Final answer:
The precise time for oil to cool from 50°C to 40°C cannot be determined without additional information. A detailed cooling model or empirical data is needed to apply Newton's Law of Cooling and solve the problem using a calorimetry equation.
Step-by-step explanation:
The time taken for a cup of oil to cool from 50°C to 40°C cannot be precisely calculated without knowing the specific cooling conditions, such as the material properties or the shape of the container. In physics, this is often approached by applying Newton's Law of Cooling, which states that the rate of heat loss of a body is directly proportional to the difference in the temperatures between the body and its surroundings. As per this law, the cooling curve is non-linear, meaning that if it took the oil 6 minutes to cool from 70°C to 50°C, it does not necessarily follow that it will take another 6 minutes to cool from 50°C to 40°C, especially since the surrounding temperature (Ts = 25°C) is closer to the final temperature.
Generally, as the temperature difference between the object and its surroundings decreases, the rate of cooling slows down. However, without additional information or a specific cooling rate constant determined from empirical data or exact conditions of the oil's cooling environment, we cannot calculate the precise time required for the oil to reach 40°C from 50°C. To solve such a problem, typically a calorimetry equation is used or a detailed cooling model taking into account the thermal properties of the oil and its environment is developed.