Understanding Temperature Scales: Converting 200°C to Other Units

If you have a specific temperature scale with freezing and boiling points of water clearly marked, the challenge is to determine the value of 200°C in that scale. However, the problem as stated does not provide the reference points, making it impossible to solve directly. Therefore, let's derive a general method for converting temperatures from Celsius to other scales.

What is Temperature?

Temperature is a measure of the average kinetic energy of the particles in a substance. Different scales exist for measuring temperature, with the most common being Celsius (°C), Fahrenheit (°F), and Kelvin (K).

Converting 200°C to Other Units

To successfully convert 200°C to another unit, you need to know the freezing and boiling points of water in the new scale. Let's go through the process step-by-step.

Step 1: Understand the Reference Points

The freezing point of water is 0°C and the boiling point is 100°C in the Celsius scale. In a hypothetical new scale, these points are indicated as:

Freezing point: (X)Boiling point: (Y)

With these points, you can determine the scale of the new temperature system.

Step 2: Use the Linear Formula for Conversion

The linear formula for converting temperatures between two scales is:

[T_{text{new}} a times T_{text{C}} b]

Where (T_{text{C}}) is the temperature in Celsius, and (T_{text{new}}) is the temperature in the new scale.

Given the freezing and boiling points in the new scale, we can solve for (a) and (b).

Step 3: Solve for the Constants

Let's assume the freezing point in the new scale is 32 (Fahrenheit) and the boiling point is 212 (Fahrenheit). Given these points, we can set up the following equations:

32 (a times 0 b)212 (a times 100 b)

From the first equation, we get (b 32).

Substituting (b 32) into the second equation:

212 (100a 32)

Solving for (a):

180 100a

(a 1.8)

Thus, the conversion formula from Celsius to Fahrenheit is:

[T_{text{F}} 1.8 times T_{text{C}} 32]

To convert 200°C to Fahrenheit, substitute (T_{text{C}} 200):

[T_{text{F}} 1.8 times 200 32 360 32 392°F]

Step 4: Convert Celsius to Kelvin

In the Kelvin scale, the freezing point of water is 273.15K and the boiling point is 373.15K. The conversion formula from Celsius to Kelvin is simpler:

[T_{text{K}} T_{text{C}} 273.15]

Converting 200°C to Kelvin:

[T_{text{K}} 200 273.15 473.15K]

Understanding the Context and Solving the Problem

The problem statement mentions "indicated below," which usually refers to a reference point or chart. If you have such a reference point, you can follow a similar process to derive the conversion formulas.

The general method involves using the freezing and boiling points to set up a system of equations for the new scale. Once you have these, you can convert any temperature from Celsius to the desired scale.

Conclusion

Temperatures can be converted between different scales using linear equations based on the freezing and boiling points of water. For 200°C, the conversions to Fahrenheit and Kelvin are 392°F and 473.15K, respectively. Always ensure you have the appropriate reference points to solve these problems accurately.

Keywords

Temperature conversion, Celsius to Fahrenheit, Celsius to Kelvin