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Thermal Properties Of Matter

Question

A metal rod at a temperature of 145°C, radiates energy at a rate of 17W. If its temperature is increased to 273°C, then it will radiate at the rate of

49.6 W

17.5 W

50.3 W

67.5 W

Solution

49.6 W

Given, initial temperature of metal rod (T)= 145° C = 418 K

Rate of radiated energy (E₁) = 17W

Final temperature ( T₂) = 273^o C

= 273 + 273

= 546 k

We know, from the Stefan's law,

E ∝ T⁴

$\frac{E_{1}}{E_{2}} = {(\frac{T_{1}}{T_{2}})}^{4}$

= ${(\frac{418}{546})}^{4}$

$\frac{E_{1}}{E_{2}}$ = 0.343

Therefore, final radiated energy

E₂ = $\frac{E_{1}}{0.343}$

= $\frac{17}{0.343}$

E₂ = 49.6 W