|Fig. 1: Microprocessor transistor counts and Moore's law. (Source: Wikimedia Commons)|
In its oft-quoted colloquial form, Moore's law states that the number of transistors in a computer processor (CPU) tends to double every two years (Fig 1). Although power consumption does not directly follow transistor count, there has nonetheless been an upward trend in microprocessor power consumption, illustrated by Fig 2. For desktop computers, this is cumbersome in that care must be taken to dissipate this heat using ever-larger fans and heat-sinks; however, it is not a problem from a power consumption standpoint (a common microwave oven uses much more electricity than the processor of a desktop computer).
On the other hand, for mobile technology, power requirement becomes a serious issue; mobile devices do not have the luxury of the effectively limitless power provided by a household power outlet. In mobile technology, the trend is towards ever-smaller and ever-faster devices. Will the batteries be able to keep up, packing enough joules in a small space?
Compared to computing power and transistor count, battery capacity has progressed on a much slower timescale. However, it is difficult to quantify this over the entire history of the battery, since batteries have been around for quite some time. For instance, lead-acid batteries have been around for about 150 years. Present-day lead-acid batteries have energy densities of around 70 watt-hours per litre, or about 250,000 joules per litre. Unfortunately, obtaining specific values for energy densities over the years is difficult; however, by consulting a list of historical milestones to the lead-acid battery, the most recent innovation which could possibly have altered the energy density was in 1970; thus, for the past 40+ years, it is reasonably safe to assume that the lead-acid battery hasn't changed in energy capacity. [1,2]
How does the modern lithium-ion battery—used in mobile devices today—compare to the ancient lead-acid? According to a 2011 book, lithium-ion energy densities are in the range of 245-430 watt-hours per litre, or roughly 1.5 megajoules per litre at the high end; so whereas (from Figs. 1 and 2) the number of transistors has gone up by a factor of roughly one million since 1970, and the power requirements per standard CPU have gone up by roughly a factor of 30 since the early 1980s, the energy density of batteries has only gone up by a factor of 6 or so. If lithium-ion batteries are compared not to lead-acids but to more sophisticated battery technology, there is even less of an improvement. 
|Fig. 2: Power consumption of various Intel processors, plotted against the date introduced. (Data from the processor datasheets.)|
An alternative to the conventional battery is the use of a fuel cell. Rather than the reversible chemical processes found in rechargeable batteries, a fuel cell essentially "burns" its fuel, and is in some sense closer to an internal combustion engine than a battery. A common fuel cell fuel is methanol (ethanol is also used), which has a theoretical energy density of roughly 15 megajoules per litre, about ten times the energy density of lithium-ion batteries (although this excludes the size of the fuel cell itself, and does not take into account efficiency losses). Current fuel cells, however, suffer from relatively low power densities; although they may have the energy to run the device for long times, they cannot provide that energy quickly enough. One advantage of the fuel cell is that "recharging" is a very quick ordeal, analogous to putting gasoline in a car. [3-5]
Clearly, I have made comparisons which aren't completely appropriate. The CPUs shown in Fig. 2 were desktop processors not made with power consumption in mind; likewise for many of the processors in Fig. 1 (indeed, the largest outlier, the Atom, was actually made with power consumption in mind). However, with more transistors, more demanding software, and increasing attention paid to svelte aesthetics, high energy density power supplies are required. Although we're used to filling up our cars with fuel and recharging our phone, there may come a time when, at least for some, the opposite takes place.
© Brannon Klopfer. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
 A. K Shukla, A. S Aricò and V. Antonucci, "An Appraisal of Electric Automobile Power Sources," Renew. Sustain. Energy Rev. 5, 137 (2001).
 J. Zhang et al., eds., Electrochemical Technologies for Energy Storage and Conversion (Wiley-VCH, 2011).
 J. Han and E.-S. Park, "Direct Methanol Fuel-Cell Combined With a Small Back-Up Battery", J. Power Sources 112, 477 (2002).
 S.-C. Yao et al., "Micro-Electro-Mechanical Systems (MEMS)-Based Micro-Scale Direct Methanol Fuel Cell Development," Energy 31, 636 (2006).
 C. Lamy et al., "Recent Progress in the Direct Ethanol Fuel Cell: Development of New Platinum-Tin Electrocatalysts," Electrochim. Acta 49, 3901 (2004).