Question 786: Thermodynamics & KTG

Question

Compare the rate of loss of heat from a metal sphere at $$627^{\circ} \mathrm{C}$$ with the rate of loss of heat from the same sphere at $$327^{\circ} \mathrm{C}$$, if the temperature of the surrounding is $$27^{\circ} \mathrm{C}$$. (nearly)

Accepted Answer

The heat loss is given as $$\mathrm{R}=\operatorname{e} \sigma \mathrm{A}\left(\mathrm{T}^4-\mathrm{T}_0^4ight)$$
Let surrounding temperature be denoted as $$\mathrm{T}$$
Heat loss from the metal sphere at a temperature $$\mathrm{T}_1$$
$$\mathrm{R}_1=\operatorname{e\sigma A}\left(\mathrm{T}_1^4-\mathrm{T}_0^4ight)$$
Heat loss from the metal sphere at a temperature $$\mathrm{T}_2$$
$$\mathrm{R}_2=\operatorname{e} \sigma \mathrm{A}\left(\mathrm{T}_2^4-\mathrm{T}^4ight)$$
$$\begin{aligned}
	herefore \quad \frac{R_1}{R_2} & =\frac{T_1^4-T^4}{T_2^4-T^4}=\frac{900^4-300^4}{600^4-300^4} \
\frac{R_1}{R_2} & =5.3
\end{aligned}$$

Answer

6.2

Answer

5.3

Answer

4.8

Answer

7.4

Thermodynamics & KTG

Compare the rate of loss of heat from a metal sphere at $627^{\circ} \mathrm{C} with the rate of loss of heat from the same sphere at 327^{\circ} \mathrm{C}, if the temperature of the surrounding is 27^{\circ} \mathrm{C}$. (nearly)

Choose the correct answer: