Ice to boiling water

Calculate the heat needed to convert 5kg of ice at a temperature of -5°C to water with a temperature of 100°C.
c (water) = 4200 J/°C/kg, c (ice) = 2100 J/°C/kg. The mass group heat of solidification of water is l = 334 kJ/kg.

Calculate the heat that 1k g of water must release to turn it into ice.

Correct answer:

Q =  3822.5 kJ

Step-by-step explanation:

$$\begin{gathered} m=5\text{kg} \\ {t}_1=100\text{°C} \\ {t}_2=0\text{°C} \\ {t}_3=-5\text{°C} \\ {c}_1=2.1\text{kJ/kg/°C} \\ {c}_2=4.2\text{kJ/kg/°C} \\ l=334\text{kJ/kg} \\ {Q}_1=m\cdot c_1\cdot (t_2-t_3)=5\cdot 2.1\cdot (0-(-5))=\frac{105}{2}=52.5\text{kJ} \\ {Q}_2=m\cdot l=5\cdot 334=1670\text{kJ} \\ {Q}_3=m\cdot c_2\cdot (t_1-t_2)=5\cdot 4.2\cdot (100-0)=2100\text{kJ} \\ Q=Q_1+Q_2+Q_3=52.5+1670+2100=3822.5\text{kJ} \end{gathered}$$

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