Q140 / 160 · TS EAMCET 2005 · Physics

Two identical bodies have temperatures $277^{\circ} \mathrm{C}$ and $67^{\circ} \mathrm{C}$. If the surroundings temperature is $27^{\circ} \mathrm{C}$, the ratio of loss of heats of the two bodies during the same interval of time is (approximately)

  • A
    4:1
  • B
    8:1
  • C
    12:1
  • Correct answer
    D
    19:1

Solution

$\begin{aligned} & T_1=277^{\circ}=277+273=550 \mathrm{~K} \\ & T_2=67^{\circ} \mathrm{C}=67+273=340 \mathrm{~K} \end{aligned}$ Temperature of surrounding, $T=27^{\circ} \mathrm{C}=27+273=300 \mathrm{~K}$ $\begin{aligned} \text { Ratio of loss of heat } & =\frac{T_1^4-T^4}{T_2^4-T^4} \\ & =\frac{\left(\frac{T_1}{T_2}\right)^4-1}{\left(\frac{T_2}{T_1}\right)^4-1}=\frac{\left(\frac{550}{300}\right)^4-1}{\left(\frac{340}{300}\right)^4-1} \\ & =\frac{9.5}{0.5}=\frac{19}{1} \end{aligned}$

Hence, the correct answer is option: 'D'.

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