The Cost of Energy to produce 1 BTC

 

The Cost of Energy to produce 1 BTC 

There would not exist any bitcoins without the existence of energy consumption. In this section, we will find bitcoin’s marginal electricity cost and use it to determine a floor price for bitcoin as it goes through market cycles.

Let’s play some science here

Power or Energy is ‘rate at which the work is done’

Thus,

Formula->Energy or Work=PowerxTime

Unit->Watt=Joule/Second

i.e., One watt of power is expended when a joule is used for a second.

For example

i)               lets’ find the power of a kitchen that consumed 1000 joules for 20 seconds

Since Energy=PowerxTime=>Power=Energy/Time=>1000 joules/20 seconds=> 50J/s=>50watts

ii)              In a party, the strobe lights used 60,000 joules for 10 minutes. How much power (in watts) did the party expend?

Power=Energy/Time=>60000joules/(60*10) seconds=>60000/600=>100/1=>100watts

Next, let’s understand the concept of kilowatts and kilowatt-hours.

Kilowatt (kW) is the unit of Power.

Kilowatt-hours (kWh) is the unit of Energy.

Where 1kW=1000 watts

Now, let’s play with J/Th, Watt and kilowatt. In this case, we will consider J/Th of Antminer S19 XP, which is 21.5 J/Th, and do the following math

We know that Energy=Power/Time=>(21.5J/Th)/(60*60)seconds=>(21.5J/Th)/(3600sec)

=>0.005972wh=>(0.005972)/1000=>0.000005972kWh/Th

Here, we deduce that 0.000005972kWh is the energy taken to perform 1 terahash

Let’s now look at how many hashes are required to generate on BTC

Bitcoin uses the SHA-256 hash function, an algorithm that generates verifiably random numbers called hashes, using a predictable amount of computing power. Generating a hash value (a number), less than the current target (a small number set by the bitcoin algorithm-the number that adjusts during a difficulty adjustment) wins the subsidy (mining reward, currently at 6.25 BTC every 10 minutes). Therefore, hashes per second shows how much computational power is being used by miners across bitcoin; the network hash rate.

There are increasing miners in the network, cranking up the total hash rate on the network, thereby, increasing the number of hashes it takes to be rewarded with BTC.

Dividing the network hash rate by the current block reward, which occurs every 10 minutes, provides the number of hashes per individual bitcoin.

= (network hash rate)/block reward=>(436339428^Th/s) / ((6.25 BTC/(600sec))

Note: The current network hash is 436.34EH/s (as of 09^th November, 2023)

=>(436339428*600)/6.25^Th/BTC=>436339428^Th/BTC=>436.34Eh/BTC

This gives us that 436.34Eh hashes are required to generate 1 BTC

Consider paying $0.2 for a unit of electricity i.e., $0.2 per kWh

Now, let’s calculate the cost of electricity required to mine 1 BTC

=436339428 Th/BTC*$0.2/kWh*0.000005972kWh

=>$5,211.64/BTC

i.e., Th/BTC X kWh/Th X $/kWh => Th/BTC X kWh/Th X $/kWh => $/BTC

=>The cost of energy to mine 1 BTC is $5,20.99

Now considering the price of 1 BTC as $36,379 (as of 22^nd November, 2023), we still earn the profit of $35,858.01.

The increasing efficiency (J/Th) of the miners reflects the reality of Moore’s Law i.e., As the hash rate of the network expands and the electricity costs remain more or less constant, miners must become increasingly efficient. They compete for marginal bitcoin production.

Finally, we deduce that because of energy expended to create BTC, BTC is an asset, akin to a commodity. Being digital in nature, however, makes bitcoin unique. 

"Energy Efficiency"-Let’s compare the efficiency between the two models

A.    Let’s consider the hash power of Antminer S19 XP. Considering the power consumption of 3010w with 140^Th/s

We derive the energy efficiency by

=(3010J/s) / (140^Th/s)=> 21.5J/Th  (Note. Since 1 watt = 1 joule /second

This shows that 21.5 joules of energy are required for every terahash of computational power.

B.    Antminer T17+ operates around 44^Th/s with the power consumption of 2200W

Energy efficiency=>(2200/44)=50J/Th

Thus, we see that Antminer S19 XP is more efficient than Antminer T17+