Answer:
The equilibrium temperature of the system is 276.494 Kelvin.
Explanation:
Let consider the system formed by the sample of aluminium and water as a control mass, in which the sample is cooled and water is heated until thermal equilibrium is reached. The energy process is represented by First Law of Thermodynamics:
Where:
- Heat received by water, measured in joules.
- Heat released by the sample of aluminium, measured in joules.
Given that no mass is evaporated, the previous expression is expanded to:
Where:
,
- Mass of water and the sample of aluminium, measured in kilograms.
,
- Specific heats of the sample of aluminium and water, measured in joules per kilogram-Kelvin.
,
- Initial temperatures of the sample of aluminium and water, measured in Kelvin.
- Temperature which system reaches thermal equilibrium, measured in Kelvin.
The final temperature is now cleared:
Given that ,
,
,
,
and
, the final temperature of the system is:
The equilibrium temperature of the system is 276.494 Kelvin.
