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A 50-gram ice cube floats in 250-gram of water in a 100-gram glass cup; all are at a temperature of 0 ° C. A piece of silver at 99.0 °C is dropped into the cup. After equilibrium, there is still 10 grams of ice left in the cup. a) What was the mass of the silver? b) What is the "additional" mass of silver (at 99.0 ° C) requi red to achieve equilibrium temperature of 10 °C? Key Assumption: Insulated Boundary Qout = 0 %3D Iusulated Boundary Qin = 0 %3D

A 50-gram ice cube floats in 250-gram of water in a 100-gram glass cup; all are at a temperature of 0 ° C. A piece of silver at 99.0 °C is dropped into the cup. After equilibrium, there is still 10 grams of ice left in the cup. a) What was the mass of the silver? b) What is the "additional" mass of silver (at 99.0 ° C) requi red to achieve equilibrium temperature of 10 °C? Key Assumption: Insulated Boundary Qout = 0 %3D Iusulated Boundary Qin = 0 %3D

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LET LOWES nstallation S HELP WITH DECKING YOUR NEXT FENCING ROOFING EYERIOR We offe INSTAL See an associate SIDING DywOwS&MORE PRVECT to get started. 1099.lowes.com) A 50-gram ice cube floats in 250-gram of water in a 100-gram glass cup; all are at a temperature of 0 ° C. A piece of silver at 99.0 ° C is dropped into the cup. After equilibrium, there is still 10 grams of ice left in the cup. a) What was the mass of the silver? b) What is the "additional" mass of silver (at 99.0 ° C) required to achieve equilibrium temperature of 10 °C? Key Assumplion: Insulated Boundary Qout = 0 Qin = 0 Insulated Boundary
Transcribed Image Text:LET LOWES nstallation S HELP WITH DECKING YOUR NEXT FENCING ROOFING EYERIOR We offe INSTAL See an associate SIDING DywOwS&MORE PRVECT to get started. 1099.lowes.com) A 50-gram ice cube floats in 250-gram of water in a 100-gram glass cup; all are at a temperature of 0 ° C. A piece of silver at 99.0 ° C is dropped into the cup. After equilibrium, there is still 10 grams of ice left in the cup. a) What was the mass of the silver? b) What is the "additional" mass of silver (at 99.0 ° C) required to achieve equilibrium temperature of 10 °C? Key Assumplion: Insulated Boundary Qout = 0 Qin = 0 Insulated Boundary
Expert Solution
Step 1

In the given problem, the system contains 50 g of ice, 250 g of water, and 100 g of glass cup. When a silver piece at 99o C is added to the system, then the system reaches an equilibrium, and 10 g of ice left in the system. That means the system again at the temperature of 0o C. The heat from the silver piece is utilized by the ice to become water. At equilibrium 10 g of ice leftover, hence 40 g of ice melts into water.

Therefore we can write

Heat from the silver=Heat of fudion of ice.......1Q=mC∆T........2m=mass of the substanceC=specific heat of the solid∆T=temperature difference.Heat of fusion of ice=Qf=mLf.....3Lf-latent heat of fusionfor ice Lf=334 J/gFrom 1,2 and 3 we can writeQS=QfmC∆Tsilver=mLficeSilver temperature fall from 99oC to 0oCmsilver=mLficeC∆Tsilver=40 g×334 J/g0.246 J/goC×99-0oC=548.58 g=0.55 kg

The mass of the silver piece is 0.55 kg.

 

 

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