NEET-XII-Physics
28: Heat Transfer
- #10A body cools down from 65°C to 60°C in minutes. It will cool down from 60°C to 55°C in
(a) 5 minutes
(b) less than 5 minutes
(c) more than 5 minutes
(d) less than or more than 5 minutes depending on whether its mass is more than or less than 1 kg.digAnsr: cAns : (c) more than 5 minutes
Let the temperature of the surrounding be T`` °\,\mathrm{\,C\,}``.
Average temperature of the liquid in first case = 62.5`` °\,\mathrm{\,C\,}``
Average temperature difference from the surroundings = (62.5 `` -`` T)`` °\,\mathrm{\,C\,}``
From newton law of cooling,
`` {1}^{°}\,\mathrm{\,C\,}\,\mathrm{\,min\,}{}^{-1}=-bA(62.5-T{)}^{°}\,\mathrm{\,C\,}``
`` \Rightarrow -bA=\frac{1}{62.5-T}{\,\mathrm{\,min\,}}^{-1}...\left(\,\mathrm{\,i\,}\right)``
For the second case,
Average temperature = 57.5`` °\,\mathrm{\,C\,}``
Temperature difference from the surroundings = (57.5 `` -`` T)`` °\,\mathrm{\,C\,}``
From Newton's law of cooling and equation (i),
`` \frac{{5}^{°}\,\mathrm{\,C\,}}{t}=-bA(57.5-T{)}^{°}\,\mathrm{\,C\,}``
`` \Rightarrow \frac{{5}^{°}\,\mathrm{\,C\,}}{t}=\frac{1}{62.5-T}(57.5-T{)}^{°}\,\mathrm{\,C\,}``
`` \Rightarrow t=\frac{5(62.5-T)}{(57.5-T)}``
`` \Rightarrow t>5\,\mathrm{\,minutes\,}``
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