A) \[25\ s\]
B) \[50\ s\]
C) \[200\ s\]
D) \[400\ s\]
Correct Answer: C
Solution :
Rate of cooling \[\frac{\Delta \theta }{t}=\frac{A\varepsilon \sigma ({{T}^{4}}-T_{0}^{4})}{mc}\] Þ \[t\propto \frac{m}{A}\] \[[\because \ \ \Delta \theta ,\ t,\ \sigma ,\ \ ({{T}^{4}}-T_{0}^{4})\ \text{are}\ \text{constant}]\] Þ \[t\propto \frac{m}{A}\propto \frac{\text{Volume}}{\text{Area}}\propto \frac{{{a}^{3}}}{{{a}^{2}}}\] Þ\[t\propto a\] Þ \[\frac{{{t}_{1}}}{{{t}_{2}}}=\frac{{{a}_{1}}}{{{a}_{2}}}\] Þ \[\frac{100}{{{t}_{2}}}=\frac{1}{2}\] Þ\[{{t}_{2}}=200sec.\]
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