Answer:
To find the temperature of the body after 1 hour, we can use Newton's Law of Cooling, which is given by the formula:
\[ T(t) = T_a + (T_0 - T_a) \cdot e^{-kt} \]
Where:
- \( T(t) \) is the temperature at time \( t \),
- \( T_a \) is the ambient temperature (room temperature),
- \( T_0 \) is the initial temperature,
- \( k \) is the cooling constant,
- \( t \) is the time.
Given:
- \( T_a = 25^\circ C \) (ambient temperature),
- \( T_0 = 80^\circ C \) (initial temperature),
- \( T(30 \text{ minutes}) = 50^\circ C \) (temperature after 30 minutes).
We need to find \( k \) first. Using the information at \( t = 30 \) minutes:
\[ 50 = 25 + (80 - 25) \cdot e^{-30k} \]
Now, solve for \( k \). Once you find \( k \), you can use it to find the temperature after 1 hour (\( t = 60 \) minutes):
\[ T(60) = 25 + (80 - 25) \cdot e^{-60k} \]
This will give you the temperature of the body after 1 hour. Please note that the units of time need to be consistent, so if your initial time is in minutes, ensure all time values are in minutes.