Question 155: Properties of Matter

Question

A metallic sphere cools from 50
o
C to 40
o
in 300 s. If atmospheric temperature around is 20
o
C,
then the sphere’s temperature after the next 5 minutes will be close to :

Accepted Answer

$${{\Delta T} \over {\Delta t}} = k\left( {{{{T_f} + {T_i}} \over 2} - {T_0}} ight)$$
$$ \Rightarrow $$ $${{50 - 40} \over {300}} = k\left( {{{90} \over 2} - 20} ight)$$
$$ \Rightarrow $$ $${{40 - T} \over {300}} = k\left( {{{40 + T} \over 2} - 20} ight)$$
$$ \Rightarrow $$ $${{10} \over {40 - T}} = {{25 	imes 2} \over {40 + T - 40}}$$
$$ \Rightarrow $$ $${1 \over {40 - T}} = {5 \over T}$$
$$ \Rightarrow $$ $$T = 200 - 5T$$
$$ \Rightarrow $$ $$6T = 200$$
$$ \Rightarrow $$ $$T = 33^\circ C$$

Answer

35
o
C

Answer

31
o
C

Answer

33
o
C

Answer

28
o
C

Properties of Matter

A metallic sphere cools from 50 o C to 40 o in 300 s. If atmospheric temperature around is 20 o C, then the sphere’s temperature after the next 5 minutes will be close to :

Choose the correct answer: