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Question
A body cools down from 65°C to 60°C in minutes. It will cool down from 60°C to 55°C in
Options
5 minutes
less than 5 minutes
more than 5 minutes
less than or more than 5 minutes depending on whether its mass is more than or less than 1 kg.
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Solution
more than 5 minutes
Let the temperature of the surrounding be `T^circ C`Average 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° C min-1 = -bA ( 62.5 - T )°C
`⇒ -bA = 1/(62.5 - t) "min"^-1 ` ...... ( i )
For the second case,
Average temperature = 57.5° 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`
`⇒ (5^circ C)/t = 1/(62.5 - t) (57.5 - T )^circ C`
`⇒ t = (5 ( 62.5 - T ))/ ((57.5 -T ))`
`⇒ t > 5 \text{minutes}`
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