At what depth will the dry mantle rock at point X begin to melt if it is uplifted closer to Eart

step 1 In this question, I want to find a mathematical model again where my temperature T is in terms o

At what depth will the dry mantle rock at point X begin to...

At what depth will the dry mantle rock at point $\mathrm{X}$ begin to melt if it is uplifted closer to Earth's surface and its temperature remains the same?
a. $35 \mathrm{~km}$
b. $25 \mathrm{~km}$
c. $18 \mathrm{~km}$
d. $12 \mathrm{~km}$

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Key Concepts

Pressure-Dependent Melting

This concept explains that the melting temperature of rocks is a function of pressure. As pressure decreases, such as when rocks are uplifted closer to the Earth's surface, the melting temperature correspondingly decreases. This means that a rock which is solid at high pressure may begin to melt at a shallower depth, even if its temperature remains constant.

Decompression Melting

Decompression melting occurs when solid rock ascends toward the surface under nearly isothermal conditions. The reduction in pressure lowers the melting point of the rock, allowing it to melt even without additional heating. This process is central to understanding how mantle material can partially melt and contribute to volcanic activity.

Isothermal Uplift

Isothermal uplift refers to the scenario where a rock is brought to a shallower depth without a significant change in its temperature. As the rock ascends and the pressure decreases, the rock can cross the melting point defined by its new, lower-pressure environment. This concept is important in explaining why, under such conditions, dry mantle rock begins to melt at a specific shallower depth.

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