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80g of water at 30° C are poured on a large block of ice at 0°C. The mass of ice that melts is
To solve this problem, we need to use the principle of conservation of energy. The heat lost by the warm water will be used to melt the ice. The formula to calculate the heat required to melt the ice is: Q = m ⋅ Lբ Where: - Q is the heat lost by the water (in calories), - m is the mass of the ice meRead more
To solve this problem, we need to use the principle of conservation of energy. The heat lost by the warm water will be used to melt the ice.
The formula to calculate the heat required to melt the ice is:
Q = m ⋅ Lբ
Where:
– Q is the heat lost by the water (in calories),
– m is the mass of the ice melted,
– Lբ is the latent heat of fusion of ice (which is 80 cal/g).
The heat gained by the ice is:
Q = m_w ⋅ c_w ⋅ ΔT
Where:
– mᵥᵥ is the mass of water,
– cᵥᵥ is the specific heat capacity of water (which is 1 cal/g°C),
– ΔT is the temperature change of the water (in this case, from 30°C to 0°C, so ΔT = 30°C).
Now, we can calculate the heat gained by the ice:
Q = 80 g ⋅ 1 cal/g°C ⋅ 30°C = 2400 cal
Now, we can find the mass of the ice that melts using the equation for heat required to melt the ice:
2400 cal = m ⋅ 80 cal/g
m = 2400 / 80 = 30 g
Thus, the mass of ice that melts is 30 g.
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