#### Question

A body cools down from 65°C to 60°C in minutes. It will cool down from 60°C to 55°C in

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.

#### 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}`