Minor typo correction made 20080401

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The United States consumes about 100 Q-BTU of energy per year while the total world consumes about 450 Q-BTU. But what is a Q-BTU or quadrillion British Thermal Units? This blog addresses this question.

British Thermal Units

British thermal units or BTU is defined as the amount of heat (meaning energy) required to be added to one pound of water to increase its temperature by one degree Fahrenheit. In the United States, it has remained as a common unit for expressing the energy release associated with fuels.

A quadrillion BTU is 1,000,000,000,000,000 BTU. This is written in scientific notation as 1 x 10^15 BTU. In this series, this is abbreviated as Q-BTU, instead of the abbreviation “quad” used by some, just to make sure that it is understood that BTU is being discussed.

For these discussions of America’s energy future, the Q-BTU is the unit used by the U.S. government to report and forecast energy consumption, as shown in Part 1 on this series (SA blog 15).

Work and power

To be useful, energy must be transformed through some mechanical means into work. Work performed in a period of time is power.

A human climbing stairs works to increase his or her potential energy. The amount of work performed is equal to person’s weight times the height climbed. Climbing two flights of stairs requires twice the work of climbing the first flight. The body’s muscles convert sugar (the energy source) into mechanical force that lifts the weight of the human.

The amount of power generated as the stairs are being climbed is the work performed divided by the time required. If the stairs are climbed twice as fast, then twice the power has been generated even though the total work performed was the same.

The U.S. consumes about 100 Q-BTU of energy, in all forms, per year. This is an expression of energy per unit of time, which is power. The common unit of power is the watt, named after James Watt.

One watt is defined as one joule of energy per second. To convert BTU per year into watts, as is done below, requires a conversion of BTU into the metric unit of energy – the joule. 1 BTU = 1055.056 joules. Hence, 1 BTU per second = 1055.056 joules per second or 1055.056 watts.

A person climbing stairs at a normal rate is expending about 200 watts of power or 200 joules per second.

When discussing electrical power, the common units in the U.S. are:

- Kilowatt (kW) = 1,000 watts

- Megawatt (MW) = 1,000,000 watts or 1,000 kW

- Gigawatt (GW) = 1,000,000,000 watts or 1,000 MW or 1,000,000 kW

Quadrillion BTU to Gigawatt conversions

- 1 Q-BTU (energy) = 1 x 10^15 BTUs x (1055.056 joules per BTU) = 1055.056 x 10^15 joules (energy)

- 1 Q-BTU of electricity produced per year (power) = 1055.056 x 10^15 joules per year / (365 days per year x 24 hours per day x 60 minutes per hour x 60 sec per minute) = 33.5 x 10^9 joules/sec or watts (power) = 33.5 x 10^6 kilowatts (kW) = 33.5 X 10^3 Megawatts (MW) = 33.5 Gigawatt (GW) of continuous production

Sustained electrical power generation

Electrical power generation is a sustained operation. To define the amount of power being continuously generated, the watt-hour is defined as one watt of power produced for one hour. This concept is also applied to yield kW-hour, MW-hour, and GW-hour with the kW-hour (or kW-hr) being the common unit for commercial power generation.

- 1 Q-BTU of electricity per year = 33.5 x 10^6 kW per year x (365 days per year x 24 hours per day) = 293.5 x 10^9 kW-hrs = 293,500 GW-hrs

Electrical power costs

Quite often comparisons of alternative forms of electrical power generation are made in terms of the cost per kW-hr.

- 1 Q-BTU of electricity per year = 293.5 x 10^9 kW-hr x $0.01 per kW-hr = $2.9 billion @ $0.01 per kW-hr

- 1 Q-BTU of electricity per year = 293.5 x 10^9 kW-hr x $0.075 per kW-hr = $22 billion @ the avg. U.S. retail electricity price of $0.075 per kW-hr

Comparisons of oil, coal, natural gas, and nuclear

Using the Q-BTU as the basis for comparison, the cost of these four energy sources can be estimated.

- 1 Q-BTU (oil) = 1 x 10^15 BTU / 5.8 x 10^6 BTU per barrel of oil = 172 million barrels

- 1 Q-BTU (oil) = 172 x 10^6 barrels x $100 per barrel (spot market price 20080220) = $17.2 billion

- 1 Q-BTU (coal) = 1 x 10^15 BTU / 22.4 x 10^6 BTU per short ton of coal = 44.6 million tons

- 1 Q-BTU (coal to produce electricity) = 44.6 million tons x $34.3 per ton (avg. 2006 price for electric utilities) / 0.35 (avg. plant generation efficiency) = $4.4 billion

- 1 Q-BTU (natural gas) = 1 x 10^15 BTU / 1031 BTU per cubic ft = 970 x 10^9 cubic ft of natural gas

- 1 Q-BTU (natural gas to produce electricity) = 970 x 10^9 cubic ft / 1000 x $7 per 10^3 cubic ft / 0.35 (avg. plant generation efficiency) = $19.4 billion

- 1 Q-BTU (uranium in the form U3O8 used to power nuclear reactors) = 1 x 10^15 BTU / 50 x 10^9 BTU per short ton of U3O8 = 20,000 short tons of U3O8

- 1 Q-BTU (U3O8 to produce electricity) = 20,000 short tons U3O8 x 2000 lb per short ton x $75 per lb of U3O8 (spot market price 20080220) / 0.35 (avg. plant conversion efficiency) = $8.6 billion