The temperature of a body in air falls from 40°C to 24°C in 4 minute. The temperature of the air is 16°C. The temperature of the body in the next 4 minutes will be [2025]

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Solution

Q.
The temperature of a body in air falls from 40°C to 24°C in 4 minute. The temperature of the air is 16°C. The temperature of the body in the next 4 minutes will be [2025]

1 14/3°C

2 28/3°C

3 56/3°C

4 42/3°C

Ans.
(3)

$\frac{T_{2} - T_{1}}{t} = K [T_{avg} - T_{s}]$

   $T_{1} = 24 ° C; T_{2} = 40 ° C; t = 4, T_{s} = 16 ° C$

$\frac{40 - 24}{4} = K [32 - 16]$

   $K = \frac{4}{16} = \frac{1}{4}$

Now $\frac{24 - T}{4} = K [\frac{T + 24}{2} - 16]$

   $24 - T = \frac{T - 8}{2}$

   $\frac{3 T}{2} = 28 \Rightarrow T = \frac{56}{3} ° C^{}$

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