91Ó°ÊÓ

Temperature gradient is a crucial concept when examining the increase in temperature with depth inside the Earth. Essentially, a temperature gradient describes the rate at which temperature changes in relation to distance. In the problem we are tackling, the given gradient is 30°C per kilometer. This means for every kilometer you go down into the Earth's interior, the temperature increases by 30°C. This increasing temperature is due to the heat from the Earth's core and mantle—scientists use these gradients to understand various subterranean processes.
By knowing the surface temperature (10°C in our case) and the rate of temperature increase, it's possible to calculate the temperature at various depths using a simple linear relationship. For instance, if you go just one kilometer down from the surface, you'd expect the temperature to be 40°C. This linear relationship serves as the basis for solving the problem of determining at what depth iron ceases to be ferromagnetic.

Ferromagnetism refers to materials that have a strong attraction to magnets. Iron, for example, is ferromagnetic. This magnetic property arises because the magnetic moments of atoms within these materials align in the same direction, creating a powerful cumulative effect. However, ferromagnetism is temperature-dependent. When a ferromagnetic material, such as iron, reaches a certain temperature, its magnetic properties disappear.
The temperature at which this occurs is known as the Curie temperature. For iron, the Curie temperature is around 770°C. Beyond this temperature, the thermal energy becomes too great for the magnetic moments to remain aligned, and the material becomes paramagnetic, meaning it is weakly attracted to magnetic fields and loses its strong magnetic properties.
Understanding ferromagnetism and the Curie temperature is essential for solving our problem. We know the Curie temperature of iron, and we can use the temperature gradient to determine the depth at which the temperature equals this value.

The Earth's interior is a complex and layered structure composed of the crust, mantle, and core. Each of these layers has distinct characteristics and temperatures. As you go deeper into the Earth, the temperature increases significantly. This phenomenon is partly due to residual heat from the planet's formation and partly due to radioactive decay within the mantle and core.
Geologists and geophysicists study the temperature gradients within these layers to understand various geological processes, like mantle convection and plate tectonics. The temperature increases at different rates depending on the materials and conditions in each layer, but for our simplified model, we've used an average rate of 30°C per kilometer. With this information, we can calculate how temperature varies with depth and solve problems like the one given.
For instance, if we take into account the surface temperature of 10°C and apply the given average temperature gradient, it allows us to determine the depth at which the iron's Curie temperature is reached. These calculations help scientists predict various behaviors of materials and phenomena occurring inside the Earth's layers.