How is Heat Transfer Calculated in Ice Melting Problems?

[sdevgon]

1. An amount of ice of mass 80.0g is in a freezer at a temp of -15 degree Celsius. The ice is removed from the freezer, and a total of 19.2KJ of heat is added to the ice. Determine the final temperature of the ice and the mass of ice (if any) which remains after the heat is supplied.



2. Ans is 0 degree Celsius, 30.0g of ice remains



I don't know know how to get that answer. Please help !
Thanks

 

[kuruman]

What do you think happens when you add heat to ice at -15 ^oC? What happens to any solid when you add heat to it?

 

[sdevgon]

adding heat to ice will cause it to melt. But what confused me is 19.2KJ of heat energy. Because i keep taking 19.2KJ of heat energy in consideration when calculating the final temperature.

 

[kuruman]

adding heat to ice will cause it to melt.

Not necessarily. Adding heat to a solid raises its temperature. It will start melting only if it reaches its melting temperature. So the 19.2 kJ of heat energy do two things: (a) first they raise the temperature of the ice from -15 ^oC to 0 ^oC and (b) whatever heat is left over melts as much ice as it can.

But what confused me is 19.2KJ of heat energy. Because i keep taking 19.2KJ of heat energy in consideration when calculating the final temperature.

Why did that confuse you? Of course you should take it in consideration. The final temperature will not rise unless all the ice melts. Evidently, here you don't have enough heat to melt all the ice.

 

[rwisz]

for your question. In order to determine the final temperature and mass of ice, we need to use the principles of phase change and specific heat capacity. First, we need to recognize that when heat is added to ice, it undergoes a phase change from solid to liquid. This means that the heat added is used to break the bonds between the water molecules in the ice, rather than increasing the temperature of the ice. This is why the final temperature is 0 degrees Celsius, as this is the melting point of ice where it transitions from solid to liquid.

To calculate the final temperature, we can use the equation Q = m * L, where Q is the heat added, m is the mass of ice, and L is the latent heat of fusion for water (which is 334 J/g). Rearranging the equation, we get m = Q / L. Plugging in the values, we get m = 19.2 kJ / 334 J/g = 0.057 g. This means that 80.0 g - 0.057 g = 79.943 g of ice has melted.

Now, we need to determine the final mass of the ice. We can use the equation Q = m * c * ΔT, where Q is the heat added, m is the mass of ice, c is the specific heat capacity of ice (which is 2.09 J/g°C), and ΔT is the change in temperature. Since we know that the final temperature is 0 degrees Celsius and the initial temperature was -15 degrees Celsius, we can plug in the values and solve for m. This gives us m = 19.2 kJ / (2.09 J/g°C * (0 - (-15)°C)) = 30.0 g.

Therefore, the final temperature of the ice is 0 degrees Celsius and the final mass of the ice is 30.0 g. I hope this helps clarify the process and calculations involved in solving this problem.