A liquid cools from `70^(@)C to 60^(@)C in 5 minutes. Calculate the time taken by the liquid to cool from `60^(@)C to 50^(@)C` , If the temperature of the surrounding is constant at `30^(@)C` .
Text Solution
AI Generated Solution
To solve the problem of how long it takes for a liquid to cool from 60°C to 50°C given that it cools from 70°C to 60°C in 5 minutes with a surrounding temperature of 30°C, we can use Newton's Law of Cooling. Here’s a step-by-step solution:
### Step 1: Calculate the average temperature during the first cooling phase
The liquid cools from 70°C to 60°C. The average temperature (θ₁) during this cooling phase can be calculated as:
\[
\theta_1 = \frac{70 + 60}{2} = 65°C
\]
...
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