A body cools down from $65^\circ$C to $60^\circ$C in minutes. It will cool down from $60^\circ$C to $55^\circ$C in

Question

KollegeApply · Accepted Answer

more than 5 minutes Let the temperature of the surrounding be T^circ CAverage temperature of the liquid in first case = 62.5^circ Average temperature difference from the surroundings = (62.5 - T )^circ C From newton law of cooling, $1^\circ$ C min-1 = -bA ( 62.5 - T )°C `$\Rightarrow$ -bA = 1/(62.5 - t) "min"^-1 ` ...... ( i ) For the second case, Average temperature = 57.$5^\circ$ C Temperature difference from the surroundings = ( 57.5 - 7 )° C From Newton's law of cooling and equation (i), `(5^circ C)/ t = -bA ( 57.5 - T )^circ C $\Rightarrow$ (5^circ C)/t = 1/(62.5 - t) (57.5 - T )^circ C $\Rightarrow$ t = (5 ( 62.5 - T ))/ ((57.5 -T )) $\Rightarrow$ t > 5 \text{minutes}`

AChoose Your Answer