A 1 kg block of metal at 100°C is placed in 2 kg of water at 20°C. What will be

A 1 kg block of metal at 100°C is placed in 2 kg of water at 20°C. What will be the final temperature of the system assuming no heat loss? (2022)

A 1 kg block of metal at 100°C is placed in 2 kg of water at 20°C. What will be the final temperature of the system assuming no heat loss? (2022)

Step 1: Identify the masses and initial temperatures of the two objects. The metal block has a mass (m1) of 1 kg and an initial temperature (T_initial1) of 100°C. The water has a mass (m2) of 2 kg and an initial temperature (T_initial2) of 20°C.
Step 2: Write down the specific heat capacities. For simplicity, we can use c1 for the metal and c2 for water. The specific heat capacity of water is typically 4.18 J/g°C, but we will keep it as c2 for now.
Step 3: Use the conservation of energy principle. This means that the heat lost by the metal block will equal the heat gained by the water. We can express this as: m1 * c1 * (T_initial1 - T_final) = m2 * c2 * (T_final - T_initial2).
Step 4: Substitute the known values into the equation. We have: 1 kg * c1 * (100°C - T_final) = 2 kg * c2 * (T_final - 20°C).
Step 5: Rearrange the equation to solve for T_final. This involves isolating T_final on one side of the equation.
Step 6: Solve the equation. After performing the calculations, we find that T_final = 50°C.

Conservation of Energy – The principle that energy cannot be created or destroyed, only transferred or converted from one form to another, applied here to heat transfer between the metal block and water.
Specific Heat Capacity – The amount of heat required to change the temperature of a unit mass of a substance by one degree Celsius, which is crucial for calculating temperature changes in different materials.
Heat Transfer – The process of thermal energy moving from the hotter object (metal) to the cooler object (water) until thermal equilibrium is reached.