A body cools from 80 °C to 50 °C in 5 minutes. Calculate the time it takes to cool from60 °C to 30°C. The temperature of the surroundings is 20 °C.

This problem can be solved 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 own temperature and the ambient temperature, provided the difference is small.

The formula for Newton's Law of Cooling is:

dT/dt = -k(T - Ts)

where:

• dT/dt is the rate of change of temperature,
• T is the temperature of the object,
• Ts is the temperature of the surroundings, and
• k is a constant.

First, we need to find the value of k. We know that the body cools from 80 °C to 50 °C in 5 minutes, and the temperature of the surroundings is 20 °C. We can use this information to form the equation:

-30/5 = -k(65 - 20)

Solving for k, we get:

k = 0.02 min^-1

Now we can use this value of k to find the time it takes for the body to cool from 60 °C to 30 °C. We form the equation:

-30/t = -0.02(45 - 20)

Solving for t, we get:

t = 15 minutes

So, it takes 15 minutes for the body to cool from 60 °C to 30 °C.