Question 118: Properties of Matter

Question

A body takes 4 min. to cool from 61$$^\circ$$ C to 59$$^\circ$$ C. If the temperature of the surroundings is 30$$^\circ$$ C, the time taken by the body to cool from 51$$^\circ$$ C to 49$$^\circ$$ C is :

Accepted Answer

$${{\Delta T} \over {\Delta t}} = K({T_t} - {T_s})$$
T
t
= average temp.
T
= surrounding temp.
$${{61 - 59} \over 4} = K\left( {{{61 + 59} \over 2} - 30} \right)$$ ..... (1)
$${{51 - 49} \over t} = K\left( {{{51 + 49} \over 2} - 30} \right)$$ ..... (2)
Divide (1) & (2)
$${t \over 4} = {{60 - 30} \over {50 - 30}} = {{30} \over {20}}$$
So, t = 6 minutes.

Answer

4 min.

Answer

3 min.

Answer

8 min.

Answer

6 min.

Properties of Matter

A body takes 4 min. to cool from 61$^\circ C to 59^\circ C. If the temperature of the surroundings is 30^\circ C, the time taken by the body to cool from 51^\circ C to 49^\circ$ C is :

Choose the correct answer: