The soil temperature in the upper layers of the earth varies with the variations in the atmospheric conditions. Before a cold front moves in, the earth at a location is initially at a uniform temperature of $10^{\circ} \mathrm{C}$. Then the area is subjected to a temperature of $-10^{\circ} \mathrm{C}$ and high winds that resulted in a convection heat transfer coefficient of $40 \mathrm{~W} / \mathrm{m}^2,{ }^{\circ} \mathrm{C}$ on the earth's surface for a period of 10 h . Taking the properties of the soil at that location to be $k=0.9 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$ and $\alpha=1.6 \times 10^{-5} \mathrm{~m}^2 / \mathrm{s}$, determine the soil temperature at distances $0,10,20$, and 50 cm from the earth's surface at the end of this $10-\mathrm{h}$ period.