Question 330: Properties of Matter

Question

A body cools from a temperature 3T to 2T in 10 minutes. The room temperature is T. Assume that Newton's law of cooling is applicable. The temperature of the body at the end of next 10 minutes will be

Accepted Answer

According to NewtonÃ¢ÂÂs law of cooling,
$${{dT} \over {dt}} = K\left( {T - {T_s}} ight)$$
For two cases,
$${{d{T_1}} \over {dt}} = K\left( {{T_1} - {T_s}} ight)$$
and $${{d{T_2}} \over {dt}} = K\left( {{T_2} - {T_s}} ight)$$
Here, $${T_s} = T,{T_1} = {{3T + 2T} \over 2} = 2.5T$$
and $${{d{T_1}} \over {dt}} = {{3T - 2T} \over {10}} = {T \over {10}}$$
$${T_2} = {{2T + T'} \over 2}$$ and $${{d{T_2}} \over {dt}} = {{2T - T'} \over {10}}$$
So $${T \over {10}} = K\left( {2.5T - T} ight)$$   ...(i)
$${{2T - T'} \over {10}} = K\left( {{{2T + T'} \over 2} - T} ight)$$   ...(ii)
Dividing eqn. (i) by eqn. (ii), we get
$${T \over {2T - T'}} = {{\left( {2.5T - T} ight)} \over {\left( {{{2T + T'} \over 2} - T} ight)}}$$
$${{2T + T'} \over 2} - T = \left( {2T - T'} ight) 	imes {3 \over 2}$$
$$T' = 3\left( {2T - T'} ight) \Rightarrow 4T' = 6T$$
$$ 	herefore T' = {3 \over 2}T$$

Answer

$${7 \over 4}\,$$ T

Answer

$${3 \over 2}$$ T

Answer

$${4 \over 3}$$ T

Answer

T

Properties of Matter

A body cools from a temperature 3T to 2T in 10 minutes. The room temperature is T. Assume that Newton's law of cooling is applicable. The temperature of the body at the end of next 10 minutes will be

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