Suppose you decide to define your own temperature scale with units of O, using the freezing point 113 _x001F_C2 and boiling point 1360 _x001F_C2 of oleic acid, the main component of olive oil. If you set the freezing point of oleic acid as 0 _x001F_O and the boiling point as 100 _x001F_O, what is the freezing point of water on this new scale?

Verified step by step guidance

Step 1: Understand the problem by identifying the freezing and boiling points of oleic acid in Celsius, which are 13°C and 360°C, respectively.

Step 2: Recognize that the new temperature scale (O) sets the freezing point of oleic acid at 0°O and the boiling point at 100°O.

Step 3: Establish a linear relationship between the Celsius scale and the new O scale using the formula: O = a * C + b, where C is the temperature in Celsius, and O is the temperature in the new scale.

Step 4: Use the given points to set up two equations: 0 = a * 13 + b and 100 = a * 360 + b. Solve these equations to find the values of a and b.

Step 5: Once you have the values of a and b, use the formula to convert the freezing point of water (0°C) to the new O scale.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Temperature Scales

Temperature scales are systems for measuring thermal energy, with common examples being Celsius, Fahrenheit, and Kelvin. Each scale has defined reference points, such as the freezing and boiling points of water. Understanding how to convert between different temperature scales is essential for solving problems involving temperature measurements.

Linear Interpolation

Linear interpolation is a mathematical method used to estimate unknown values that fall within a range of known values. In the context of temperature scales, it allows us to determine the equivalent temperature on a new scale by establishing a linear relationship between the known freezing and boiling points of two substances. This concept is crucial for converting temperatures accurately.

Freezing and Boiling Points of Substances

The freezing and boiling points of a substance are the temperatures at which it changes state from solid to liquid and from liquid to gas, respectively. For water, these points are 0°C and 100°C under standard atmospheric pressure. Knowing the freezing and boiling points of oleic acid is necessary to establish the new temperature scale and to find the corresponding freezing point of water.

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