Heat transfer question from surroundings to a thin sheet of ice

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SUMMARY

The discussion focuses on calculating the mass of ice that melts when exposed to radiant energy from sunlight and surrounding air. Given a net energy transfer of 20W and a heat transfer coefficient of 9.5W*m^-2*K^-1, the correct mass of melted ice in one minute is determined to be 8.74 x 10^-3 kg. Participants attempted to apply the heat transfer equations, including H=qAΔT and ΔQ=Lm, but encountered discrepancies in their calculations, leading to confusion regarding the necessity of the heat transfer coefficient.

PREREQUISITES
  • Understanding of heat transfer principles, specifically convection and phase change.
  • Familiarity with the latent heat of fusion for water (333 kJ/kg).
  • Knowledge of basic thermodynamic equations, including H=qAΔT and ΔQ=Lm.
  • Ability to perform unit conversions and energy calculations (Joules to kJ).
NEXT STEPS
  • Review the principles of heat transfer, focusing on convection and conduction.
  • Study the concept of latent heat and its application in phase changes.
  • Learn how to apply the heat transfer equation H=qAΔT in practical scenarios.
  • Explore energy conservation and calculations involving Joules and kilojoules.
USEFUL FOR

Students in physics or engineering courses, educators teaching thermodynamics, and anyone interested in understanding heat transfer and phase change phenomena.

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Homework Statement



A thin sheet of ice with an area of 0.15m^2 on each side hangs from a roof.
The ice is at 0C (Celsius) and the surrounding air is at 10C.
The net rate at which radiant energy is transferred to the ice from the sunlight and
from the surroundings is 20W; q=9.5W*m^-2*K^-1
What mass of ice melts in 1 minute?

Homework Equations


Heat trasfer by convection: H=qAΔT (A: surface area)
Latent heat for phase change: ΔQ=Lm (L:latent heat, specific to material, m=mass)

The Attempt at a Solution


I'm in trouble. The correct answer is 8.74X10^-3kg but me and all of my classmates failed to get the correct answer. And I don't know why q is provided in the question. Do I really need that to solve this problem?
Anyways, this is my attempt to solve the problem.

The net rate at which radiant energy is transferred to the ice = 20W (J/s)
Thus, in 1 minute = 20Wx60sec=1200J=The heat ΔQ provided to change the phase of ice.
(solid to liquid)

Latent heat of fusion (water) = 333KJ/kg required (solid to liquid)
Therefore, 1200J=(333Kj/kg)*m
m=0.003604kg

or this:
the heat transferred from surrounding area to the sheet of ice:
H = qAΔT = (9.5W*m^-2*K^-1)(0.3m^2)(10k)=14.25W
in 1 minute = 14.25Wx60sec=855J
Latent heat of fusion (water) = 333KJ/kg (solid to liquid)
Therefore, 855J=(333Kj/kg)*m
m=0.002567kg

please tell me what I did wrong. Thanks a lot and have a nice day :D
 
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That's odd. Are you given the specific heat of the surrounding environment?
 

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