A body cools in 7 minutes from 60°C to 40°C. The temperature of the surrounding is 10°C. The temperature of the body after the next 7 minutes will be:

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.

Given:

• Initial temperature, T1 = 60°C
• Temperature after 7 minutes, T2 = 40°C
• Surrounding temperature, Ts = 10°C
• Time, t = 7 minutes

We need to find the temperature of the body after the next 7 minutes.

First, we need to find the value of k. We can rearrange the formula to solve for k:

k = -1/t * ln((T2 - Ts) / (T1 - Ts))

Substituting the given values:

k = -1/7 * ln((40 - 10) / (60 - 10)) k = -1/7 * ln(30 / 50) k = -1/7 * ln(0.6) k ≈ 0.079

Next, we use this value of k to find the temperature of the body after the next 7 minutes. We rearrange the formula to solve for T:

T = Ts + (T2 - Ts) * e^(-k*t)

Substituting the given values:

T = 10 + (40 - 10) * e^(-0.079*7) T = 10 + 30 * e^(-0.553) T ≈ 10 + 30 * 0.575 T ≈ 27.25°C

So, the temperature of the body after the next 7 minutes will be approximately 27.25°C.