First slide

Heat transfer-Radiation

Question

If the temperature of the hot body is increased by 50%. The percentage of amount of radiation emitted is increased by

Easy

A

50%
B

400%
C

250%
D

500%

Solution

${let initial temperature of the hot body beT}_{1} =100K: temperature i n c r e a s e d b y 50 %, t h e n f i n a l t e m p e r a t u r e i s T_{2} =150K l e t i n i t i a l e n e r g y r a d i a t e d b e E_{1} {=E; final energy is E}_{2} percentage increase of amount of radiation emitted=? \frac{ΔE}{E} ×100=? {ΔE=E}_{2} {-E}_{1} f r o m s t e f a n s l a w E= σ T^{4} \Rightarrow E α T^{4} \Rightarrow \frac{E_{2}}{E_{1}} = {(\frac{T_{2}}{T_{1}})}^{4} \Rightarrow \frac{E_{2}}{E_{1}} = {(\frac{150}{100})}^{4} s u b t r a c t 1 f r o m e a c h s i d e \frac{E_{2}}{E_{1}} -1= \frac{81}{16} -1 \frac{E_{2} {-E}_{1}}{E_{1}} = \frac{81-16}{16} m u l t i p l y b y 100 b o t h s i d e, t o g e t p e r c e n t a g e \frac{ΔE}{E} ×100= \frac{65}{16} \times 100 = 406 % \approx 400 % percentage increase of amount of radiation emitted = 400 %$

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