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Ch.1 - Introduction: Matter, Energy, and Measurement
All textbooksBrown 14th EditionCh.1 - Introduction: Matter, Energy, and MeasurementProblem 78
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Chapter 1, Problem 78

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
1
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.
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