Question

The temperature of a substance increases by \(27^{\circ} \mathrm{C}\) What is the value of this increase of Kelvin scale? (A) \(300 \mathrm{~K}\) (B) \(2-46 \mathrm{~K}\) (C) \(7 \mathrm{~K}\) (D) \(27 \mathrm{~K}\)

Short answer

The value of the temperature increase on the Kelvin scale is \(27 \mathrm{~K}\).

Step-by-step solution

Understand the relationship between Celsius and Kelvin scales

The Celsius and Kelvin scales have the same interval or "size" between their degrees. The difference between them is that the Kelvin scale starts at absolute zero (-273.15°C), while the Celsius scale starts at the freezing point of water (0°C).

Convert the temperature increase from Celsius to Kelvin

Since both Celsius and Kelvin scales have the same interval, a temperature change of 27°C is equal to a temperature change of 27K.

Identify the correct answer

Comparing our result with the given options, we can see that the correct answer is: (D) \(27 \mathrm{~K}\)

Key concepts

Celsius to Kelvin

Converting temperatures from Celsius to Kelvin is a straightforward process, as they both measure temperature increments similarly. The fundamental distinction is their starting points. Celsius begins at the freezing point of water, which is 0°C, while Kelvin starts from absolute zero, the lowest possible temperature where particles have minimal motion. This is defined as 0 K.

The conversion formula from Celsius to Kelvin is simple:

• Add 273.15 to the Celsius temperature to get Kelvin.

For example, if you have a temperature increase of 27°C, as in the exercise, this change is exactly equivalent to a 27 K increase because the interval between degrees is the same for both scales.

This consistency in degree size is precisely why switching between Celsius and Kelvin for temperature changes is so seamless. It's a handy fact when solving temperature-related problems in physics and chemistry.

Temperature Scales

Temperature scales help us measure how hot or cold a system is. These scales are essential in various scientific measurements and daily life.

The three main temperature scales you'll encounter are:

• Celsius (°C): Often used worldwide, the Celsius scale is based on the freezing and boiling points of water at 0°C and 100°C, respectively.
• Kelvin (K): Primarily used in scientific contexts, Kelvin starts at absolute zero, ensuring no negative temperatures within its range. It uses the same interval size as Celsius but shifts the scale by 273.15 units.
• Fahrenheit (°F): Common in the United States, this scale sets the freezing point of water at 32°F and boiling at 212°F.

Each temperature scale has its specific context and usage.

In scientific research, particularly in physics and chemistry, Kelvin is preferred because it ties directly into thermodynamics with absolute zero as its base. Understanding these scales is crucial, as they provide the context needed for interpreting temperature changes and maintaining accuracy in scientific experiments.

Absolute Zero

Absolute zero is a theoretical temperature where particles possess minimal thermal energy, practically no motion at all. It's the coldest limit of the thermodynamic temperature scale and is measured as 0 K on the Kelvin scale.

On the Celsius scale, absolute zero is expressed as -273.15°C. This fundamental thermodynamic anchor signifies a point where entropy reaches its minimum value, which is crucial in quantum mechanics and statistical mechanics.

Absolute zero is significant because it represents a boundary condition for several scientific laws and theories:

• At absolute zero, a system has minimal internal energy.
• There are no thermal vibrations of particles.
• Experiments near absolute zero have led to the discovery of phenomena like superconductivity and Bose-Einstein condensation.

While achieving absolute zero is theoretically impossible due to the third law of thermodynamics, scientists can approach it very closely with advanced cooling techniques. Understanding absolute zero is vital in grasping the principles of energy distribution in a system and has profound implications in fields such as cryogenics and material science.