A metallic sphere having radius 0-08 m and mass m -10 kg is heated to a temperature of 227- Cand suspended inside a box whose walls are at a temperature of 27- C- The maximum rate at which its temperature will fall is Take e -1- -5-8 - 10-8 W m -2 K -4 and specific heat of the metal S -90 cal - kg - k - J -4-2 J - cal A- 0-055- C - sB- 0-044- C - sC- 0-066- C - sD- 0-033- C - s

The correct option is C 0.066^∘ C/s P=e σ A(Δ T)^4=ms dT/dt ⇒dT/dt= e σ A(Δ T)^4/ms ...

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Standard XII

Physics

Stefan-Boltzman's Law

A metallic sp...

Question

A metallic sphere having radius 0.08m and mass m = 10 kg is heated to a temperature of $227^{\circ} C$ and suspended inside a box whose walls are at a temperature of $27^{\circ} C$ . The maximum rate at which its temperature will fall is Take $e = 1, σ = 5.8 \times 10^{- 8} W m^{- 2} K^{- 4}$ and specific heat of the metal $S = 90 c a l / k g / k; J = 4.2 J / c a l)$

${0.055}^{\circ} C / s$

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${0.044}^{\circ} C / s$

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${0.066}^{\circ} C / s$

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${0.033}^{\circ} C / s$

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Solution

The correct option is C
${0.066}^{\circ} C / s$

$P = e σ A (Δ T)^{4} = m s \frac{d T}{d t} \Rightarrow \frac{d T}{d t} = \frac{e σ A (Δ T)^{4}}{m s}$

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The correct option is C 0.066∘ C/s P=eσA(ΔT)4=msdTdt⇒dTdt=eσA(ΔT)4ms

The correct option is C
${0.066}^{\circ} C / s$

$P = e σ A (Δ T)^{4} = m s \frac{d T}{d t} \Rightarrow \frac{d T}{d t} = \frac{e σ A (Δ T)^{4}}{m s}$