The final equilibrium temperature of the mixture of lead, silver, and water is 24.65°C. The result is obtained by using the Black's Principle.
<h3>What is Black's Principle?</h3>
The Black's Principle states that heat released by a higher-temperature object is equal to the heat absorbed by a lower-temperature object. It can be expressed as
<em>Q release = Q absorbs</em>
Where
- Q release is the heat released by high-temperature objects.
- Q absorb is the heat absorbed by low-temperature objects.
The mass of lead is 125 g at 85°C, the mass of silver is 320 g at 34°C, and the mass of water is 0.5 kg at 22°C. All of them are mixed, so that the temperature of the lead and silver will fall and otherwise the temperature of water will rise.
The equation of the heat energy with the temperature change is
Q = m × c × ΔT
Where
- m = mass
- c = specific heat capacity
- ΔT = change in temperature
The data shows that:
- c lead = 128 J/kg °C
- c silver = 234 J/kg °C
- c water = 4,186 J/kg °C
The equilibrium temperature is
<em>Q release = Q absorbs</em>
(m × c × ΔT)lead + (m × c × ΔT)silver = (m × c × ΔT)water
(0.125 × 128 × (85-T)) + (0.320 × 234 × (34-T)) = (0.500 × 4,186 × (T-22))
(16 × (85-T)) + (74.88 × (34-T)) = (2,100 × (T-22))
1,360 - 16T + 2,545.92 - 74.88T = 46,200 - 2,100T
2,190.88T = 50,105.92
T = 24.65°C
Hence, the final equilibrium temperature of the mixture is 24.65°C.
Learn more about Black's Principle here:
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