Problem 103 - General Chemistry: Principles and Modern Applications

Question

The highest temperature of the following group is (a) \(217 \mathrm{K} ;\) (b) \(273 \mathrm{K} ;\) (c) \(217^{\circ} \mathrm{F} ;\) (d) \(105^{\circ} \mathrm{C} ;\) (e) \(373 \mathrm{K}\).

Step-by-Step Solution

Answer

The highest temperature given in the exercise is \(105^{\circ} \mathrm{C}\), which is equivalent to \(378 \mathrm{K}\).

Step 1: Convert Kelvin to Celsius

Keep temperatures in Kelvin as is, as it's the SI unit for temperature. So, \(217 \mathrm{K}\) remains \(217 \mathrm{K}\) and \(273 \mathrm{K}\) remains \(273 \mathrm{K}\) and \(373 \mathrm{K}\) remains \(373 \mathrm{K}\). These will be compared with the Celsius and Fahrenheit readings once those are converted to Kelvin units.

Step 2: Convert Fahrenheit to Kelvin

Convert \(217^{\circ} \mathrm{F}\) to Kelvin using the formula \( K = \frac{5}{9}(F - 32) + 273 \). This gives \( K = \frac{5}{9}(217 - 32) + 273 \approx 373.6 \mathrm{K} \).

Step 3: Convert Celsius to Kelvin

Convert \(105^{\circ} \mathrm{C}\) to Kelvin by using the formula \( K = C + 273 \). This gives \( K = 105 + 273 = 378 \mathrm{K} \).

Step 4: Compare all temperatures in Kelvin

Compare all temperatures: \(217 \mathrm{K}\), \(273 \mathrm{K}\), \(373.6 \mathrm{K}\), \(378 \mathrm{K}\) and \(373 \mathrm{K}\). Even though all values are close, the highest is \(378 \mathrm{K} \), which was initially given as \(105^{\circ} \mathrm{C}\).

Key Concepts

Kelvin

Kelvin is the base unit of temperature in the International System of Units (SI). It is named after the physicist Lord Kelvin. The Kelvin scale is an absolute temperature scale, and it starts from absolute zero. Absolute zero is the theoretical point where all thermal motion ceases. This makes Kelvin unique because it doesn't involve negative numbers, providing a clear measure from zero upwards.
One Kelvin is equal to one degree Celsius in terms of energy change, as both scales increase at the same rate, but their starting points are different. To convert Kelvin to Celsius, subtract 273 from the Kelvin temperature:

• For example, 373 K becomes 100°C because 373 - 273 equals 100 degrees Celsius.

Celsius

Celsius is a temperature scale used and understood worldwide. Named after the Swedish astronomer Anders Celsius, it is based on the properties of water, with 0 degrees Celsius set as the freezing point and 100 degrees Celsius as the boiling point of water at standard atmospheric pressure.
Unlike Kelvin, Celsius is not used for scientific computations where absolute zero calculations are needed, because it can go into negative numbers. Importantly, Celsius can be converted to Kelvin by just adding 273. Hence,

• Example: 105°C becomes 378K (105 + 273 = 378).

This conversion makes it handy for scientific work when absolute measurements are necessary.

Fahrenheit

Fahrenheit is mostly used in the United States. This scale, proposed by Daniel Gabriel Fahrenheit, sets the freezing point of water at 32°F and boils at 212°F under standard conditions. The Fahrenheit scale creates smaller degrees than both Celsius and Kelvin, making its increments tighter.
Converting Fahrenheit to either Celsius or Kelvin requires careful calculation. For conversion to Kelvin, you first convert Fahrenheit to Celsius, then Celsius to Kelvin. The formula involves these steps:

• Convert to Celsius: Subtract 32 from the Fahrenheit value, multiply by 5, and then divide by 9.
• Convert to Kelvin: Add 273 to the resultant Celsius figure.

For instance, 217°F translates to approximately 373.6K using this two-step conversion.

SI units

SI units, or the International System of Units, form the global standard for measurement. The use of SI units ensures consistency and clarity in scientific data across different regions and disciplines.
Temperature in SI units is measured in Kelvin, a choice grounded in the need for an absolute scale where zero represents a complete lack of thermal energy. Using SI units allows scientists and engineers consistent communication and the ability to predict physical behavior universally.
Adopting the Kelvin scale in scientific research is crucial because it aligns with real-world physical laws and constants, making exactness and precision much easier to achieve.