Terawatt to Joules/second

The Sun delivers about 173,000 TW to Earth's surface. Human civilisation uses roughly 18 TW total. So we'd only need to capture 0.01% of incoming solar energy to power everything — an area of solar panels roughly 400 km × 400 km, about the size of Montana. The challenge isn't total energy availability; it's cost, storage, transmission, and the fact that sunlight is spread thin and intermittent.

Imagine 18 trillion light bulbs burning continuously, or 9 billion people each running a 2 kW heater non-stop. That 18 TW figure includes everything — electricity, transport fuel, industrial heat, cooking, heating. About 40% comes from oil, 27% from coal, 24% from gas, and the rest from nuclear and renewables. The US alone accounts for about 3 TW despite having only 4% of world population.

Replacing all 18 TW of human energy with clean sources would require roughly 60–75 TW of installed solar capacity (accounting for ~25% average capacity factor). That's about 40 times current installed solar. At 2023 installation rates of ~0.4 TW/year, it would take 150 years — but installation rates are doubling every 2–3 years. If that exponential trend holds, we could theoretically reach 60 TW of solar within 15–20 years.

Earth radiates about 47 TW of geothermal heat from its interior, driven by radioactive decay and residual primordial heat. That's 2.5× human energy consumption, but it's spread across the entire surface at extremely low density (~0.09 W/m²). Iceland, sitting atop a mantle plume, exploits geothermal for 90% of its heating. Globally, geothermal electricity capacity is only about 16 GW — a tiny fraction of what's theoretically available.

No — the terawatt scale is a very recent phenomenon. In 1800, global human power consumption was about 0.5 TW (mostly biomass burning). By 1900 it reached 1 TW with coal industrialisation. We crossed 10 TW around 1985. The jump from 1 to 18 TW in just 120 years tracks almost perfectly with global population growth times rising per-capita energy use. Pre-industrial humans used about 0.1 kW each; Americans now average 10 kW per person.

In dimensional analysis and physics derivations, writing J/s keeps the units transparent — you can see exactly what's being divided and multiplied. If you're calculating power as force × velocity (N·m/s = J/s), keeping it as J/s avoids a mental leap. Students and textbook authors prefer it when teaching the concept of power, because "energy per time" is more intuitive than a named unit. Once you understand it, you switch to watts for brevity.

The SI system officially defines the watt as the named unit for power, with J/s as its definition. In metrology documents and BIPM publications, you'll see W = J/s = kg·m²/s³. Some ISO standards for calorimetry and heat flow measurements express power in J/s to maintain consistency with energy measurements also given in joules. In practice, scientific papers in thermodynamics and physical chemistry often prefer J/s for clarity.

It makes unit cancellation visible. If you know a machine delivers 500 J of work over 10 seconds, writing 500 J ÷ 10 s = 50 J/s is a complete, self-checking calculation. Converting immediately to "50 W" obscures the path. In thermodynamics, where you track joules of heat, joules of work, and joules per second of power flow, keeping J/s prevents sign and unit errors that plague students.

J/s = W = V·A = kg·m²/s³. Each form has its domain: electrical engineers think V·A, mechanical engineers think N·m/s, and physicists think kg·m²/s³. The beauty of SI is that they're all identical. A volt is a J/C, an ampere is C/s, so V·A = J/C × C/s = J/s. This chain of definitions means you can derive any electrical quantity from mass, length, time, and current.

Never — they are exactly identical by definition, with zero rounding or conversion error. 1 J/s = 1 W, always. This is unlike, say, calories per second vs. watts, where a conversion factor (4.184) introduces potential rounding issues. The equivalence is definitional, not empirical. If someone claims a difference exists, they're confusing joules per second with some other energy-per-time unit like calories per second or BTU per hour.