Answer :
Final answer:
The temperature of the body after 15 minutes can be calculated using Newton's Law of Cooling and the given information. The temperature difference between the body and the surroundings is 50°C. Using the formula T(t) = T_s + (T_0 - T_s) × e^(-kt), we can find that the temperature of the body after 15 minutes will be approximately 52.7°C. Hence the correct answer is option C
Explanation:
The temperature of the body after 15 minutes can be calculated using Newton's Law of Cooling, which states that the rate of change of temperature of an object is proportional to the difference between its temperature and the surrounding temperature. In this case, the temperature difference will be 70°C - 20°C = 50°C.
We can use the formula:
T(t) = T_s + (T_0 - T_s) × e^(-kt)
Where:
- T(t) is the temperature of the body at time t
- T_s is the surrounding temperature
- T_0 is the initial temperature of the body
- k is a constant that depends on the nature of the cooling process
- t is the time in minutes
Given that the body cools from 80°C to 70°C in 5 minutes, we can substitute these values into the equation and solve for k:
70 = 20 + (80 - 20) × e^(-5k)
Simplifying the equation, we get:
e^(-5k) = 0.5
Taking the natural logarithm of both sides:
-5k = ln(0.5)
Solving for k, we find:
k = -ln(0.5) / 5 = 0.1386
Now we can use this value of k to find the temperature of the body after 15 minutes:
T(15) = 20 + (80 - 20) × e^(-0.1386 * 15) = 52.7°C
Therefore, the temperature of the body after 15 minutes will be approximately 52.7°C.
Hence the correct answer is option C
