How much ice taken at a temperature of t1 – 10 degrees can be completely melted if you transfer

How much ice taken at a temperature of t1 – 10 degrees can be completely melted if you transfer to it the energy released during condensation of water vapor weighing 25 grams at t2 = 100C

t1 = – 10 ° С.

t2 = 100 ° C.

t3 = 0 ° C.

mp = 25 g = 0.025 kg.

q = 3.4 * 10 ^ 5 J / kg.

C = 2100 J / kg * ° C.

r = 2.3 * 10 ^ 6 J / kg.

ml -?

To melt ice, the required amount of heat is expressed by the formula: Ql = C * ml * (t3 – t1) + q * ml, where C is the specific heat capacity of ice, ml is the mass of molten ice, t3, t1 are the final and initial temperatures of ice, q is specific heat of melting of ice.

When water vapor condenses, the amount of heat Qp is released, which is determined by the formula: Qp = r * mp, where r is the specific heat of vaporization of water, mp is the mass of water vapor that has condensed.

Ql = Qp.

C * ml * (t3 – t1) + q * ml = r * mp.

ml = r * mp / (C * (t3 – t1) + q).

ml = 2.3 * 10 ^ 6 J / kg * 0.025 kg / (2100 J / kg * ° C * (0 ° C – (- 10 ° C)) + 3.4 * 10 ^ 5 J / kg) = 0.16 kg.

Answer: water vapor can melt ml = 0.16 kg of ice.