Thermodynamics Ice Melting Question

AI Thread Summary
The discussion revolves around calculating the time it takes for ice in a cooler to melt under specific conditions. The cooler's dimensions and insulation properties are provided, with assumptions about the internal convection coefficient and the temperatures involved. Participants clarify that the mass of ice can be determined from its density and the cooler's volume, despite the problem not explicitly stating it. The inner convection coefficient is considered infinite, allowing for simplifications in the heat transfer calculations. Overall, the focus is on understanding the heat transfer dynamics to estimate the time before the ice completely melts.
ConnorM
Messages
77
Reaction score
1

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?
 
Physics news on Phys.org
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.
 
  • Like
Likes 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.
 
  • Like
Likes ConnorM
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Back
Top