To convert \(10 g\) of ice at \(-10^{\circ} C\) to water at \(50^{\circ} C\) will require three stages
Stage 1
\(Q _{1}=\) heat required to change raise the temp. of \(10 g\) of ice from \(-10^{\circ} C\) to water at \(0^{\circ} C\)
\(Q=m c \Delta \theta\)
Stage 2
\(Q _{2}=\) heat required to melt
all the ice completely at \(0^{\circ} C\)
\(Q _{2}= m l_{ f }\)
Stage 3
\(Q _{3}=\) heat required to raise the temp. of \(10 g\) of heat from \(0^{\circ} C\) to water
at \(50^{\circ} C , Q_{ T }=Q_{1}+Q_{2}+Q_{3}\)
\(m c \Delta \theta+m l_{f}+m c \Delta \theta\)
we note that the mass is the same through the different stages.
\(m\left[2100(0-(-10))+3.4 \times 10^{5}+4200(50-0)\right]\)
\(0.01[21000+340000+210000]\)
\(0.01(571000)=5710 J =5.71 kJ\).