Question

How many watts are in 1 gigawatt (GW)? a) \(10^{3}\) c) \(10^{9}\) e) \(10^{15}\) b) \(10^{6}\) d) \(10^{12}\)

Short answer

Answer: c) \(10^9\)

Step-by-step solution

Understand the meaning of watts and gigawatts.

Watt is the unit of power in the International System of Units (SI). One watt is equal to the power produced when one joule of energy is transferred per second. A gigawatt (GW) is a larger unit of power, with "giga-" representing one billion (1,000,000,000) watts.

Choose the correct conversion factor.

As we've understood that "giga-" means one billion, the correct conversion factor between watts and gigawatts is \(10^9\). This means that 1 GW is equal to \(10^9\) watts. Therefore, the correct answer is c) \(10^9\).

Key concepts

Power Units

When dealing with electricity and energy, it's fundamental to understand the concept of power units. The most basic unit of power as defined in the International System of Units (SI) is the watt, symbolized by 'W'. Power, in a scientific sense, is the rate at which energy is consumed or generated.

Power units help us quantify the amount of energy being transferred or used in a certain amount of time. To accommodate for different scales of power, we have multiples of watts such as kilowatts (kW), megawatts (MW), and gigawatts (GW). Each multiple is a power of ten larger than the one before. For example:

• 1 kilowatt (kW) = 1,000 watts (W) or \( 10^3 \) W.
• 1 megawatt (MW) = 1,000,000 watts (W) or \( 10^6 \) W.
• 1 gigawatt (GW) = 1,000,000,000 watts (W) or \( 10^9 \) W.

This scale allows for easy communication about power levels in various contexts like electrical power generation, the power rating of appliances, or even the power consumption of a country.

International System of Units

The International System of Units (SI) is the modern form of the metric system and is the most widely used system of measurement worldwide. It plays a crucial role in science and engineering by providing a standard that allows for clear and consistent communication of measurements.

SI comprises seven base units from which others are derived; these include the meter for length, kilogram for mass, second for time, and watt for power. Derived units are formed by combining these base units according to mathematical rules. For example, the watt is derived from the base units of kilograms, meters, and seconds.

The prefix 'giga' in gigawatts denotes a factor of \( 10^9 \), or one billion, which is consistent across all SI units. This prefix helps represent very large quantities of a given unit without having to use unwieldy numbers with many zeros, simplifying understanding and calculations.

Energy Transfer Rate

Understanding the energy transfer rate is pivotal when studying power units. The energy transfer rate is essentially what we are talking about when we mention power. In physical terms, it's the amount of energy that is moved, or transferred, from one system to another in a given time period.

This concept underlies the definition of the watt. As per the SI units, one watt equates to a transfer of one joule of energy per second. A joule is a measurement of energy in itself. So when we say a lightbulb is 60 watts, we mean it transfers 60 joules of energy per second from the electrical circuit to light and heat.

Large energy transfer rates are often discussed in terms of gigawatts in the context of power plants or nationwide energy consumption. This facilitates practical understanding of big-scale energy generation and consumption in a way that is quantifiable and comparable, crucial for everything from engineering to environmental policy-making.