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Question: The emissive power of a sphere of area \( 0.02{m^2} \) is \( 0.5\,kcal\,{s^{ - 1}}\,{m^{ - 2}} \) .W...

The emissive power of a sphere of area 0.02m20.02{m^2} is 0.5 kcal s−1 m−20.5\,kcal\,{s^{ - 1}}\,{m^{ - 2}} .What is the amount of heat radiated by the spherical surface in 2020 seconds?

Explanation

Solution

Hint : With the help of the given values we can solve this problem. Using the formula of heat radiation we can find out the solution where heat radiation is the multiplication of area of the sphere, emissive power and the time.All these values are given use this in the radiation formula.
Q=AEtQ = AEt
Where,
The amount of heat radiation = Q
Area of the sphere = A
Emissive power of the sphere = E
Time = t.

Complete Step By Step Answer:
Heat radiation is the transfer of internal energy in the form of electromagnetic waves.
As per the given problem,
We know,
The emissive power of a sphere =0.5kcal s−1 m−2= 0.5kcal\,{s^{ - 1}}\,{m^{ - 2}}
Area of the sphere =0.5m2= 0.5{m^2}
Time given as,t =20seconds= 20{\text{seconds}}
We need to calculate the amount of heat radiating from the spherical body at the given amount of time.
As we know the formula for heat radiation by using it we will get,
Q=AEtQ = AEt
Putting the given respective value in the above formula we will get,
Q=0.02m2×0.5 kcal s−1 m−2×20sQ = 0.02{m^2} \times 0.5\,kcal\,{s^{ - 1}}\,{m^{ - 2}} \times 20s
Here second is denoted as s.
Now forthur multiplying we will get,
Q=0.2kcal m−2+2s−1+1Q = 0.2kcal\,{m^{ - 2 + 2}}{s^{ - 1 + 1}}
⇒Q=0.2kcal \Rightarrow Q = 0.2kcal\,
Therefore the amount of heat radiated by the spherical surface in 2020 seconds is 0.2kcal 0.2kcal\, .

Note :
Always keep in mind there are many different formulas for calculating the heat radiation of a body. According to the requirement and the given values we have to choose the formula for it. Heat of radiation is also known as converter heat of induction heat so don’t get confused.