Question

2 kg of ice melts when water at 100 C is poured in a hole drilled in a block of ice. what mass of water was used? specific heat capacity of water= 4200 Jkg^-1K^-1, L_ice = 336 x 10³ Jkg^-1.

Answer 1

$$\begin{gathered} \mathrm{Suppose}\mathrm{the}\mathrm{mass}\mathrm{of}\mathrm{water}\mathrm{used}\mathrm{is}\mathrm{m}. \\ \mathrm{Heat}\mathrm{gained}\mathrm{by}\mathrm{ice}\mathrm{to}\mathrm{melt}\mathrm{water}\mathrm{at}{0}^0\mathrm{C}=\mathrm{mL}=2\times 336\times {10}^3\mathrm{J} \\ \mathrm{Heat}\mathrm{lost}\mathrm{by}\mathrm{water}\mathrm{of}\mathrm{mass}\mathrm{m}\mathrm{to}\mathrm{water}\mathrm{at}{0}^0\mathrm{C} \\ \mathrm{m}\times 4200\times (100-0) \\ \mathrm{By}\mathrm{the}\mathrm{principle}\mathrm{of}\mathrm{calorimetry}, \\ \mathrm{Heat}\mathrm{lost}=\mathrm{Heat}\mathrm{gained} \\ \mathrm{m}\times 4200\times (100-0)=2\times 336\times {10}^3 \\ \mathrm{m}=\frac{2\times 336\times {10}^3}{4200\times 100}=1.6\mathrm{kg} \end{gathered}$$