Final answer:
The heat required to convert 175 g of ice at -1°C to water at 1°C includes the heat to warm the ice to 0°C, the heat to melt the ice, and the heat to warm the water to 1°C using the specific heats and latent heat of fusion.
Step-by-step explanation:
To calculate the heat required to convert 175 g of ice at -1°C to water at 1°C, the problem is broken into two parts: heating the ice to 0°C and melting the ice to water at 0°C. Finally, heating the resultant water from 0°C to 1°C. To heat the ice from -1°C to 0°C, we use the specific heat of ice. To melt the ice at 0°C, we use the latent heat of fusion for water. The specific heat of ice is approximately 2.09 J/g°C and the latent heat of fusion for water is 334 J/g.
Firstly, to warm the ice to its melting point, the heat required (Q1) is Q1 = m * Cice * ΔT, where m = 175 g, Cice is the specific heat of ice, and ΔT is the temperature change.
Secondly, to melt the ice at 0°C, the heat required (Q2) is Q2 = m * Lf, where Lf is the latent heat of fusion.
To heat the resultant water from 0°C to 1°C, the heat required (Q3) is Q3 = m * Cwater * ΔT, where Cwater is the specific heat of water (4.184 J/g°C) and ΔT is the temperature change. Summing these three amounts of heat gives us the total heat required to achieve the desired change.