91Ó°ÊÓ

The free energy principle defines how non-equilibrium steady-states are maintained in living and non-living systems by restricting their states to a minimal number. It establishes that systems minimise a free energy function of their internal states, implying hidden states in the environment.

Using the Energy Principle, determine the water's ultimate temperature. Subscriptis used to indicate the$300\mathrm{g}$ of water and subscript $2$to designate the water already in the glass ( $800\mathrm{g}$).

Take the sum of both the energies${\mathrm{Δ·¡}}_1\text{and}\mathrm{Δ}{\text{E}}_2$

$\begin{array}{l}{\mathrm{Δ·¡}}_1+{\mathrm{Δ·¡}}_2=0\\ {\mathrm{m}}_1{\mathrm{C}}_{\mathrm{H}20}({\mathrm{T}}_{\mathrm{f}}−{\mathrm{T}}_{1,\mathrm{i}})+{\mathrm{m}}_2{\mathrm{C}}_{\mathrm{H}20}({\mathrm{T}}_{\mathrm{f}}−{\mathrm{T}}_{2,\mathrm{i}})=0\end{array}$

Here Solve the equation for ${\mathrm{T}}_{\mathrm{f}}$.

$\begin{array}{c}{\mathrm{T}}_{\mathrm{f}}=\frac{{\mathrm{m}}_1{\mathrm{T}}_{1,\mathrm{i}}+{\mathrm{m}}_2{\mathrm{T}}_{2,\mathrm{i}}}{{\mathrm{m}}_1+{\mathrm{m}}_2}\\ =\frac{(300\mathrm{g})\left({25}^{°}\mathrm{C}\right)+(800\mathrm{g})\left({20}^{°}\mathrm{C}\right)}{300\mathrm{g}+800\mathrm{g}}\\ ={21.36}^{°}\mathrm{C}\end{array}$

The following assumptions had to be made in order to calculate the final temperature:

• As the glass is so thin, heat transmission between water and the glass is minimal.
• No heat is sent to the environment.
• Enough time has passed for the ultimate temperature to be attained.

Therefore, the final temperature of the water is$21.36°\mathrm{C}$ and the assumption made is heat transfer only occurs between the two masses of water.