How much energy do you need to heat and melt a sample of ice from -5°C to 50°C? [closed]








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A 67.8 g sample of ice initially at -5.00 oC is heated until the final temperature is 50.0 oC. Calculate the amount of energy gained by the sample. ANSWER IN kJ for sig figs. 


The specific heat capacity of ice is 2.09 J/g oC, the specific heat capacity of water is 4.184 J/g oC, the specific heat capacity of steam is 2.03 J/g oC, the ΔHfus = 3.35 x 10^5 J/kg, and the ΔHvap = 2.26 x 10^6 J/kg.




Knowing that 


* The mass is $m=67.8$ g;
* The specific heat capacity of ice is $c\_{\text{ice}}=2.09$ J/(g°C);
* The specific heat capacity of water is $c\_{\text{water}}=4.184$ J/(g°C);
* The latent heat of fusion is $\Delta H\_{\text{fusion}} = 3.35\cdot10^5$ J/kg$=335$ J/g.




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1. To go from $T\_1=-5$ °C to $T\_2=0$ °C you need $c\_{\text{ice}}\cdot m\cdot(T\_2-T\_1)=708.51$ J.
2. To transform from ice to water you need $\Delta H\_{\text{fusion}}\cdot m=22713$ J.
3. To go from $T\_2=0$ °C to $T\_3=50$ °C you need $c\_{\text{water}}\cdot m\cdot(T\_3-T\_2)=14183.76$ J.




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So, in total you need $708.51$ J+$22713$ J+$7085.1$ J = $37605.27$ J $\approx 37.6$ kJ.


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