The final temperature of the water when thermal equilibrium is reached is approximately 24.36°C.
What is the final temperature of the water?The principle of conservation of energy which states that the heat lost by the metal cubes must be equal to the heat gained by the water is used to determine the final temperature of the water.
The formula to calculate the heat lost by a metal cube is:
Q = m × c × ΔT
where;
Q is the heat lost,m is the mass of the cube,c is the specific heat capacity of the metal, and ΔT is the change in temperature of the metal.For the silver cube:
m = density × volume
m = 10.49 g/cm³ × (2.31 cm)³
m = 58.48 g
c = 0.235 J/g°C (specific heat capacity of silver)
ΔT = (82.2°C - 19.6°C)
ΔT = 62.6°C
Q = 58.48 g × 0.235 J/g°C × 62.6°C
Q = 877.4 J
For the gold cube:
m = density × volume
m = 19.32 g/cm³ × (2.78 cm)³
m = 170.5 g
c = 0.129 J/g°C (specific heat capacity of gold)
ΔT = (82.2°C - 19.6°C)
ΔT = 62.6°C
Q = 170.5 g × 0.129 J/g°C × 62.6°C = 1354.4 J
The total heat lost by both cubes is:
Qtotal = 877.4 J + 1354.4 J
Qtotal= 2231.8 J
To calculate the final temperature of the water, we can use the formula:
Q = mwater × cwater × ΔT
where;
mwater is the mass of water,cwater is the specific heat capacity of water, and ΔT is the change in temperature of the water.Solving for ΔT:
ΔT = Qtotal / (mwater × cwater)
ΔT = 2231.8 J / (113.0 g × 4.184 J/g°C)
ΔT = 4.76°C
Final temperature = 19.6°C + 4.76°C
Final temperature= 24.36°C
Learn more about specific heat capacity at: https://brainly.com/question/21406849
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