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When we consider two oceanic crusts, the older oceanic crust is heavier and the newer oceanic crust is lighter.

But when we consider two crusts, one continental and the other oceanic, continental crust is the older one yet LIGHTER of the two; while oceanic crust, the newer one, is HEAVIER of the two.

Why is that?

I know that continental crust has a granite composition while oceanic crust has a basalt composition.

Hence, I am not sure if the question can be reduced to: "Why is older basalt heavier than newer basalt?" (iff that actually is the case)

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I know that continental crust has a granite composition while oceanic crust has a basalt composition.

That's the key. Granitic rock has a significantly higher silicon composition compared to basaltic rock and has a significantly lower iron and magnesium composition compared to basaltic rock. This results in continental crust being less dense than oceanic crust. Cooling does not change the chemical composition.

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With oceanic, older crust is denser because it is cooler (old=cold=dense=faster subduction).

Even when several millions of years old, the sheer thickness of the layer and the heat capacity of the rock require that there must be a lot of thermal energy locked up.

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