- #1
peripatein
- 880
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Hi,
I am trying to find how long it will take 8 kg of ice whose temperature is -10 C, kept in a sealed isolating box placed in room temperature (25 C), to turn into water whose temp. is 20 C. The box is a cube whose side is 20 cm, the thickness of the box is 2 cm, and κ = 0.04 W/m*K, CW = 4190 J/Kg*K, Ci = 2000 J/Kg*K, Lf = 3.34*105 J/Kg, Lv = 2.256*106 J/Kg.
1. Warming the ice to melting point (0 C)
2. Melting ALL the ice AT 0 C
3. Warming the water to 20 C
These will all be achieved through heat conduction, from the surrounding to the box.
I believe stages 1 and 3 ought to be calculated via T(t) = Tc + (TH - Tc)*e-t/τ, where T(t) - Tc denotes the temp. difference between the box and its surrounding through a separating medium (in this case, one of the walls of the box), TH denotes the temp. of the body giving off heat at t=0, and τ = mCLf / κA.
I believe stage 2 needs to be calculated via t = Lfm/H, where H = κA(TH - Tc)/L, where L is thickness of isolating layer.
I'd truly appreciate comments on the validity of this approach.
Homework Statement
I am trying to find how long it will take 8 kg of ice whose temperature is -10 C, kept in a sealed isolating box placed in room temperature (25 C), to turn into water whose temp. is 20 C. The box is a cube whose side is 20 cm, the thickness of the box is 2 cm, and κ = 0.04 W/m*K, CW = 4190 J/Kg*K, Ci = 2000 J/Kg*K, Lf = 3.34*105 J/Kg, Lv = 2.256*106 J/Kg.
Homework Equations
The Attempt at a Solution
1. Warming the ice to melting point (0 C)
2. Melting ALL the ice AT 0 C
3. Warming the water to 20 C
These will all be achieved through heat conduction, from the surrounding to the box.
I believe stages 1 and 3 ought to be calculated via T(t) = Tc + (TH - Tc)*e-t/τ, where T(t) - Tc denotes the temp. difference between the box and its surrounding through a separating medium (in this case, one of the walls of the box), TH denotes the temp. of the body giving off heat at t=0, and τ = mCLf / κA.
I believe stage 2 needs to be calculated via t = Lfm/H, where H = κA(TH - Tc)/L, where L is thickness of isolating layer.
I'd truly appreciate comments on the validity of this approach.