The depth in the soil of the Earth at which freezing temperatures penetrate is often of importance in agriculture and construction. During a certain fall day, the temperature in the Earth is constant at 15.6 oC to a depth of several meters. A cold wave suddenly reduces the air temperature from 15.6 oC to -17.8 oC. The convective coefficient above the soil is 11.36 W/m2 K. The soil properties are a = 4.65 x 10-7 m2/s and k = 0.865 W/m K. Neglect any latent heat effects. a) What is the surface temperature after 5.0 hours? b) To what depth in the soil will the freezing temperature of 0 °C penetrate in 5.0 hours?

The depth in the soil of the Earth at which freezing temperatures penetrate is often of importance in agriculture and construction. During a certain fall day, the temperature in the Earth is constant at 15.6 ^oC to a depth of several meters. A cold wave suddenly reduces the air temperature from 15.6 ^oC to -17.8 ^oC. The convective coefficient above the soil is 11.36 W/m² K. The soil properties are a = 4.65 x 10^-7 m²/s and k = 0.865 W/m K. Neglect any latent heat effects.

a) What is the surface temperature after 5.0 hours?

b) To what depth in the soil will the freezing temperature of 0 °C penetrate in 5.0 hours?