# A piece of ice was placed in a vessel with water, what is the ratio of the mass of ice to the mass of water

A piece of ice was placed in a vessel with water, what is the ratio of the mass of ice to the mass of water, if all the ice has melted both in the vessel and in the vessel the temperature is set to 0 degrees. The initial water temperature is 33 degrees Celsius.

We know that:
Q cooling = Q melting;
Then:
Melting Q = λ * m;
Formula designations:
λ is the specific heat of melting of ice;
m is the mass of ice.
In this way:
Q cooling = c * m * Δt;
Formula designations:
c – specific heat capacity of water;
m is the mass of water;
Δt is the difference (t2 – t1);
Let’s substitute:
Q cooling = 1.386 * 10 ^ 5 * m;
Melting Q = 3.3 * 10 ^ 5 * m;
We get:
1.386 * 10 ^ 5 * m = 3.3 * 10 ^ 5 * m;
Then:
m = 2.3809 * m.
Answer: m = 2.3809 * m.

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