What is the result of mixing 10g of ice at -10 deg celcius?

[postthreads]

Homework Statement

Find the result of mixing 10g of ice at -10 deg celcius. Specific heat capacity of ice = 2.1 J/g K. Specific heat capacity of water is 4.2 J/g K. Specific latent heat of ice = 336 J/g.

Homework Equations

The Attempt at a Solution

0.625g, temperature will remain at 0 deg celcius.

 

[SteamKing]

Your problem statement is incomplete. Mixing 10g of ice with what?

 

[postthreads]

mixing with water

 

[SteamKing]

OK. How much water? Is this going to be a Twenty Questions session?

 

[HalfLostAndSearching]

I would approach this problem by using the principles of thermodynamics and heat transfer. First, I would calculate the energy required to melt 10g of ice at -10 deg celcius using the specific latent heat of ice (336 J/g). This would give me a total energy of 3360 J.

Next, I would calculate the energy needed to raise the temperature of 10g of water from 0 deg celcius to its melting point of 0 deg celcius, using the specific heat capacity of water (4.2 J/g K). This would give me an energy of 42 J.

Therefore, the total energy required to melt 10g of ice and raise its temperature to 0 deg celcius is 3360 J + 42 J = 3402 J.

Using the specific heat capacity of ice (2.1 J/g K), I would then calculate the energy required to raise the temperature of 10g of ice from -10 deg celcius to 0 deg celcius. This would give me an energy of 210 J.

Subtracting this energy from the total energy required (3402 J - 210 J = 3192 J), I can determine that the remaining energy is used to melt the ice. Dividing this energy by the specific latent heat of ice (336 J/g), I can calculate that 9.5g of ice will melt.

Therefore, the final result of mixing 10g of ice at -10 deg celcius is 0.5g of ice remaining and 9.5g of water at 0 deg celcius. The temperature will remain at 0 deg celcius due to the energy being used for phase change (melting) rather than temperature change.