How much heat is needed to melt 1.43 grams of ice into water from -5.34 to 84.3 c?

1 Answer
Apr 25, 2018



We need to find three heat values; the heat to raise the ice to melting point, the heat to melt the ice into water, and the heat to raise the temperature of the water to 84.3°C. Thus, we need three equations.

#q = mcDeltaT# is what we will use, with #q_1# as the heat needed to raise the ice's temperature, #q_2# as the heat to melt it, and #q_3# as the heat to raise the water's temperature.

Note: The Specific Heat Capacity (c) for liquid water is 4.18J; for ice, 2.10J

Firstly, we need to raise the ice's temperature from -5.34°C to 0°C.

#q_1 = 1.43cancelg * "2.10J"/cancel"g°C" * 5.34cancel"°C" = 16.0J#

Secondly, find the energy needed to melt the ice. For this equation we must find the #DeltaH_"fus"#, or the energy required to melt ice, which is 334J/g of ice.
#q_2 = DeltaH_"fus" = 1.43cancelg * "334J"/cancelg = 478J#

Lastly, find the energy needed to raise the water to 84.3°C.

#q_3 = 1.43cancelg * "4.18J"/cancel"g°C" * 84.3cancel"°C" = 504J#

Now that we have all three values, add them to find the total energy required.

#16.0J + 478J + 504J = 998J#