Question:
A body cools down from \(75^\circ\text{C}\) to \(65^\circ\text{C}\) in \(10\) minutes. It will cool down from \(65^\circ\text{C}\) to \(55^\circ\text{C}\) in a time:
A body cools down from \(75^\circ\text{C}\) to \(65^\circ\text{C}\) in \(10\) minutes. It will cool down from \(65^\circ\text{C}\) to \(55^\circ\text{C}\) in a time:
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According to Newton’s law of cooling, cooling is faster when the temperature difference between the body and surroundings is larger.
Updated On: Jun 24, 2026
- \(10\) minutes
- Less than \(10\) minutes
- More than \(10\) minutes
- Less than or more than \(10\) minutes depending on its mass
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The Correct Option is C
Solution and Explanation
Step 1: Recall Newton’s law of cooling.
According to Newton’s law of cooling, \[ \frac{dT}{dt}\propto (T-T_s) \] where \[ T_s \] is the surrounding temperature.
Thus, the rate of cooling depends on the temperature difference between the body and surroundings.
Step 2: Analyze the first cooling interval.
Initially, the body cools from \[ 75^\circ\text{C} \text{ to } 65^\circ\text{C} \] During this interval, the temperature excess above surroundings is relatively large. Therefore, cooling is faster.
Step 3: Analyze the second cooling interval.
Next, the body cools from \[ 65^\circ\text{C} \text{ to } 55^\circ\text{C} \] Now the temperature difference between the body and surroundings becomes smaller. Hence, the rate of cooling decreases.
Step 4: Compare the cooling times.
Since cooling becomes slower at lower temperatures, the body takes more time to lose the same temperature difference of \[ 10^\circ\text{C} \] Therefore, the time required from \[ 65^\circ\text{C} \text{ to } 55^\circ\text{C} \] will be greater than \(10\) minutes.
Step 5: Final conclusion.
Hence, the required time is \[ \boxed{\text{More than }10\text{ minutes}} \]
According to Newton’s law of cooling, \[ \frac{dT}{dt}\propto (T-T_s) \] where \[ T_s \] is the surrounding temperature.
Thus, the rate of cooling depends on the temperature difference between the body and surroundings.
Step 2: Analyze the first cooling interval.
Initially, the body cools from \[ 75^\circ\text{C} \text{ to } 65^\circ\text{C} \] During this interval, the temperature excess above surroundings is relatively large. Therefore, cooling is faster.
Step 3: Analyze the second cooling interval.
Next, the body cools from \[ 65^\circ\text{C} \text{ to } 55^\circ\text{C} \] Now the temperature difference between the body and surroundings becomes smaller. Hence, the rate of cooling decreases.
Step 4: Compare the cooling times.
Since cooling becomes slower at lower temperatures, the body takes more time to lose the same temperature difference of \[ 10^\circ\text{C} \] Therefore, the time required from \[ 65^\circ\text{C} \text{ to } 55^\circ\text{C} \] will be greater than \(10\) minutes.
Step 5: Final conclusion.
Hence, the required time is \[ \boxed{\text{More than }10\text{ minutes}} \]
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