Question
Two bodies A and B at temperatures 327°C and 127°C respectively are placed in an evacuated enclosure maintained at a temperature of 27°C. Compare their rates of cooling.
✓
Answer
Here. $\text{T}_1=327^\circ\text{C}= 327+273=600\text{K}$
$\text{T}_2=127^\circ\text{C}=127+273=400\text{ K}$
$\text{T}_0= 27^\circ\text{C}=27+273=300\text{ K}$
$\frac{\text{E}_1}{\text{E}_2}= \frac{\sigma(\text{T}_{1}^4-\text{T}_{0})}{\sigma(\text{T}_{2}^{4}-\text{T}_1^4)}=\frac{(600)^4-(300)^4}{(400)^4-(300)^4}$
$=\frac{10^8[6^4-3^4]}{10^8[4^4-3^4]}$
$= \frac{1296-81}{256-81} $
$=\frac{1215}{175}= 6.94$
$\text{T}_2=127^\circ\text{C}=127+273=400\text{ K}$
$\text{T}_0= 27^\circ\text{C}=27+273=300\text{ K}$
$\frac{\text{E}_1}{\text{E}_2}= \frac{\sigma(\text{T}_{1}^4-\text{T}_{0})}{\sigma(\text{T}_{2}^{4}-\text{T}_1^4)}=\frac{(600)^4-(300)^4}{(400)^4-(300)^4}$
$=\frac{10^8[6^4-3^4]}{10^8[4^4-3^4]}$
$= \frac{1296-81}{256-81} $
$=\frac{1215}{175}= 6.94$
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