# Thermodynamics Ice Melting Question

• ConnorM
In summary, the chest filled with ice has a mass of 1kg and therefore the time needed to melt it is 0.5 hours.
ConnorM

## Homework Statement

1. On a hot summer day, you planned a trip to a beach, but you inadvertently took a wrong turn and now you’re worried the ice in your cooler is going to melt. The cooler is 0.5 m × 0.5 m × 0.4 m, and is made with 5 cm thick Styrofoam (k = 0.033 W/m2K). Help your panicking friends by calculating the available time to find the beach before the ice melts away completely. Assume that internal convection coefficient is high enough that the inner surface of the Styrofoam matches that of the melting ice. Assume also that the temperature at the outer surface of the cooler is 10°C and the temperature of the surroundings is 35°C. Neglect any heat transfer from the bottom of the cooler (assume the cooler is resting on the foam filled seat of your car which acts as an insulator). The latent heat of fusion of the ice is 334 kJ/kg.

## Homework Equations

Basic conduction/convection equations
Q=mL
L - heat of fusion

## The Attempt at a Solution

I'm wondering how to determine the inner h value of the cooler and the outer h value in order to determine the heat transfer via convection. I'm confused as to what "Assume that internal convection coefficient is high enough that the inner surface of the Styrofoam matches that of the melting ice. " means.

Also, should a mass have been given in this problem?

My opinion is that mass should be given and if this is in steady state condition i think we have assume that the rate of heat flowing through the styrafoam is completley taken by melting ice to do its change of state.

Last edited:
ConnorM said:
should a mass have been given in this problem?
Assume it is filled with ice.
ConnorM said:
Assume that internal convection coefficient is high enough that the inner surface of the Styrofoam matches that of the melting ice.
You have not been told the initial temperature of the ice, so you will have to assume 0C. This statement just means that all the ice will melt before any of the meltwater rises above 0C.

ConnorM
haruspex said:
Assume it is filled with ice.

You have not been told the initial temperature of the ice, so you will have to assume 0C. This statement just means that all the ice will melt before any of the meltwater rises above 0C.
Is the mass of ice is required in order to calculate the time?

Regarding the convection heat transfer coefficients, the statement about the interface between the styrofoam and the ice means that the inner h is infinite. You don't need to know the outer h because you are told that the temperature at the interface between the styrofoam and the air is 10 C.

Regarding Zer0's question, Haruspex has made it clear that you are supposed to assume that initially, you have a solid block of ice in the chest. Knowing the density of ice and the volume of the chest tells you the mass of ice.

ConnorM

## What is thermodynamics?

Thermodynamics is the branch of physics that studies the relationship between heat, energy, and work.

## Why does ice melt?

Ice melts when it absorbs enough heat energy to break the bonds between its molecules, causing it to turn into liquid water.

## What factors affect the rate of ice melting?

The rate of ice melting can be affected by temperature, pressure, and the presence of impurities or other substances.

## Why does adding salt to ice make it melt faster?

Salt lowers the freezing point of water, which means that it requires lower temperatures to freeze. When salt is added to ice, it lowers the temperature at which the ice can melt, thus speeding up the melting process.

## Is there a limit to how much ice can melt?

As long as there is enough heat energy and the temperature remains above freezing, ice can continue to melt. However, once all the ice has turned into water, it will not melt any further.

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