Final answer:
The final temperatures of a heated metal block and the water in which it is placed will be equal due to reaching thermal equilibrium. The heat lost by the metal block equals the heat gained by the water, assuming no heat is lost or gained by the environment or calorimeter.
Step-by-step explanation:
If a heated metal block is placed into a beaker of water, the relationship between the final temperatures of the water and the metal block is that they will reach thermal equilibrium. This means that the temperature of the metal block will decrease while the temperature of the water will increase until they both are at the same temperature. This scenario assumes ideal conditions with perfect heat transfer, where no heat is lost to the surroundings or gained from the calorimeter itself.
The principle governing this process is the conservation of energy. For the combined system of the metal and water, the total amount of heat lost by the metal is equal to the total amount of heat gained by the water (qmetal = -qwater). Here, 'q' represents the heat exchanged, which depends on the mass, specific heat, and change in temperature of each substance.
Using the formula q = mcΔT, where 'm' is mass, 'c' is specific heat capacity, and ΔT is the change in temperature, one can calculate the final temperature once mass and specific heat are known for both the metal block and the water.