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Answer :
The equilibrium temperature of the lead and the water is 20.5°C.
To find the equilibrium temperature, we can use the principle of conservation of energy. The heat lost by the lead is equal to the heat gained by the water.
The heat lost by the lead is given by:
Q = mcΔT
where m is the mass of the lead, c is the specific heat of lead, and ΔT is the change in temperature.
Substituting the given values, we get:
Q = 1 kg x 128 J/kg.K x (300°C - T)
The heat gained by the water is given by:
Q = mcΔT
where m is the mass of the water and c is the specific heat of water.
Substituting the given values, we get:
Q = 10 kg x 4.18 J/kg.K x (T - 20°C)
Setting the two equations equal to each other, we get:
128 J/kg.K x (300°C - T) = 10 kg x 4.18 J/kg.K x (T - 20°C)
Solving for T, we get:
T = 20.5°C
Therefore, the equilibrium temperature of the lead and the water is 20.5°C.
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