**Introduction**

The temperature change of an isolated body can be explained using the concept of heat transfer and the specific heat capacity of the material. When a body undergoes a temperature change, it gains or loses heat energy depending on the direction of the change. This heat energy transfer can be quantified using the specific heat capacity, which is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius.

**Heat Transfer**

Heat transfer occurs in three main ways: conduction, convection, and radiation. In an isolated body, heat transfer is primarily through conduction as there is no medium for convection and radiation is usually negligible.

**Conduction**

Conduction is the transfer of heat energy through direct contact between molecules. In an isolated body, the heat energy flows from regions of higher temperature to regions of lower temperature. The rate of heat conduction can be expressed by Fourier's Law of Heat Conduction:

Q = -kA(dt/dx)

Where Q is the heat transfer rate, k is the thermal conductivity of the material, A is the cross-sectional area of heat flow, and (dt/dx) is the temperature gradient.

**Specific Heat Capacity**

The specific heat capacity (C) of a substance is the amount of heat energy required to raise the temperature of a unit mass of the substance by one degree Celsius. It is a property that depends on the nature of the material.

**Temperature Change**

When an isolated body of mass m undergoes a temperature change from T1 to T2 over a time period t, the heat transfer can be determined using the equation:

Q = mC(T2 - T1)

Where Q is the heat energy transferred, m is the mass of the body, C is the specific heat capacity, and (T2 - T1) is the temperature change.

**Example**

Let's consider an example to illustrate this concept. Suppose we have a block of copper with a mass of 100 grams (m = 100 g) and a specific heat capacity of 0.39 J/g°C (C = 0.39 J/g°C). If the initial temperature of the copper block is 100°C (T1 = 100°C) and it cools down to 50°C (T2 = 50°C) over a period of 10 minutes (t = 10 min), we can calculate the heat energy transferred.

Q = (100 g)(0.39 J/g°C)(50°C - 100°C)
Q = -1950 J

Therefore, the heat energy transferred during the temperature change is -1950 Joules. The negative sign indicates that the heat is leaving the body, causing the temperature to decrease.

**Conclusion**

In conclusion, the temperature change of an isolated body of mass m can be explained by the transfer of heat energy. The specific heat capacity of the material determines the amount of heat required to raise or lower the temperature of the body. Through conduction, heat energy flows from regions of higher temperature to regions of lower temperature. By applying the equation Q = mC(T2 - T1), we can calculate the heat energy transferred during the temperature change.

MC(T2-T1)