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The temperature of a piece of metal is raised from 27°C to 51.2°C. the rate at which metal radiates energy increases nearly (a) 1.36 times (b) 2.36 times (c) 3.36 times (d) 4.36 times

The temperature of a piece of metal is raised from 27°C to 51.2°C. the rate at which metal radiates energy increases nearly
(a) 1.36 times
(b) 2.36 times
(c) 3.36 times
(d) 4.36 times

Grade:Upto college level

2 Answers

Saurabh Koranglekar
askIITians Faculty 10341 Points
11 months ago
The rate at which a substance radiates is directly proportional to the fourth power of the absolute temperature.
The temperature increases from300Kto324.2Kwhich is an increase by1.080
Hence the rate at which the metal radiates would increase by(1.08)4=1.36
Vikas TU
14149 Points
11 months ago
according to Stefan's law radiation energy is directly proportional to (temperature)⁴
i.e., 
or, E = kT⁴ , here k is proportionality constant.
initially, T = 27° C = 27 + 273 = 300K
so,  = k(300)⁴ = 81 × 10^8 k
finally, T = 51°C = 51 + 273 = 324K
so,  = k(324)⁴ = 110.2 × 10^8 k
change in energy , ∆E = (110.2 - 81) × 10^8 k = 29.2 × 10^8k
percentage increases in energy = 29.2 × 10^8k/81 × 10^8k × 100
= (2920)/81
= 36.04 %
 
 

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