High School

A 38.1 g sample of copper at 99.8°C is dropped into a beaker containing 205 g of water at 18.5°C. Assume no heat is lost to the environment. If the heat capacities of water and copper are 4.184 J/g°C and 0.385 J/g°C, respectively, what is the final temperature of the water and copper when thermal equilibrium is reached?

Answer :

The final temperature can be calculated using the conservation of energy formula. Solving the equation yields a final temperature of approximately 21.9°C.

After simplification, the equation becomes:

14.6763T_final - 1414.0294 = -864.22T_final + 16106.54

Combining like terms, we get:

878.8963T_final = 17520.5694

Dividing both sides by 878.8963, we get:

T_final = 19.925°C

Therefore, the final temperature of the water and copper when thermal equilibrium is reached is approximately 19.925°C.

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