Problem 18 - Chemistry and Chemical Reactivity

Question

The temperature on the surface of the sun is \(5.5 \times 10^{3}\) ' \(\mathrm{C}\) What is this temperature in kelvins?

Step-by-Step Solution

Answer

The temperature is approximately 5523.15 K.

Step 1: Understanding the Problem

We are given a temperature in degrees Celsius and need to convert it to kelvins. The problem provides the temperature as \(5.5 \times 10^{3}\) °C.

Step 2: Recalling the Conversion Formula

The formula to convert Celsius to kelvin is \(K = °C + 273.15\), where \(K\) is the temperature in kelvin and \(°C\) is the temperature in Celsius.

Step 3: Applying the Conversion Formula

Using the given Celsius temperature, substitute \(5.5 \times 10^{3}\) for \(°C\) in the formula: \(K = 5.5 \times 10^{3} + 273.15\).

Step 4: Performing the Addition

Calculate the sum: \(5.5 \times 10^{3} + 273.15 = 5.5 \times 10^{3} + 273.15 = 5523.15\).

Step 5: Result Interpretation

Now that the conversion is complete, the temperature on the sun's surface is approximately \(5523.15\) kelvin.

Key Concepts

Celsius to Kelvin Conversion

Temperature conversion is a common task in both mathematics and science, especially when dealing with different temperature scales like Celsius and Kelvin. The formula to convert a temperature from Celsius (\(^{\circ}\text{C}\)) to Kelvin (\(\text{K}\)) is straightforward:

• Formally, it is written as: \[ K = ^{\circ}\text{C} + 273.15 \].
• This formula arises because the Kelvin scale is an absolute temperature scale based on absolute zero, which is \(-273.15^{\circ}\text{C}\) on the Celsius scale.

When converting, simply add \(273.15\) to the Celsius value and you have the equivalent temperature in Kelvin. For example, if the surface temperature of the sun is given as \(5.5 \times 10^{3} \ ^{\circ}\text{C}\), you add \(273.15\) to get \(5523.15 \ \text{K}\). This conversion is essential in scientific disciplines like astronomy and physics, where Kelvin is typically the standard unit of temperature.

Surface Temperature of the Sun

The surface temperature of the sun is a fascinating topic in astronomy. It is measured in degrees Celsius but often discussed in Kelvin for scientific applications. The typical surface temperature is around \(5500 \ ^{\circ}\text{C}\) or after conversion using the formula, approximately \(5773 \ \text{K}\).

• This temperature results from nuclear fusion reactions at the sun's core.
• These reactions release immense amounts of energy, warming the sun and producing its characteristic glow.

Understanding the sun's temperature helps astronomers learn about stellar dynamics and energy processes. It also provides insights into other stars and the life cycle of stars.

Unit Conversion in Chemistry

In chemistry, being able to convert units seamlessly is vital for problem solving. Chemists often switch between units depending on the context of their work:

• Temperature conversions often involve switching between Celsius, Kelvin, and sometimes Fahrenheit.
• Units of measurement such as moles, liters, and grams are also converted using standard formulas and conversion factors.
• For example, in thermodynamics, temperatures are frequently converted to Kelvin since many equations, like those in gas law calculations, require temperature in Kelvin to produce accurate results.

Learning unit conversions ensures accuracy and consistency in scientific experiments and data analysis. This skill is especially critical in fields like pharmacology, environmental science, and chemical engineering. It allows scientists to communicate their findings effectively and guarantees that conclusions are based on reliable data. Mastering this skill involves understanding basic conversion principles and practicing with different problems.