The Carbon Footprint of Bitcoin

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The Carbon Footprint of Bitcoin ( the-carbon-footprint-bitcoin )

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Methods This section provides the methodology for calculating the range of power consumption, and the approach to derive a best-guess estimate. (1) Lower limit The lower limit is defined by a scenario in which all miners use the most efficient hardware. We calculate the lower limit of the range by multiplying the required computing power – indicated by the hash rate – by the energy efficiency of the most efficient hardware: 𝐸𝐿𝐿 =𝐻∗𝑒𝑒𝑓, (1) with: - 𝐻=h𝑎𝑠h𝑟𝑎𝑡𝑒[𝐻/𝑠] - 𝑒𝑒𝑓=energyefficiencyofmostefficienthardware[𝐽/𝐻] (2) Upper limit The upper limit is defined by the break-even point of revenues and electricity cost. Rational behavior would lead miners to disconnect their hardware from the network as soon as their costs exceed their revenues from mining and validation. 𝐸𝑈𝐿 = (𝑅𝐵+𝑅𝑇)∗𝑀 ∗ 1 , (2) 𝑃𝑁 𝑡 - 𝑅 = 𝑏𝑙𝑜𝑐𝑘 𝑟𝑒𝑤𝑎𝑟𝑑 [𝐵𝑇𝐶] with: 𝐵 - 𝑅𝑇 = 𝑡𝑟𝑎𝑛𝑠𝑎𝑐𝑡𝑖𝑜𝑛 𝑓𝑒𝑒𝑠 [𝐵𝑇𝐶] - 𝑀=𝑚𝑎𝑟𝑘𝑒𝑡𝑝𝑟𝑖𝑐𝑒[𝑈𝑆𝐷/𝐵𝑇𝐶] - 𝑃 = 𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 𝑝𝑟𝑖𝑐𝑒 [𝑈𝑆𝐷/𝑘𝑊h] 𝑁 - 𝑡=𝑡𝑖𝑚𝑒𝑝𝑒𝑟𝑖𝑜𝑑𝑒[h] (3) Best-guess The best-guess estimate follows the approach of the lower limit, but includes the anticipated energy efficiency of the network, as well as further losses from cooling and IT components. 𝐸𝐵𝐺 =𝐻∗𝑒𝑁∗𝑃𝑈𝐸𝑁, (3) 16

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