In an insulated vessel, 0.05 ~kg steam at 373 ~K and 0.45 ~kg of ice at 253 ~K are mixed. Find the final temperature of the mixture (in kelvin). Given, aligned L_ fusion & =80 cal / g =336 ~J / g , L_ vaporization =540 cal / g =2268 ~J / g , S_ ice & =2100 ~J / kg , K=0.5 cal / gK and S_ water =4200 ~J / kg , K=1 cal / gK . aligned

Step-by-step solution

0.05 ~kg steam at 373 ~K Q₁ 0.05 ~kg water at 373 ~K 0.05 ~kg water at 373 ~K Q₂ 0.05 kg water at 273 ~K 0.45 ~kg ice at 253 ~K Q₃ 0.45 ~kg ice at 273 ~K 0.45 ~kg ice at 273 ~K Q₄ 0.45 ~kg water at 273 ~K aligned & Q₁=(50)(540)=27,000 cal =27 kcal & Q₂=(50)(1)(100)=5000 cal =5 kcal & Q₃=(450)(0.5)(20)=4500 cal =4.5 kcal & Q₄=(450)(80)=36000 cal =36 kcal aligned Now since Q₁+Q₂>Q₃ but Q₁+Q₂ < Q₃+Q₄ ice will come to 273 ~K from 253 ~K , but whole ice will not melt. Therefore temperature of the mixture is 273 ~K .