At 0 degrees, the soil is covered with a 10 cm thick layer of snow and a density of 500 kg / m (cubic).

At 0 degrees, the soil is covered with a 10 cm thick layer of snow and a density of 500 kg / m (cubic). What layer of rainwater at 4 degrees will melt the entire layer of snow?

tcn = 0 “C. ρsn = 500 kg / m ^ 3. dsn = 10 cm = 0.1 m. ρw = 1000 kg / m ^ 3. Sv = 4200 J / kg *” C. λ = 3.4 * 10 ^ 5 J / kg. tv = 4 “C.
dv -?
decision
The amount of heat Qw, which is released when the water is cooled, goes to melt snow
Qsn: Qw = Qsn. Qw = Sv * mw * (tv – tcn).
mw = Vw * ρw = S * dw * ρw,
where S is the surface area of the water.
Qw = Sv * S * dw * ρw * (tv – tcn).
Qsn = λ * msn. mсн = Vсн * ρсн = S * dсн * ρсн.
Qsn = λ * S * dsn * ρsn.
Sv * S * dw * ρw * (tv – tcn) = λ * S * dsn * ρsn.
в = λ * dsn * ρsn / Sv * ρw * (tv – tcn).
dv = 3.4 * 10 ^ 5 J / kg * 0.1 m * 500 kg / m ^ 3/4200 J / kg * “C * 1000 kg / m ^ 3 * (4” C – 0 “C) = 1.01 m.
Answer: the water layer should be dw = 1.01 m.