Final answer:
To calculate the time it takes for the temperature of an object to change from one value to another, we can use Newton's Law of Cooling.
Step-by-step explanation:
To calculate the time it takes for the temperature of an object to change from one value to another, we can use Newton's Law of Cooling. This law states that the rate of change of temperature is proportional to the difference between the current temperature and the surrounding temperature. The equation for Newton's Law of Cooling is:
T(t) = T0 + (T1 - T0) * exp(-kt)
Where T(t) is the temperature at time t, T0 is the initial temperature, T1 is the final temperature, k is the cooling rate constant, and exp() is the exponential function.
In this case, the initial temperature is 140F and the final temperature is 70F. We need to find the time it takes for the temperature to change from 140F to 70F.
Let's assume that the cooling rate constant, k, is a constant value. We can rearrange the equation to solve for t:
t = (ln((T1 - T0) / (T(t) - T0))) / k
Substituting the values, we get:
t = (ln((70 - 140) / (70 - T(t)))) / k
Since we don't have the value of the cooling rate constant, we cannot calculate the exact time it takes for the temperature to change. We would need additional information about the specific cooling rate constant or the time it takes for the temperature to change by a certain rate.