Question

Use the formulas for converting degrees Celsius into kelvins to determine the relative size of the Celsius degree over kelvins.

Short answer

A Celsius degree has the same relative size as one kelvin.

Step-by-step solution

Understand the Conversion Formula

The conversion between degrees Celsius (°C) and kelvins (K) is given by the formula: \[ K = °C + 273.15 \] This tells us that to convert temperatures from Celsius to kelvins, we add 273.15 to the Celsius temperature.

Identify the Relative Size Concept

The relative size of the Celsius degree compared to the Kelvin is determined by comparing the unit change in each scale. This essentially means we'll compare how a change of 1°C compares to a change of 1 K.

Compare Unit Changes

If the temperature in Celsius changes by 1 degree, that is:\[ (K = °C + 1) \] and applying the conversion:\[ K = (°C + 1) + 273.15 = °C + 273.15 + 1 = °C + 274.15 \] In the Kelvin scale, a change of 1 degree Celsius corresponds to a change of 1 K. Therefore, both scales increase or decrease by the same unit measure.

Conclude the Relative Size

Thus, given that a change of 1°C is identical to a change of 1 K in magnitude, each degree on the Celsius scale corresponds exactly to one kelvin. Therefore, the relative size of a degree on the Celsius scale is equal to that of one kelvin.

Key concepts

Celsius to Kelvin conversion

To convert Celsius to Kelvin, we use a simple and straightforward formula. The Kelvin scale is an absolute temperature scale and has its zero point at absolute zero, the point where molecular motion stops. Here's the conversion formula:

• \[K = °C + 273.15\]

This equation tells us that to find the Kelvin equivalent of a temperature in degrees Celsius, we simply add 273.15 to the Celsius temperature.

For example, if you have a temperature of 25°C and want to convert it to Kelvin, you apply the formula: \[25 + 273.15 = 298.15 \text{ K}\].

The Kelvin scale is particularly convenient in scientific calculations because it starts at absolute zero, meaning there are no negative numbers to work with.

temperature scales comparison

Understanding how temperature scales compare is crucial for temperature conversion.

In most scientific settings, the Kelvin and Celsius scales are employed. These scales increase incrementally by the same amount, meaning that a change of 1 degree Celsius is equivalent to a change of 1 kelvin.

The defining difference between these two scales is their starting points. The Celsius scale is based on the freezing and boiling points of water, 0°C and 100°C, respectively.

• K: Absolute zero starts at 0 K
• °C: Zero degrees is the freezing point of water

While the Kelvin scale starts at 0, representing absolute zero, the Celsius scale's zero is the point where water freezes at sea level.

Another common scale is Fahrenheit, used mainly in the United States, which has different value increments and starting points. But Kelvin and Celsius are directly related, making the conversion simple and intuitive.

unit conversion in chemistry

In chemistry, unit conversion is fundamental for calculations involving temperature, volume, pressure, and other measurements. Understanding how to convert between different units is essential for conducting accurate experiments and interpreting data.

Temperature conversions often come up in chemical equations and thermodynamic calculations. The precise conversion between Celsius and Kelvin is critical because many scientific equations require temperatures in Kelvin due to its absolute nature.

• Kinetic energy, \[E_k\], is dependent on temperature in Kelvin
• Equilibrium constants often require Kelvin to calculate accurately

It's important to familiarize yourself with common unit conversions, such as

• meters to centimeters,
• liters to milliliters, and
• kilograms to grams.

Being comfortable with these conversions ensures that you can handle more complicated calculations with confidence.