Heat Transfer Coefficient for Phase Change

[Point Conception]

Homework Statement

One liter of water at 30 C (30000 calories )
A 100 gram sphere of ice at 0 C in center of water volume .
The ice will absorb 80000 calories melting, and final water temperature
= 22000 cal/1100g = 20 C.
Assume mixing and uniform water temp during melting and water vessel
insulated from surroundings. How long for ice to melt ?

Homework Equations

Heat Transfer Coefficient
h =q/A delta T
q = cal/sec
h = cal/sec/M² C for ice , .523 cal/sec ( converted watts to cal/sec )
A = surface area. for approx 100 cc ice = .01034 M² ( initial)
delta T 30 C ( initial )

The Attempt at a Solution

This is difficult since both Area and delta T are decreasing
For initial conditions only: q = ( .523 cal/sec/ M² C ) ( .01034 M²(30 C
q= .162 cal/sec. so 8000 cal/ .162cal/sec. = 13.7 hrs
But in the real case this is not correct as A and delta T are decreasing

 

[Point Conception]

Homework Statement

One liter of water at 30 C (30000 calories )
A 100 gram sphere of ice at 0 C in center of water volume .
The ice will absorb 80000 calories melting, and final water temperature
= 22000 cal/1100g = 20 C.
Assume mixing and uniform water temp during melting and water vessel
insulated from surroundings. How long for ice to melt ?

Homework Equations

Heat Transfer Coefficient
h =q/A delta T
q = cal/sec
h = cal/sec/M² C for ice , .523 cal/sec ( converted watts to cal/sec )
A = surface area. for approx 100 cc ice = .01034 M² ( initial)
delta T 30 C ( initial )

The Attempt at a Solution

This is difficult since both Area and delta T are decreasing
For initial conditions only: q = ( .523 cal/sec/ M² C ) ( .01034 M²(30 C
q= .162 cal/sec. so 8000 cal/ .162cal/sec. = 13.7 hrs
But in the real case this is not correct as A and delta T are decreasing

1. That should be 8000 calories melting: ice heat of fusion (80 cal/g) (100g)
Can anyone do this problem or should something else be applied in place of
Heat Transfer Coefficient ?