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Entropy can be defined as the measure of a system’s thermal energy per unit temperature that is unavailable for doing useful work. It is also the measure of randomness of system.

Formula of change in entropy

$∆\mathrm{S}=\frac{\mathrm{Q}}{\mathrm{T}}$

Where, $∆\mathrm{S}$ is the change in entropy of gas, $\mathrm{Q}$is the heat gain by the gas and $\mathrm{T}$is the temperature of gas.

For the body, there are two sides with different heat and temperature .So, the total change in the entropy of system is sum of change in entropy of both inner and outer side of body.

So,

$$\begin{gathered} ∆\mathrm{S}=∆\mathrm{S}\left(\mathrm{Hotside}\right)+∆\mathrm{S}\left(\mathrm{Coldside}\right) \\ ∆\mathrm{S}=\frac{{\mathrm{Q}}_{\mathrm{H}}}{{\mathrm{T}}_{\mathrm{H}}}+\frac{{\mathrm{Q}}_{\mathrm{C}}}{{\mathrm{T}}_{\mathrm{C}}} \end{gathered}$$

Using relation

$∆\mathrm{S}=\frac{{\mathrm{Q}}_{\mathrm{H}}}{{\mathrm{T}}_{\mathrm{H}}}+\frac{{\mathrm{Q}}_{\mathrm{C}}}{{\mathrm{T}}_{\mathrm{C}}}$

Now, putting the values of constants in above equation and multiply it by $0.250\mathrm{g}$

$$\begin{gathered} ∆\mathrm{S}=2.50\mathrm{g}\left(\frac{3.12×{10}^4\mathrm{J}/\mathrm{g}}{310.0\mathrm{K}}+\frac{-3.12×{10}^4\mathrm{J}/\mathrm{g}}{303.0\mathrm{K}}\right) \\ ∆\mathrm{S}=-5.80\mathrm{J}/\mathrm{K} \end{gathered}$$

Thus, The total change in entropy of body is $-5.80\mathrm{J}/\mathrm{K}$