 593 K for Tpele.

FpeleFIo=(593 K)4(123 K)4=540.3

Conclusion:

Therefore, Pele has a higher surface temperature, and each square meter of its surface emits 540.3 times more energy compared to a square meter of the surface of Io.

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