Question

if the temperature of a body is raised by 5%, then the heat energy radiated would increase by ​

Answer 1

To Find :

Percentage increase in radiation if the temperature of body is raised by 5%.

Solution :

■ Stefan's law : Energy emitted per second per unit area by a black body at absolute temperature T is given by [H = σ T⁴]

where, σ = Stefan's constant

So we can say that heat energy emitted per second per unit area is directly proportional to the T⁴.

❇ Let initial temperature of the body be T.

ATQ, temperature of body is raised by 5%

$:\implies\tt\:T'=T+(5\%\:of\:T)$

$:\implies\tt\:T'=T+\dfrac{5T}{100}$

$:\implies\tt\:T'=\dfrac{105T}{100}$

$:\implies\:\tt\orange{T'=1.05T}$

By applying stefan's law,

$:\implies\tt\:\dfrac{H'}{H}=\dfrac{T'^4}{T^4}$

$:\implies\sf\:\dfrac{H'}{H}=\dfrac{(1.05T)^4}{(T)^4}$

$:\implies\tt\:\pink{H'=1.22H}$

Percentage increase in the radiation of heat energy :

$:\implies\tt\:\%(\Delta H)=\dfrac{H'-H}{H}\times 100$

$:\implies\tt\:\%(\Delta H)=\dfrac{1.22H-H}{H}\times 100$

$:\implies\tt\:\%(\Delta H)=\dfrac{0.22H}{H}\times 100$

$:\implies\tt\:\%(\Delta H)=0.22\times 100$

$:\implies\:\underline{\boxed{\bf{\purple{\%(\Delta H)=22\%}}}}$

Answer 2

Answer:

correct answer is 22%

Explanation:

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