An insulated vessel contains 1 kg of ice and water at 0 ° C. Water vapor is admitted into the vessel at 100 ° C

An insulated vessel contains 1 kg of ice and water at 0 ° C. Water vapor is admitted into the vessel at 100 ° C. Find the minimum vapor mass at which all the ice will melt.

In order to melt the ice, it is necessary to absorb the energy released during the condensation of steam and the cooling of water from 100 degrees to 0 degrees. Qcold = Qcondensteam + Qcooling water.

Qlda = λ * mlda; λ = 3.4 * 10 ^ 5 J \ kg;

Qkond.pair = mpair * r; r = 2.3 * 10 ^ 6 J \ kg;

Q cooling water = m steam * s * (t1 – t2); s = 4200 J \ kg * degree;

λ * mlda = mpair * r + mpair * s * (t1-t2);

mpair = λ * mlda \ r + c * (t1-t2);

m pairs = 3.4 * 10 ^ 5 * 1 \ 2.3 * 10 ^ 6 + 4200 * (100 – 0) = 0.125 kg.