To build a mountain
As you might imagine, this post drew substantial ire from atheists! My original calculations were mathematically correct, but in the spirit of accuracy and fairness I have revised some of my language to describe the meaning and relevance of kinetic energy correctly in this context. I have also revised my calculation of the energy needed to "boil the oceans" using more real-world numbers, as I explain below. For clarity and transparency, my original language now appears struck-through where I have made changes, and my additions are teal-colored.
Needless to say, our oceans still fare quite well in spite of the revisions.
A brief recap
As we have previously noted, skeptics – and particularly atheists – are fond of asserting that a global flood is physically impossible. Their arguments are generally based on Genesis 7:20, which states that the waters prevailed above the mountains, covering them fifteen cubits deep. Since Mount Everest is 8.8 km tall, they have calculated the volume of water necessary to cover the surface of the earth to that depth and concluded that such a volume of water either falling as rain or resting on the earth would destroy the planet. They separately ask where all that water has gone.
But as we have also noted, scripture plainly teaches that the surface of the earth was dramatically altered as the flood waters abated:
He set the earth on its foundations,
so that it should never be moved.
You covered it with the deep as with a garment;
the waters stood above the mountains.
At your rebuke they fled;
at the sound of your thunder they took to flight.
The mountains rose, the valleys sank down
to the place that you appointed for them.
You set a boundary that they may not pass,
so that they might not again cover the earth.
Psalms 104:5-9 (ESV)
Like Genesis, the psalmist describes a time when the waters stood above the mountains, but he notes that as they abated, the mountains rose and the valleys sank down. Indeed, he notes that their movement was sufficient to ensure that the waters might not again cover the earth. Thus, any calculation that determines that a global flood is physically impossible in light of Earth's modern topography validates the truth of scripture rather than refuting it.
But that would boil the oceans!
When presented with the scripture above, skeptics typically assert that the tectonic activity necessary to raise mountains in a short time frame would somehow destroy the world. They are especially fond of asserting that the oceans would boil.
Let's take a look.
We can calculate the energy required
The energy $E$ required to lift an object on Earth is given by
$$E = mgh $$
where $m$ is the mass to be lifted in kilograms, $h$ is the height the mass is to be raised in meters, and $g$ is the acceleration due to gravity on Earth, $9.80665 {m \over s^2}$.1 But importantly, mountain ranges are taller than the areas surrounding them in spite of gravity. Their height is attributed to the thickness and density of the tectonic plates that comprise the earth's crust. The equilibrium that is maintained between gravity and the effective buoyancy of tectonic plates is referred to as isostasy, and in light of this phenomenon, it is not appropriate to use the $mgh$ equation to determine the energy required for mountain building.2
Additionally, the energy calculated by the $mgh$ equation is the energy needed to lift some mass $m$ by the height $h$. It is not a measure of the heat generated by doing so. For our purposes, $mgh$ is not a useful equation. Instead, we will use the equation for kinetic energy, the amount of energy necessary to move accelerate or decelerate a particular mass at to or from a particular velocity.
The kinetic energy of a moving object describes the amount of work that must be done on that object to bring it to rest. If we wish to determine how much heat could possibly be generated by friction in the process of stopping a moving object, that amount is limited by the object's kinetic energy. Friction reduces a moving object's kinetic energy and thus reduces its velocity. Once a moving object's kinetic energy has been reduced to 0, the object has stopped moving and no further heat due to friction can be generated.
The equation for kinetic energy is
$$E_k = {1 \over 2}mv^2 $$
where $m$ is the mass in kg and $v$ is the velocity in m/s.3
Determining the mass
The Himalayan mountain range is believed to have formed due to movement of the Indian tectonic plate.4 The surface area of the Indian plate is approximately 11.9 million km$^2$, and it is 100 km thick.5 Thus, its approximate volume is 1.190 billion km$^3$.
The Indian plate is composed of continental crust, and the density of continental crust is 2.83 g/cm$^3$. 6 7 Thus, the mass $m$ of the Indian plate is approximately $3.368 \times 10^{21}$kg.
Determining the velocity
The surface area of the Earth is 510.1 million km$^2$. The current volume of water on Earth is 1.386 billion km$^3$. Thus, the water on Earth could cover the entire surface of the Earth to a depth of 2.717 km if the surface of the Earth were perfectly smooth, or if the highest peak were <2.717 km tall and the sum of all elevations above sea level and all depressions below sea level evened out to zero.
The current height of Mount Everest is 8.848 km. If we assume that Everest was 2.717 km tall, less 15 cubits (about 22 feet) when it was submerged by the flood, then it has subsequently risen 6.131 km to reach its present height.
Everest has been observed to rise 5 mm a year, as a result of the Indian plate moving 67 mm per year.8 At that rate, for Everest to rise 6.131 km, or 6,131,000 mm, the Indian plate would need to move 82,155,400 mm, or 82.155 km.
The biblical floodwaters abated for 150 days before the ark came to rest in the mountains of Ararat, and then continued to abate for 74 more days, for a total of 224 days.9 1 day is 86,400 seconds. 224 days is 19.354 million seconds.
Thus, if the Indian plate moved 82.155 km in 224 days, causing the Himalayan mountain range to rise as the floodwaters abated, then the plate traveled at a velocity $v$ of 0.004245 m/s.
Determining the kinetic energy
Substituting our values for $m$ and $v$, the necessary kinetic energy to move accelerate or decelerate the Indian plate as to or from the velocity described is ${1 \over 2} \times (3.368 \times 10^{21}) \times ( 0.004245 )^2 = 3.035 \times 10^{16}$ joules.
The largest recorded earthquake in history had a magnitude of 9.5 on the Richter scale. An earthquake of 9.0 magnitude generates $2.0 \times 10^{18}$ joules – over 65 times the amount of energy needed to move accelerate or decelerate the Indian plate 82.2 km in 224 days to or from the described velocity.10
In fact, the estimated mass of the earth's entire crust is $2.77 \times 10^{22}$ kg, roughly 8 times the mass of the Indian plate.11 Thus, the kinetic energy required to move accelerate or decelerate the earth's entire crust 82.155 km in 224 days to or from the described velocity is ${1 \over 2} \times (2.77 \times 10^{22}) \times ( 0.004245 )^2 = 2.496 \times 10^{17}$ joules. This is still only 1/8th of the energy produced by a single earthquake of 9.0 magnitude.
And what about "boiling the oceans?"
It takes 2.257 million joules to boil 1 liter of water. 12
The amount of energy required to boil water depends on the starting temperature. It takes 4,200 joules to raise the temperature of 1 kg of water by 1°C.13 The current volume of water on Earth is 1.386 billion km$^3$, with 1.35 billion km$^3$ of it residing in the oceans. 1 km$^3$ = $10^{12}$ liters. The average temperature of water at the surface (the upper 10%) of our oceans is 17°C, but the average temperature of the remaining 90% ranges from 0-3°C.14 If we generously use 3°C for that 90%, the average temperature of our oceans is 4.4°C. To boil them, we would need to increase their temperature by 95.6°, requiring 401,520 joules per kg. Thus, it would take $5.421 \times 10^{26}$ joules to "boil the oceans." This is over 12 2.172 billion times more energy than would be necessary to move accelerate or decelerate the crust of the entire planet 82 km in 224 days to or from the described velocity.
It seems that our oceans can breathe a sigh of relief.
In summary
Given a different topography, there is enough water on Earth today to cover the surface of the entire planet to a substantial depth. The amount of energy necessary to rapidly reshape the surface of the earth has been generated by recent, known seismic events. The oceans did not boil away as a result, and from our calculations it is easy to see why.
There is no scientific basis for asserting that a global flood is an impossibility.
- https://power-calculation.com/potential-energy-gravitational-calculator.php ↩︎
- https://en.wikipedia.org/wiki/Isostasy ↩︎
- https://en.wikipedia.org/wiki/Kinetic_energy ↩︎
- https://en.wikipedia.org/wiki/Himalayas ↩︎
- https://en.wikipedia.org/wiki/Indian_Plate ↩︎
- https://en.wikipedia.org/wiki/Himalayas ↩︎
- https://en.wikipedia.org/wiki/Continental_crust ↩︎
- https://en.wikipedia.org/wiki/Himalayas ↩︎
- Genesis 8:2-5 ↩︎
- https://www.volcanodiscovery.com/earthquakes/energy.html ↩︎
- https://ui.adsabs.harvard.edu/abs/2007AGUFM.V33A1161P/abstract ↩︎
- The link I originally cited, https://www.ck12.org/physics/heat-temperature-and-thermal-energy-transfer/rwa/Boiling-Water/, gives a requirement of 2.257 million joules to boil 1 liter of water, but I think a lower number better reflects real world conditions. Thus, I have revised my calculation. ↩︎
- https://www.bbc.co.uk/bitesize/guides/z2gjtv4/revision/5 ↩︎
- https://www.windows2universe.org/earth/Water/temp.html ↩︎