MHTCET 16 May 2024 Shift 1 Paper

Concept:Newton's law of cooling states that the rate of cooling is directly proportional to the mean temperature difference between the body and its surroundings.Explanation:For a small fall in temperature, the cooling rate is given by:$$\frac{\text{Fall in temperature}}{\text{Time}} \propto \left(\frac{\theta_1 + \theta_2}{2} - \theta_0\right)$$Here, $\theta_1$ and $\theta_2$ are the initial and final temperatures, and $\theta_0$ is the room temperature.In each interval, the fall is the same, i.e., $5^\circ C$.So, the time taken is inversely proportional to the mean temperature difference.Calculate the mean temperature for each interval:For $75^\circ C$ to $70^\circ C$: $\frac{75+70}{2} = 72.5^\circ C$For $70^\circ C$ to $65^\circ C$: $\frac{70+65}{2} = 67.5^\circ C$For $65^\circ C$ to $60^\circ C$: $\frac{65+60}{2} = 62.5^\circ C$The mean temperature decreases as $72.5 > 67.5 > 62.5$.Hence, the cooling rate is highest in the first interval and lowest in the last interval.Therefore, the time required increases as the water cools: $t_1 < t_2 < t_3$.Answer:$t_1 < t_2 < t_3$, which is option A.