GATE-2018 (24) :Wyllie – Time average equation

CSIR-NET 2014 (June)

107. A continental crust contains uniformly distributed radiogenic heat sources with the heat generation rate 2 μW/m^3 in the upper 20 km crust. This crust is eroded at the rate of 0.5 km/Ma for 40 million years. Assuming a steady state thermal regime at the end of erosion episode, the final surface heat flux will be

A) less then the mantle heat flux

B) equal to the mantle heat flux

C) 1.5 times the mantle heat flux

D) 2 times the mantle heat flux

Solution:

Heat flux or thermal flux is the rate of heat energy transfer through 

a given surface per unit time. The SI unit is joule/second, or Watt.

Heat flux density is the heat rate per unit area.

SI units : W / m²

20 km crust heat generation rate =2 µW/m³

= 2* 10^-6 W/ m³

The crust eroded rate 0.5 km/ Ma for 40 million years

So, we have to know the 40 million years how much crust is eroded

0.5 km ---------------1 million year

? km ----------------40 million year

40Ma * 0.5 km = 1 Ma * x

x = (40 * 0.5 ) / 1

x= 20 km

Therefore 40 million years total crust become eroded, so no crust is 

left

The final surface heat flux will be equal to the mantle heat flow.

Answer : B