# Heat transfer question from surroundings to a thin sheet of ice

• hanjy85
In summary, the problem involves calculating the mass of ice that melts in one minute given the net rate of radiant energy transfer, the surface area of the ice, and the temperature of the ice and surrounding environment. The correct answer is 8.74x10^-3kg, but the student and their classmates were unable to get the correct answer. The student attempts to solve the problem using the equations for heat transfer by convection and latent heat for phase change, but is unsure if the provided value of q is necessary. They also consider the specific heat of the surrounding environment, but are still unable to get the correct answer.
hanjy85

## 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

That's odd. Are you given the specific heat of the surrounding environment?

## 1. How does heat transfer occur between surroundings and a thin sheet of ice?

Heat transfer occurs through the process of conduction, where heat energy is transferred from a warmer object (surroundings) to a colder object (ice) through direct contact.

## 2. What factors affect the rate of heat transfer from surroundings to a thin sheet of ice?

The rate of heat transfer depends on the temperature difference between the surroundings and the ice, as well as the thermal conductivity of the materials involved.

## 3. What happens to the temperature of the surroundings as heat is transferred to the thin sheet of ice?

The temperature of the surroundings will decrease as heat is transferred to the ice, due to the conservation of energy principle.

## 4. How can the rate of heat transfer be increased between surroundings and a thin sheet of ice?

The rate of heat transfer can be increased by increasing the temperature difference between the surroundings and the ice, or by using materials with higher thermal conductivity.

## 5. What is the purpose of heat transfer from surroundings to a thin sheet of ice?

The purpose of heat transfer is to melt the ice and bring it to the same temperature as the surroundings. This can be useful for cooling purposes or for melting ice in order to use it for drinking or other purposes.

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