Physics - Heat & Thermo Question with Solution | TestHub

$0.05\mathrm{kg}$ steam at $373\mathrm{K}\stackrel{Q_1}{⟶}0.05\mathrm{kg}$ water at $373\mathrm{K}$ $0.05\mathrm{kg}$ water at $373\mathrm{K}\stackrel{Q_2}{⟶}0.05$ kg water at $273\mathrm{K}$ $0.45\mathrm{kg}$ ice at $253\mathrm{K}\stackrel{Q_3}{⟶}0.45\mathrm{kg}$ ice at $273\mathrm{K}$ $0.45\mathrm{kg}$ ice at $273\mathrm{K}\stackrel{Q_4}{⟶}0.45\mathrm{kg}$ water at $273\mathrm{K}$ $$\begin{array}{rl}& Q_1=(50)(540)=27,000\mathrm{cal}=27\mathrm{kcal}\\ & Q_2=(50)(1)(100)=5000\mathrm{cal}=5\mathrm{kcal}\\ & Q_3=(450)(0.5)(20)=4500\mathrm{cal}=4.5\mathrm{kcal}\\ & Q_4=(450)(80)=36000\mathrm{cal}=36\mathrm{kcal}\end{array}$$ Now since $Q_1+Q_2>Q_3$ but $Q_1+Q_2<Q_3+Q_4$ ice will come to $273\mathrm{K}$ from $253\mathrm{K}$, but whole ice will not melt. Therefore temperature of the mixture is $273\mathrm{K}$.