Skip to main content
Ch.1 - Chemical Tools: Experimentation & Measurement
Chapter 1, Problem 58d

Suppose you were dissatisfied with both Celsius and Fahrenheit units and wanted to design your own temperature scale based on ethyl alcohol (ethanol). On the Celsius scale, ethanol has a melting point of -117.3 °C and a boiling point of 78.5 °C, but on your new scale calibrated in units of degrees ethanol, °E, you define ethanol to melt at 0 °E and boil at 200 °E. (d) What is normal human body temperature (98.6 °F) on the ethanol scale?

Verified step by step guidance
1
Convert the normal human body temperature from Fahrenheit to Celsius using the formula: \( T_{\text{C}} = \frac{5}{9}(T_{\text{F}} - 32) \).
Identify the relationship between the Celsius scale and the ethanol scale. Ethanol melts at -117.3 °C (0 °E) and boils at 78.5 °C (200 °E).
Calculate the conversion factor between the Celsius and ethanol scales by finding the difference in temperature for both scales: \( 78.5 - (-117.3) \) °C corresponds to \( 200 - 0 \) °E.
Use the conversion factor to create a linear equation relating °C to °E: \( T_{\text{E}} = m(T_{\text{C}} - (-117.3)) \), where \( m \) is the conversion factor.
Substitute the Celsius temperature of the human body into the linear equation to find the temperature in degrees ethanol, °E.

Verified Solution

Video duration:
3m
This video solution was recommended by our tutors as helpful for the problem above.
Was this helpful?

Key Concepts

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

Temperature Scales

Temperature scales, such as Celsius and Fahrenheit, provide a way to quantify thermal energy. Each scale has defined reference points; for instance, the freezing and boiling points of water are 0 °C and 100 °C in Celsius, and 32 °F and 212 °F in Fahrenheit. Understanding how to convert between these scales is essential for solving temperature-related problems.
Recommended video:

Linear Interpolation

Linear interpolation is a mathematical method used to estimate unknown values that fall within a range of known values. In this context, it can be applied to convert temperatures from one scale to another by establishing a linear relationship between the defined points of the scales. For example, knowing the melting and boiling points of ethanol allows us to create a linear equation to find other temperatures.
Recommended video:
Guided course
01:37
Linear Form of Arrhenius Equation

Conversion Formulas

Conversion formulas are equations that allow for the transformation of values from one unit to another. In this case, to convert Fahrenheit to the new ethanol scale, one must first convert Fahrenheit to Celsius and then apply the linear relationship established for the ethanol scale. Understanding how to derive and apply these formulas is crucial for accurate temperature conversions.
Recommended video:
Guided course
01:56
Conversion Factors
Related Practice
Textbook Question
Tungsten, the element used to make filaments in light bulbs, has a melting point of 6192 °F. Convert this temperature to degrees Celsius and to kelvin.
1597
views
Textbook Question

Suppose you were dissatisfied with both Celsius and Fahrenheit units and wanted to design your own temperature scale based on ethyl alcohol (ethanol). On the Celsius scale, ethanol has a melting point of -117.3 °C and a boiling point of 78.5 °C, but on your new scale calibrated in units of degrees ethanol, °E, you define ethanol to melt at 0 °E and boil at 200 °E. (b) How does an ethanol degree compare in size with a Fahrenheit degree?

709
views
Textbook Question

Suppose you were dissatisfied with both Celsius and Fahrenheit units and wanted to design your own temperature scale based on ethyl alcohol (ethanol). On the Celsius scale, ethanol has a melting point of -117.3 °C and a boiling point of 78.5 °C, but on your new scale calibrated in units of degrees ethanol, °E, you define ethanol to melt at 0 °E and boil at 200 °E. (c) What are the melting and boiling points of water on the ethanol scale?

1555
views
Textbook Question

Suppose you were dissatisfied with both Celsius and Fahrenheit units and wanted to design your own temperature scale based on ethyl alcohol (ethanol). On the Celsius scale, ethanol has a melting point of -117.3 °C and a boiling point of 78.5 °C, but on your new scale calibrated in units of degrees ethanol, °E, you define ethanol to melt at 0 °E and boil at 200 °E. (e) If the outside thermometer reads 130 °E, how would you dress to go out?

514
views
Textbook Question
Sodium chloride has a melting point of 1074 K and a boil-ing point of 1686 K. Convert these temperatures to degrees Celsius and to degrees Fahrenheit.
1985
views
Textbook Question
A 125 mL sample of water at 293.2 K was heated for 8 min, 25 s so as to give a constant temperature increase of 3.0 °F/min. What is the final temperature of the water in degrees Celsius?
739
views
1
rank