Find Time to Melt Ice Ball in Water Bath: Heat Conduction

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To determine the time needed for an ice ball to completely melt in a water bath, the heat transfer is analyzed using the principles of heat conduction. The relevant equation for the heat required to melt the ice is Q=4/3*πR_0^3ρλ, where R_0 is the radius of the ice ball, ρ is the density of ice, and λ is the heat of fusion. The problem is classified as a moving boundary problem with phase change, indicating it may require advanced understanding of thermodynamics. The thermal conductivity of water plays a crucial role in the rate of heat transfer. A comprehensive solution will involve applying these principles to calculate the melting time accurately.
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Homework Statement



An ice ball is melting in a water bath. Find the time needed for the ice ball to completely melt. Heat transfer is only due to heat conduction. The radius of the ball is R_0=1cm. The temperature of the water in the bath is t=10°. There is an infinite amount of water compared to the size of the ice ball.
Heat of fusion of water is \lambda=334 kJ/kg
Density of ice is \rho=900 kg/m^3
Thermal conductivity of water is K=0,6 W/(m*K)

Homework Equations


Q=4/3*\pi R_0^3\rho\lambda


The Attempt at a Solution


The equation above is the only thing i know.
 
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What class are you taking? The reason why I ask is because this can be considered a moving boundary boundry problem with phase change which is rather advanced.
 

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