The final stabilized temperature will be between 0 °C and 50 °C.
The enthalpy of fusion of ice is 334 J/g. The specific heat of water is 4.2 J/g.
To cool 100 g of water from 100 °C to 0 °C would require the removal of
4.2 x 100 x 100 = 42000 J.
To melt the ice would require the addition of
334 x 100 = 33400 J
∴ 42000 > 33400 thus you can melt all the ice and have some heat to spare, specifically 42000 - 33400 = 8600 J
Now use this to warm up 100+100 = 200 g of water at 0 °C
The final stabilized temperature;
8600 / (200 x 4.2) = 10.23 °C
Therefore, the final stabilized temperature is 10.23 °C
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