Question

Which of the following can be thought of as conversion factors? (a) \(49.3 \mathrm{~kg}\) (b) \(4.184 \mathrm{j} /{ }^{\circ} \mathrm{C}\) (c) 350 miles \(/ \mathrm{h}\) (d) 12 eggs per dozen (c) 1 dozen grams

Short answer

Options (b) \(4.184 \mathrm{J}/^{\circ}\mathrm{C}\) and (d) 12 eggs per dozen are conversion factors, as they have a ratio between two different units that can be used to convert from one unit of measurement to another.

Step-by-step solution

Option (a) 49.3 kg

49.3 kg is an amount of mass in kilograms, not a conversion factor because it does not have a ratio between two different units.

Option (b) 4.184 J/\(^\circ\)C

This is a conversion factor for the specific heat capacity of water. It tells us how much energy is needed to raise the temperature of water by 1 degree Celsius. It has a ratio between two different units, Joules and degrees Celsius, so this can be considered as a conversion factor.

Option (c) 350 miles/h

350 miles/h is a measurement of speed, not a conversion factor. There isn't a ratio between two different units here, it only tells us the distance traveled in a certain amount of time.

Option (d) 12 eggs per dozen

This option is a conversion factor since it relates two different units: eggs and dozens. It tells us how many eggs make up a dozen, which is useful to convert between these units.

Option (e) 1 dozen grams

This option is not a conversion factor because it does not have a ratio between two different units, it's just a quantity of grams (incorrectly) labelled as "dozen". In conclusion, options (b) and (d) can be considered as conversion factors.

Key concepts

Specific Heat Capacity

Specific heat capacity is a property of a material that tells us how much energy is required to change its temperature. More precisely, it refers to the amount of heat needed to raise the temperature of 1 kilogram of a substance by 1 degree Celsius. This is measured in units of joules per kilogram per degree Celsius, or J/kg°C.

To make this concept easier, imagine you're heating up water for tea. Water has a high specific heat capacity. This means it takes a lot of energy to increase its temperature, which is why it takes time for water to boil.

Understanding specific heat capacity is crucial in many fields, such as cooking, where it helps in knowing how long it will take to heat or cool a food item. Engineers and scientists use it to compare the thermal properties of different materials.

Units Conversion

Units conversion is the process of changing one set of measurement units to another. It's like translating words from one language to another, but for numbers and measurements. This process is essential when dealing with different systems of measurement, such as converting miles to kilometers or ounces to grams.

The key to a successful units conversion is knowing the correct conversion factor. A conversion factor is a numerical value used to multiply or divide a quantity when changing from one unit to another. This factor is usually represented as a ratio, such as 1 inch = 2.54 centimeters.

When converting units, always ensure the units you are converting from and to are compatible. Also, make sure to cancel out the original units for accuracy in the final result. Conversion is crucial in science, engineering, and everyday calculations to ensure clarity and accuracy across different measurement systems.

Mass and Weight

Mass and weight are two distinct concepts that are often confused. Mass measures the amount of matter in an object and is usually always the same, regardless of where you are in the universe. The unit of mass is kilograms, or grams in the metric system.

Weight, on the other hand, is the force exerted by gravity on that object. It's a vector quantity and can change depending on the gravitational field strength. For instance, your weight on Earth differs from your weight on the Moon due to different gravitational forces. Weight is measured in newtons in the metric system.

Understanding the difference is important, especially in scientific calculations where mass remains constant but weight can vary depending on location. It helps avoid confusion and ensures precision, particularly in physics and engineering.

Speed Measurement

Speed measurement tells us how fast something is moving. It is calculated as the distance traveled divided by the time taken to travel that distance. The most common units of speed are meters per second (m/s) and miles per hour (mph).

Speed is a scalar quantity, which means it only has magnitude and no direction. To measure the speed of an object accurately, knowing both the distance it travels and the time taken is crucial.

Speed can vary according to the context, with different situations requiring different methods of measurement. For example, cars usually have their speed measured in miles per hour in some countries, while in others, kilometers per hour is preferred. Measurement of speed is vital in sports, transportation, and safety assessments to ensure efficiency, reliability, and safety in various activities.