Question

Suppose that convection extends through the entire mantle and that \(10 \%\) of the mean surface heat flow originates in the core. If the surface thermal boundary layer and the boundary layer at the core-mantle interface have equal thicknesses, how does the temperature rise across the lower mantle boundary layer compare with the temperature increase across the surface thermal boundary layer?

Short answer

The temperature rise across the lower mantle boundary layer is one ninth of the rise across the surface boundary layer.

Step-by-step solution

Understand the Heat Flow Distribution

Given that 10% of the mean surface heat flow originates from the core, it implies that 90% of the heat flow must originate from the mantle itself. This is an important factor to consider when analyzing the temperature differences across different boundary layers.

Interpret Boundary Layer Characteristics

The problem states that the thicknesses of the surface thermal boundary layer and the core-mantle boundary (CMB) layer are equal. This suggests symmetry in terms of geometry, but the heat flow and thermal gradients are governed by different factors at each boundary.

Analyze Temperature Difference Proportionality

The primary difference is that only 10% of the heat flow originates from the core, compared to 90% coming from the mantle. This means that the temperature rise across the CMB boundary layer, which derives its heat from the core, will reflect only 10% of the total heat compared to the surface layer. In terms of proportion, it implies a smaller temperature rise is expected across the CMB due to the limited heat contribution from the core.

Compare Temperature Rise Across Boundary Layers

Considering the proportion of heat flow from each section, the temperature rise across the core-mantle boundary layer will be one ninth (i.e., 10% of 90%) of the temperature rise across the surface thermal boundary layer. This is based on the heat flow influencing temperature gradient in the thickness of the layers.

Key concepts

Core-Mantle Boundary

The core-mantle boundary (CMB) is a critical layer within the Earth's internal structure. It signifies the transition between the Earth's outer core and the solid mantle above. This boundary is located roughly 2,900 kilometers beneath the Earth's surface. It is integral in understanding mantle convection because this is where the heat from the core enters the mantle.

• The core is composed primarily of iron and nickel, and it is extremely hot, with temperatures reaching up to 3,500 degrees Celsius or more.
• The mantle, on the other hand, is composed of silicate rocks, creating a stark contrast at the boundary.

The differences in composition and heat at the CMB lead to significant thermal gradients, crucial for driving convection currents that affect geological and tectonic activity.

Thermal Boundary Layer

A thermal boundary layer is a region where there is a noticeable change in temperature, acting like a blanket that separates hotter parts of Earth's interior from cooler parts. In this exercise, the thermal boundary layers of focus are the ones at the surface and the one at the core-mantle boundary.

• These layers restrict heat flow and are crucial for understanding temperature distribution.
• When the thermal boundary layers of the surface and the core-mantle boundary are equal in thickness, it implies balanced insulation.

Even though they might be equal in thickness, the heat flow and temperature distribution within each layer depend on the source of heat and the materials involved.

Heat Flow Distribution

Heat flow distribution in the Earth indicates how heat is transferred from the internal layers to the surface. In the exercise, it is noted that 10% of the surface heat flow originates from the core, while 90% is derived from the mantle itself.

• This distribution affects the rates of temperature change and the dynamic processes within the mantle.
• Heat flow is calculated as heat energy moving per unit time per unit area, often measured in watts per square meter.

Understanding the distribution of heat flow helps in predicting the temperature gradients and the behavior of convection currents in the mantle, influencing tectonic and volcanic activity.

Temperature Gradient

A temperature gradient refers to the change in temperature over a certain distance within the Earth. It provides insight into the efficiency of heat transfer across different layers. In this scenario, the thicker and proportional thermal boundary layers aid in visualizing the temperature gradient.

• In regions with a steep temperature gradient, heat transfer is rapid, often leading to convective activity.
• Given that only 10% of the heat is sourced from the core, the temperature rise at the core-mantle boundary is much smaller compared to the surface thermal boundary layer.

Knowing the temperature gradients helps scientists to model and anticipate geological phenomena, including seismic activity and volcanic eruptions.