A ball of radius 2.20 cm, temperature 280 K, and emissivity 0.700 is suspended i

Question

A ball of radius 2.20 cm, temperature 280 K, and emissivity 0.700 is suspended in an environment of constant temperature 300 K.

a.) What is the net radiative energy transfer rate of the ball (relative to its environment)?
Pnet =  ??? W

b.) What is the peak wavelength initially emitted by this ball?
??? µm
Is this infrared or visible?

c.) Over time, as the ball approaches thermal equilibrium with the environment,

the temperature of the ball will:  ---Select--- increase/decrease/stay the same ???
the peak wavelength of this ball will:  ---Select--- increase/decrease/stay the same ???
Pball (the rate the ball only transfers energy to its environment) will:  ---Select--- increase/decrease/stay the same ???
Pnet (the overall exchange rate with the environment) will:  ---Select--- increase/decrease/stay the same ???

d.) Both Abe and Bob set their light meters to measure the intensity of light emitted from the ball, over a fixed range of wavelengths.
Bob is standing 2 times farther away from the ball as Abe.
Note: you may assume they calibrated their instruments to remove the effect of the environment.

Initially, the relative values of their measurements will be:
IBob =  ??? · IAbe

At a later time, how are their readings different?
IAbe  ---Select--- has increased/has decreased/has stayed the same ???
IBob  ---Select--- has increased/has decreased/has stayed the same ???
IBob =  ??? · IAbe

Explanation / Answer

Given that

A ball of radius (r) = 2.20 cm=0.022m, temperature 280 K,

and emissivity 0.700 is suspended in an environment of constant temperature 300 K.

Power =Shape factor*Sigma*A*(t14-t24)

Where A is the surface area of the sphere =pir2 =3.14*(0.022)2=1.52*10-3m2

shape factor =1

Sigma =0.700

t1 =280K and T2 =300K

Now the net radiative energy transfer rate of the ball is given by

Pnet =Shape factor*Sigma*A*(t14-t24)

substitute the values to get the requird answer

Accordind to the wein displacement law lamda*T =2.8997/mmk

So, now calcaulate for lamda

From the above we can say that the intensity of the bob will be (1/9)th of the intensity of b abe (inverse square law)

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