Repeat Exercise 1, except choose the new temperature scale Q so that absolute zero is 0°Q and T_bp,_water - T_mp,_water = 100 Q° (a) What is the conversion formula from Celsius to Q? (b) What is T_bp,water water and T_mp,_water in Q? (c) This scale actually exists. What is the official name?

To tackle this question, we need to establish a temperature scale where absolute zero is defined as 0°Q and the difference between the boiling point and melting point of water is 100 Q°. This is similar to how the Celsius scale is structured, where 0°C is the melting point of ice and 100°C is the boiling point of water. Let's break this down step by step.

Conversion Formula from Celsius to Q

First, we need to derive the conversion formula from Celsius (°C) to our new temperature scale (°Q). We know that:

• Absolute zero (0 K) corresponds to -273.15°C.
• The boiling point of water (100°C) corresponds to 100 Q°.
• The melting point of water (0°C) corresponds to 0 Q°.

Given that the range from the melting point to the boiling point of water is 100°C in Celsius and 100 Q° in the new scale, we can set up the following linear relationship:

Let’s denote the temperature in Celsius as T_C and in the new scale as T_Q. The relationship can be expressed as:

T_Q = (T_C + 273.15) × (100 Q° / 100°C)

Thus, the conversion formula becomes:

T_Q = T_C + 273.15

Boiling and Melting Points of Water in Q

Next, we need to determine the boiling point (T_bp, water) and melting point (T_mp, water) of water in the Q scale:

• For T_mp, water: 0°C corresponds to 0 Q°.
• For T_bp, water: 100°C corresponds to 100 Q°.

Therefore:

• T_mp, water = 0 Q°
• T_bp, water = 100 Q°

Official Name of the Temperature Scale

This temperature scale is known as the Kelvin scale, which is widely used in scientific contexts. The Kelvin scale is an absolute temperature scale, starting at absolute zero (0 K), where 0 K is equivalent to -273.15°C. The scale increments are equivalent to those of Celsius, making it easy to convert between the two.

In summary, we derived the conversion formula from Celsius to Q as T_Q = T_C + 273.15, identified the boiling and melting points of water in Q as 100 Q° and 0 Q°, respectively, and recognized that this scale is officially known as the Kelvin scale. Understanding these relationships is crucial for working with temperature in scientific applications.