On a new Jekyll temperature scale, water freezes at 17 °J and boils at 97 °J. On another new temperature scale, the Hyde scale, water freezes at 0 °H and boils at 120 °H. If methyl alcohol boils at 84 °H, what is its boiling point on the Jekyll scale?

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Identify the freezing and boiling points of water on both the Jekyll and Hyde scales: Jekyll (17 °J, 97 °J) and Hyde (0 °H, 120 °H).

Determine the range of temperatures for each scale: Jekyll range is 97 °J - 17 °J, and Hyde range is 120 °H - 0 °H.

Calculate the conversion factor between the two scales by dividing the range of the Jekyll scale by the range of the Hyde scale.

Use the conversion factor to convert the boiling point of methyl alcohol from the Hyde scale (84 °H) to the Jekyll scale.

Add the freezing point of the Jekyll scale (17 °J) to the converted temperature to find the boiling point of methyl alcohol on the Jekyll scale.

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주요 개념

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Temperature Scales

Temperature scales, such as Celsius, Fahrenheit, and Kelvin, provide a way to measure thermal energy. Each scale has specific reference points, like the freezing and boiling points of water, which are used to define the scale. Understanding how to convert between different temperature scales is essential for solving problems involving temperature.

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 find the equivalent temperature on one scale based on known temperatures on another scale. This technique is crucial for converting temperatures between the Jekyll and Hyde scales.

Boiling Point of Substances

The boiling point of a substance is the temperature at which it transitions from a liquid to a gas. This property varies depending on the substance and the pressure conditions. Knowing the boiling point of methyl alcohol on the Hyde scale is necessary to determine its corresponding boiling point on the Jekyll scale through conversion.