Questions: A thermometer reads 6°C is brought into a room with a constant temperature of 23°C. If the thermometer heats 1/2 all the way for 5 minutes, what will read after that?

Solution Steps

We have a thermometer initially reading \(6^\circ \text{C}\) placed in a room with a constant temperature of \(23^\circ \text{C}\). The thermometer heats halfway towards the room temperature in 5 minutes. We need to find the thermometer's reading after 5 minutes.

The problem suggests that the thermometer's temperature changes according to an exponential model, where it moves halfway towards the ambient temperature in a given time period. This is a characteristic of Newton's Law of Cooling/Heating.

The initial temperature difference between the thermometer and the room is: \[ \Delta T_{\text{initial}} = 23^\circ \text{C} - 6^\circ \text{C} = 17^\circ \text{C} \]

After 5 minutes, the thermometer heats halfway, so the temperature difference is halved: \[ \Delta T_{\text{final}} = \frac{1}{2} \times 17^\circ \text{C} = 8.5^\circ \text{C} \]

The final temperature of the thermometer is the room temperature minus the final temperature difference: \[ T_{\text{final}} = 23^\circ \text{C} - 8.5^\circ \text{C} = 14.5^\circ \text{C} \]

Final Answer