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Thermal energy is the energy that regulates a system's temperature. The term "heat" refers to the transfer of thermal energy. Thermodynamics is a branch of physics that analyses how heat is transferred across systems and how work is done in the process.

Aluminium has a specific heat of 0.4 J/g⁰ C, whereas water has a specific heat of 4.2J/g⁰ C, .

Heat is solely transferred between the water and the pan means no heat goes to the surrounding air.

Equate the sum of energy change in the water and the energy change in the metal pan to zero.

$螖E_{H2O}+螖E_{Al}=0$

Use the thermal energy equation, substitute these energy changes for the respective formulas.

$$\begin{gathered} (mC螖T{)}_{H2O}+(mC螖T{)}_{Al}=0 \\ (mC{)}_{H2O}\left(T_f-T_{i,H2O}\right)+(mC{)}_{Al}\left(T_f-T_{i,Al}\right)=0 \end{gathered}$$ where is the mass, is specific heat capacity and is the change in temperature.

Solve for the final temperature .

$T_f=\frac{{\left(mC{T}_i\right)}_{H2O}+{\left(mC{T}_i\right)}_{Al}}{{\left(mC\right)}_{H2O}+{\left(mC\right)}_{Al}}$

Substitute the values into the obtained formula and solve.

Therefore, it is assumed that the time elapsed is long enough for the water and pan to reach the same end temperature.