How much ice must melt at 0 deg. C to gain 5 g of mass?

In summary, the conversation discusses finding the amount of ice that must melt at 0 deg. C to gain 5 g of mass and possible equations that could be used, including Q=Lm and E=mc^2. One suggestion is to convert the energy needed to melt the ice into calories and divide by the Latent Heat of Fusion to find the amount of ice needed.
  • #1
jimmypoopins
65
0

Homework Statement


How much ice must melt at 0 deg. C to gain 5 g of mass?

Latent Heat of Fusion =
limg145.gif


Homework Equations


I cannot seem to find many equations that relate thermodynamics and mass, maybe that is my biggest problem... The only one i could find was
Q=Lm


The Attempt at a Solution


I know the latent heat of fusion, but i do not know Q. I tried dividing both sides by L, giving me Q/L=m, but i wasn't sure where to go from there.
 

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  • #2
This question is incomplete or bizarre. Heating or cooling will certainly affect density but not mass. In other words, you know that ice floats. On melting, it becomes more dense as it now occupies less volume ( a very useful property of H2O BTW). Now in the bizarro realm you could I suppose use Einstein's mass-energy equivalency E=Mc^2 by computing the energy required to double the apparent mass. But that is way, way out there. Check the ? and repost.
 
  • #3
wow i have the same exact problem for my physics class and i can not figure it out either.
 
  • #4
Someone suggested something to me and i tried it and it worked. E=mc^2
E=.005 kg* (3.0x10^8)^2. Thats the energy (in Joules) needed so take that convert it to cal and divide by the Latent Heat Fusion. Thatwill give you the # of grams. Hope this helps.
 

1. How is the amount of ice that must melt at 0 degrees Celsius to gain 5 g of mass calculated?

The amount of ice that must melt at 0 degrees Celsius to gain 5 g of mass is calculated using the specific heat capacity of ice, which is 2.09 J/g°C. This means that it takes 2.09 Joules of energy to raise the temperature of 1 gram of ice by 1 degree Celsius. By using the formula Q = mCΔT, where Q is the heat energy, m is the mass, C is the specific heat capacity, and ΔT is the change in temperature, we can calculate the amount of ice that must melt to gain 5 g of mass at 0 degrees Celsius.

2. Is the specific heat capacity of ice the same as that of water?

No, the specific heat capacity of ice is different from that of water. The specific heat capacity of water is 4.18 J/g°C, which means it takes 4.18 Joules of energy to raise the temperature of 1 gram of water by 1 degree Celsius. This is because the molecular structure of ice is more rigid and requires less energy to raise its temperature compared to the more fluid molecular structure of water.

3. Can the amount of ice that must melt at 0 degrees Celsius to gain 5 g of mass vary?

Yes, the amount of ice that must melt at 0 degrees Celsius to gain 5 g of mass can vary depending on the initial temperature of the ice. The specific heat capacity of ice only applies at 0 degrees Celsius. If the initial temperature of the ice is below 0 degrees Celsius, it will require more energy to raise its temperature to 0 degrees Celsius and melt 5 g of ice. On the other hand, if the initial temperature is above 0 degrees Celsius, it will require less energy to melt 5 g of ice.

4. What other factors can affect the amount of ice that must melt to gain 5 g of mass?

Aside from the initial temperature of the ice, other factors that can affect the amount of ice that must melt to gain 5 g of mass include the pressure and the purity of the ice. As pressure increases, the melting point of ice also increases, so more energy will be required to melt the ice at 0 degrees Celsius. Impurities in the ice can also affect its melting point and require more or less energy to melt 5 g of ice at 0 degrees Celsius.

5. What is the practical application of knowing the amount of ice that must melt at 0 degrees Celsius to gain 5 g of mass?

Knowing the amount of ice that must melt at 0 degrees Celsius to gain 5 g of mass can be useful in various scientific and engineering fields. For example, in the food industry, it can be used to determine the amount of ice needed to be added to a drink to maintain its desired temperature. In environmental studies, it can be used to measure the amount of melting ice in polar regions due to rising temperatures. It can also be applied in heat transfer calculations for designing refrigeration systems.

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