Question 176: Properties of Matter

Question

A body takes 10 minutes to cool from 60oC to 50oC. The tempertature of surroundings is constant at 25oC. Then, the temperature of the body after next 10 minutes will be approximately :

Accepted Answer

Time taken to cool from 60$$^\circ$$C to 50$$^\circ$$C = 10 minutes
Temperature of surroundings = 25$$^\circ$$C
Temperature of body in next 10 minutes = T
Therefore, $${{60 - 50} \over {10\,\min }} = {k_B}\left[ {{{60 + 50} \over 2} - 25} \right] \Rightarrow {k_B}30 = 1$$ ...... (1)
and $${{60 - T} \over {20\,\min }} = {k_B}\left[ {{{60 + T} \over 2} - 25} \right] = {k_B}\left[ {{{60 + T - 50} \over 2}} \right]$$ ..... (2)
Taking ratio of Eqs. (1) and (2), we get
$${{20} \over {60 - T}} = {{30{k_B}} \over {{k_B}\left( {{{10 + T} \over 2}} \right)}} \Rightarrow {{20} \over {60 - T}} = {{30} \over {5 + T/2}}$$
$$ \Rightarrow 20\left( {5 + {T \over 2}} \right) = 30(60 - T) \Rightarrow 100 + T10 = 1800 - 30T$$
$$ \Rightarrow 1800 - 100 = 30T + 10T$$
$$ \Rightarrow 1700 = 40T \Rightarrow T = {{1700} \over {40}} = 42.5^\circ C \sim 43^\circ C$$

Answer

47oC

Answer

41oC

Answer

45oC

Answer

43oC

Properties of Matter

A body takes 10 minutes to cool from 60oC to 50oC. The tempertature of surroundings is constant at 25oC. Then, the temperature of the body after next 10 minutes will be approximately :

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