A bowl filled with very hot soup cools from 98°C to 86°C in 2 minutes when the room temperature is 22°C. How long will it take to cool from 75°C to 69°C? [2023]

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Solution

Q.
A bowl filled with very hot soup cools from 98°C to 86°C in 2 minutes when the room temperature is 22°C. How long will it take to cool from 75°C to 69°C [2023]

1 2 minutes

2 1 minute

3 1.4 minutes

4 0.5 minute

Ans.
(3)

$\frac{θ_{2} - θ_{1}}{t} = k (\frac{θ_{1} + θ_{2}}{2} - θ_{0})$

$\frac{98 - 86}{2 min} = k (\frac{98 + 86}{2} - 22)$ ...(i)

$\frac{75 - 69}{t_{min}} = k [\frac{75 + 69}{2} - 22]$ ...(ii)

$Solving (i) and (ii), we get t = 1.4 min$

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