Question

Steam at 100^oC is passed over 1000 g of ice at 0^oC.After sometime 600 g of ice at 0^oC is left and 450 g of water at 0^oC is formed.Calculate the specific latent heat of vaporisation of steam.[Specific latent heat of ice is 336 Jg-¹ and specific heat capacity of water is 4.2 Jg^-1K^-1.

Answer 1

$$\begin{gathered} \mathrm{Given}, \\ \mathrm{Specific}\mathrm{heat}\mathrm{capacity}\mathrm{of}\mathrm{water}=4.2\mathrm{J}/\mathrm{g}/\mathrm{K}=4200\mathrm{J}/{\mathrm{kg}}^0\mathrm{C} \\ \mathrm{Specific}\mathrm{latent}\mathrm{heat}\mathrm{of}\mathrm{fusion}\mathrm{of}\mathrm{ice}=336\mathrm{J}/\mathrm{g}=336000\mathrm{J}/\mathrm{kg} \\ \mathrm{Total}\mathrm{mass}\mathrm{of}\mathrm{ice}\mathrm{before}\mathrm{passing}\mathrm{steam}=1000\mathrm{g}=1\mathrm{kg} \\ \mathrm{Mass}\mathrm{of}\mathrm{ice}\mathrm{left}\mathrm{after}\mathrm{passing}\mathrm{steam}=600\mathrm{g}=0.600\mathrm{kg} \\ \mathrm{So},\mathrm{mass}\mathrm{of}\mathrm{ice}\mathrm{melted}\mathrm{by}\mathrm{steam}\mathrm{to}\mathrm{form}\mathrm{water}=400\mathrm{g}=0.400\mathrm{kg} \\ \mathrm{Mass}\mathrm{of}\mathrm{steam}\mathrm{condensed}\mathrm{to}\mathrm{form}\mathrm{water}\mathrm{at}{0}^0\mathrm{C}=0.450\mathrm{kg}-0.400\mathrm{kg}=0.050\mathrm{kg} \\ \mathrm{Now}, \\ \mathrm{Heat}\mathrm{gained}\mathrm{by}\mathrm{ice}=0.400\mathrm{kg}\times 336\times {10}^3\mathrm{J}/\mathrm{kg}=134400\mathrm{J} \\ \mathrm{Heat}\mathrm{lost}\mathrm{by}\mathrm{steam}=0.050\times \mathrm{L}\times 0.050\times 4200\mathrm{J}/\mathrm{kg}/\mathrm{K}\times {100}^0\mathrm{C} \\ =(\frac{\mathrm{L}}{20}+21000)\mathrm{J} \\ \mathrm{As}\mathrm{we}\mathrm{know}\mathrm{that}, \\ \mathrm{Heat}\mathrm{gained}=\mathrm{Heat}\mathrm{lost} \\ (\frac{\mathrm{L}}{20}+21000)\mathrm{J}=134400 \\ \mathrm{Or}\mathrm{L}=2268\times {10}^3\mathrm{J}/\mathrm{kg} \end{gathered}$$