Chapter 18, Problem 8PEB

A teacher would like to demonstrate the behavior of continental and oceanic crust floating in the mantle by using wood blocks and a pan of water. What density of wood is required to model how the continental crust floats in the mantle? What density of wood is required to model the oceanic crust?

To determine

The density of wood required to model the continental crust and oceanic crust floating in mantle.

Answer to Problem 8PEB

Solution:

$0.818{\text{ g/cm}}^3$ and $0.909{\text{ g/cm}}^3$

Explanation of Solution

Given Data:

The density of continental crust is $2.7{\text{g/cm}}^{\text{3}}$.

The density of mantle is $3.3{\text{ g/cm}}^{\text{3}}$.

The density of oceanic crust is $3.0{\text{ g/cm}}^{\text{3}}$.

The density of water is $1{\text{ g/cm}}^3$.

Formulae used:

Density of the wood required to represent the continental crust.

${\left({\rho }_{wood}\right)}_{continental}={\rho }_{water}\left(\frac{{\rho }_{continental}}{{\rho }_{mantle}}\right)$ …… (1)

Here, ${\rho }_{water}$ is the density of water, ${\rho }_{mantle}$ is the density of the mantle and ${\rho }_{continental}$ is the density of the continental crust.

Density of the wood required to represent the ocean crust.

${\left({\rho }_{wood}\right)}_{ocean}={\rho }_{water}\left(\frac{{\rho }_{ocean}}{{\rho }_{mantle}}\right)$ …… (2)

Here, ${\rho }_{ocean}$ is the density of the oceanic crust.

Explanation:

The expression of density of the wood required to represent the continental crust is:

${\left({\rho }_{wood}\right)}_{continental}={\rho }_{water}\left(\frac{{\rho }_{continental}}{{\rho }_{mantle}}\right)$

Substituting $2.7{\text{g/cm}}^{\text{3}}$ for ${\rho }_{continental}$, $1{\text{ g/cm}}^3$ for ${\rho }_{water}$ and $3.3{\text{ g/cm}}^{\text{3}}$ for ${\rho }_{mantle}$.

$\begin{array}{c}{\rho }_{wood}=\left(1{\text{ g/cm}}^3\right)\left(\frac{2.7{\text{g/cm}}^{\text{3}}}{3.3{\text{ g/cm}}^{\text{3}}}\right)\\ =0.818{\text{ g/cm}}^3\end{array}$

Hence, for modeling of the continental crust in the mantle, the density of wood required is $0.818{\text{ g/cm}}^3$.

The density of the wood required to represent the ocean crust is:

${\left({\rho }_{wood}\right)}_{ocean}={\rho }_{water}\left(\frac{{\rho }_{ocean}}{{\rho }_{mantle}}\right)$

Substituting $3.0{\text{ g/cm}}^{\text{3}}$ for ${\rho }_{ocean}$, $1{\text{ g/cm}}^3$ for ${\rho }_{water}$ and $3.3{\text{ g/cm}}^{\text{3}}$ for ${\rho }_{mantle}$.

$\begin{array}{c}{\rho }_{wood}=\left(1{\text{ g/cm}}^3\right)\left(\frac{3.0{\text{g/cm}}^{\text{3}}}{3.3{\text{ g/cm}}^{\text{3}}}\right)\\ =0.909{\text{ g/cm}}^3\end{array}$

Hence for the modeling of the continental crust in mantle the density of wood required is $0.909{\text{ g/cm}}^3$.

Conclusion:

The continental crust and oceanic crust floating in mantle can be represented by density of wood $0.818{\text{ g/cm}}^3$ and $0.909{\text{ g/cm}}^3$ floating in water respectively.