   Chapter 11, Problem 12CQ

Chapter
Section
Textbook Problem

Objects A and B have the same size and shape with emissivities eA and eB and temperatures TA and TB, respectively. (a) if eA = eB and TB = 4TA, what is the ratio PB/PA of their radiated powers? (b) If, instead, they radiate the same power and eA = 4eB, what is the ratio TB/TA of their kelvin temperatures?

(a)

To determine
The ratio PB/PA of the radiated power.

Explanation

Given Info: Objects A and B have the same size and shape with emissivities eA and eB and temperatures TA and TB respectively.

Formula to calculate the radiated power from object A is,

PA=σAeATA4 (I)

• PA is the power radiated by the object A
• σ is the Stefan Boltzmann constant
• A is the area of the object A and B
• eA is the emissivity of the object A
• TA is the temperature of the object A

Formula to calculate the radiated power from object B is,

PB=σAeBTB4 (II)

• PB is the power radiated by the object B
• eB is the emissivity of the object B
• TB is the temperature of the object B

Divide (II) by (I)

(b)

To determine
The ratio TB/TA of the temperatures.

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