Question

Tick the correct relation (a) \(1 \mathrm{~J}=1 \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-2}\) (b) \(1 \mathrm{~J}=1 \mathrm{~kg} \mathrm{~m}^{2} \mathrm{~s}^{-2}\) (c) \(1 \mathrm{~J}=1 \mathrm{~kg} \mathrm{~m}^{2} \mathrm{~s}^{-1}\) (d) \(1 \mathrm{~J}=1 \mathrm{~kg} \mathrm{~m}^{3} \mathrm{~s}^{-1}\)

Short answer

(b) \(1 \mathrm{~J}=1 \mathrm{~kg} \mathrm{~m}^{2} \mathrm{~s}^{-2}\) is the correct answer.

Step-by-step solution

Retrieve definition of Joule

A Joule is the unit used to express energy, work, or the amount of heat. In SI base units, a Joule is defined as 1 kg·m²·s⁻². This means 1 Joule equals one kilogram meter squared per second squared.

Compare retrieved definition with options

Next, match the retrieved definition of Joule to the four options given in the exercise. The option that states \(1 \mathrm{~J}=1 \mathrm{~kg}\mathrm{~m}^{2} \mathrm{~s}^{-2}\) matches our retrieved definition.

Cross-check the remaining options

After finding the correct option, go through the other options for a quick cross-check. None of the other provided relations match the correct definition of Joule in base units.

Key concepts

Energy Unit Conversion

Understanding energy unit conversion is crucial for students delving into physics and engineering. Energy, the capacity to do work or produce heat, has several units depending on the context. The most common unit is the Joule (J), named after the English physicist James Prescott Joule. It's essential to note that energy can be expressed in various units like calories, kilowatt-hours, or British thermal units, depending on the type of energy measured.

For instance, when discussing electrical energy, we often convert Joules to kilowatt-hours, the typical billing unit for electricity. To convert Joules to kilowatt-hours, you would use the conversion factor of 1 kilowatt-hour being equal to 3.6 x 10^6 Joules. As such, a light bulb rated at 1000 Joules of electrical energy per second (1000 Watts) uses 1 kilowatt-hour after 3600 seconds (or one hour) of use.

Similarly, in the context of heat energy, you might encounter calories, especially when talking about food energy. One calorie is the amount of heat needed to raise the temperature of one gram of water by one degree Celsius. The conversion factor in this case is 1 calorie = 4.184 Joules. This shows that unit conversion is not only a mathematical exercise but also a way to contextualize energy according to its use.

SI Base Units

The Systeme International d'Unites (SI), or the International System of Units, provides a standard for measurements across the globe. This system is built on seven fundamental 'base units' from which all other units of measure can be derived. These base units include the meter (m) for length, the kilogram (kg) for mass, the second (s) for time, the ampere (A) for electric current, the kelvin (K) for temperature, the mole (mol) for the amount of substance, and the candela (cd) for luminous intensity.

In the realm of physics, these base units are used in tandem to describe an enormous range of measurements. For example, the Joule, which is the SI unit of energy, is derived from three base units: kilograms (kg), meters (m), and seconds (s). As shown in the exercise, the Joule is defined as the work done when an object is subjected to a force of one newton over a distance of one meter. In base units, this is expressed as kilograms times meters squared per second squared (kg·m²/s²).

The importance of SI base units cannot be overstated as they allow for universal comprehension and repeatability of scientific experiments. Without this standardization, collaboration and comparison of scientific work would be exceedingly difficult.

Work and Heat Measurement

The measurement of both work and heat is expressed in Joules within the International System of Units. Work is defined as the force applied to an object over the distance it moves, which is directly related to energy. If you push a book across a table with a force of one newton for a distance of one meter, you've done one Joule of work.

Heat measurement, on the other hand, quantifies the transfer of thermal energy. When energy is transferred from a hotter object to a cooler one, we often describe this energy transfer as heat. For example, heating a pot of water on a stove involves transferring heat from the stove to the water, and the amount of heat energy transferred can be measured in Joules.

Interestingly, work and heat are interchangeable under the right conditions due to their connection through the principle of conservation of energy. This means that any amount of work done can be fully converted into heat and vice versa. For example, when brakes stop a car, the kinetic energy of the car is converted into heat through the force of friction – this heat can then be measured in Joules. Understanding these measurements is fundamental to physics, as it encompasses the law of energy conservation, an essential principle governing the physical world.