10 g of ice at -20C and 100g of water at +5C is mixed together. How much water and ice will there be once the system reaches equilibrium (assuming no heat is lost)?

Specific heat of water and ice: [tex]4.186*10^3, 2.108*10^3 [/tex]

Latent heat of fusion of ice: [tex]333.55*10^3 [/tex]

All in units [tex](kg^{-1} * C^{-1})[/tex]

My try:

[tex]Energy_{water} = (0.1 * 5 * 4.186 * 10^3) = 2093 J [/tex]

[tex]Energy_{water} - Heating_{ice} = 2093 - (0.01 * 2.108 * 10^3 * 20) = 2071.92J [/tex]

Melting the ice with the remaning energy:

[tex]2071.92 = 333.55*10^3 * x [/tex]

[tex]x ≈ 0.062 grams [/tex]

But the right answer is supposed to be 5 grams of ice melted.

Where did I go wrong? I thought it was a bit to simple to be correct.

Edit: +5 not -5 for water.

Thank you!

Specific heat of water and ice: [tex]4.186*10^3, 2.108*10^3 [/tex]

Latent heat of fusion of ice: [tex]333.55*10^3 [/tex]

All in units [tex](kg^{-1} * C^{-1})[/tex]

My try:

[tex]Energy_{water} = (0.1 * 5 * 4.186 * 10^3) = 2093 J [/tex]

[tex]Energy_{water} - Heating_{ice} = 2093 - (0.01 * 2.108 * 10^3 * 20) = 2071.92J [/tex]

Melting the ice with the remaning energy:

[tex]2071.92 = 333.55*10^3 * x [/tex]

[tex]x ≈ 0.062 grams [/tex]

But the right answer is supposed to be 5 grams of ice melted.

Where did I go wrong? I thought it was a bit to simple to be correct.

Edit: +5 not -5 for water.

Thank you!

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