Heat of Fusion and Phase Change . What will be the final temperature if we add 1000. cal of heat to 10.0 g of ice at 0°C?

Question

Strategy : The first thing the added heat does is to melt the ice. So we must first determine if 1000 cal is sufficient to melt the ice completely. If less than 1000. cal is required to melt the ice to liquid water, then the remaining heat will serve to raise the temperature of the liquid water. The specific heat (SH; Section 1.9) of liquid water is 1.00 cal/g ∙ °C (Table 1.4)

Substance	Specific Heat (cal/g · °C)	Substance	Specific Heat (cal/g · °C)
Water	1	Wood (typical)	0.42
Ice	0.48	Glass (typical)	0.22
Steam	0.48	Rock (typical)	0.2
Iron	0.11	Ethanol	0.59
Aluminum	0.22	Methanol	0.61
Copper	0.092	Ether	0.56
Lead	0.038	Carbon tetrachloride	0.21

Accepted Answer

Step 1: This phase change will use [latex] 10.0 imes 80. cal/g = 8.0 imes 10^2 cal [/latex], which leaves [latex]2.0 imes 10^2[/latex] cal to raise the temperature of the liquid water.

Step 2: The temperature of the liquid water is now raised by the remaining heat. The relationship between specific heat, mass, and temperature change is given by the following equation (Section 1.9):

[latex]Amount of heat = SH imes m imes (T_{2} - T_{1} )[/latex]

Solving this equation for [latex](T_{2} - T_{1} ) [/latex] gives:

[latex](T_{2} - T_{1} ) = amount of heat imes \frac{1}{SH} imes \frac{1}{m} [/latex]

[latex](T_{2} - T_{1} ) =200 \cancel{cal} imes \frac{\cancel{g} • °C }{100 \cancel{cal} } imes \frac{1}{10.0 \cancel{g}} = 20 °C[/latex]

Thus the temperature of the liquid water will rise by 20°C from 0°C, and it is now 20°C.

Question 5.10: Heat of Fusion and Phase Change . What will be the final tem...

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