How much energy is required to melt and heat 25 grams of ice at 0ºC to 25ºC?
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To calculate the energy required to melt and heat a substance, you need to consider two steps: the energy required to melt the ice and the energy required to heat the resulting water to 25ºC.
1. Energy required to melt the ice:
The energy required to melt a substance is given by the formula: Q = m * ΔH_fusion, where Q is the heat energy, m is the mass, and ΔH_fusion is the specific heat of fusion for ice.
The specific heat of fusion for ice is 334 J/g. Therefore, the energy required to melt the ice is: Q = 25 g * 334 J/g = 8350 J.
2. Energy required to heat the water:
The energy required to heat a substance can be calculated using the formula: Q = m * c * ΔT, where Q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
The specific heat capacity of water is 4.18 J/(gºC). To increase the temperature from 0ºC to 25ºC, the change in temperature is 25ºC - 0ºC = 25ºC.
Therefore, the energy required to heat the water is: Q = 25 g * 4.18 J/(gºC) * 25ºC = 2612.5 J.
Finally, we add the energy required for both steps together:
Total energy required = Energy to melt the ice + Energy to heat the water = 8350 J + 2612.5 J = 10962.5 J.
So, approximately 10962.5 Joules of energy are required to melt and heat 25 grams of ice at 0ºC to 25ºC.