Question 192: Properties of Matter

Question

A body takes 10 minutes to cool from 60
o
C to 50
o
C. The tempertature of surroundings is constant at 25
o
C. 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

47
o
C

Answer

41
o
C

Answer

45
o
C

Answer

43
o
C

Properties of Matter

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

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