A body with a temperature of 143°C is immersed in a liquid that is kept constant temperature of 23°C. After 21 minutes, the temperature of the body decreased to 46°C. What will be the temperature of the body in °C after 44 minutes?

The problem you're describing is a classic example of Newton's Law of Cooling, which states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature (i.e., the temperature of its surroundings).

The formula for Newton's Law of Cooling is:

dT/dt = -k(T - Ts)

where:

• dT/dt is the rate of change of the body's temperature,
• T is the body's temperature at a given time,
• Ts is the surrounding temperature, and
• k is a constant that depends on the properties of the body and the surrounding medium.

In this case, we know that:

• The body's initial temperature (T0) is 143°C,
• The surrounding temperature (Ts) is 23°C,
• The body's temperature after 21 minutes (T21) is 46°C, and
• We want to find the body's temperature after 44 minutes (T44).

First, we need to find the value of k. We can rearrange the formula and integrate both sides to get:

ln|T - Ts| = -kt + C

where C is the constant of integration. We can find C by substituting T0 and t = 0 into the equation:

ln|T0 - Ts| = C ln|143 - 23| = C C = ln|120|

Next, we substitute T21 and t = 21 into the equation to find k:

ln|46 - 23| = -k21 + ln|120| ln|23| = -k21 + ln|120| k = (ln|120| - ln|23|) / 21

Now that we have k, we can find T44 by substitifying t = 44 into the equation:

ln|T44 - 23| = -k44 + ln|120| T44 = e^(-k44 + ln|120|) + 23

This will give us the temperature of the body after 44 minutes.