Math Problem Statement

Matter is in a liquid state when its temperature is between its melting point and its boiling point. Suppose that some substance has a melting point of

negative 48.36 degrees Upper C−48.36°C

and a boiling point of

306.17 degrees Upper C306.17°C.

What is the range of temperatures in degrees Fahrenheit for which this substance is not in a liquid​ state?

Solution

To determine the range of temperatures in degrees Fahrenheit for which the substance is not in a liquid state, we first need to convert the melting point and boiling point from degrees Celsius to degrees Fahrenheit.

The formula for converting Celsius to Fahrenheit is:

F=(95×C)+32F = \left(\frac{9}{5} \times C\right) + 32

Step 1: Convert the melting point to Fahrenheit

The melting point is 48.36C-48.36^\circ C.

Fmelting=(95×48.36)+32F_{\text{melting}} = \left(\frac{9}{5} \times -48.36\right) + 32

Fmelting=(87.048)+32=55.048FF_{\text{melting}} = \left(-87.048\right) + 32 = -55.048^\circ F

Step 2: Convert the boiling point to Fahrenheit

The boiling point is 306.17C306.17^\circ C.

Fboiling=(95×306.17)+32F_{\text{boiling}} = \left(\frac{9}{5} \times 306.17\right) + 32

Fboiling=551.106+32=583.106FF_{\text{boiling}} = 551.106 + 32 = 583.106^\circ F

Step 3: Determine the range of temperatures for which the substance is not in a liquid state

The substance is in a liquid state between 55.048F-55.048^\circ F and 583.106F583.106^\circ F. Therefore, the substance is not in a liquid state at temperatures below 55.048F-55.048^\circ F or above 583.106F583.106^\circ F.

Answer:

The range of temperatures in degrees Fahrenheit for which the substance is not in a liquid state is:

Temperature <55.048ForTemperature >583.106F\text{Temperature } < -55.048^\circ F \quad \text{or} \quad \text{Temperature } > 583.106^\circ F

Would you like more details or have any questions?

Here are five related questions to explore further:

  1. How do we convert temperatures from Fahrenheit to Celsius?
  2. What would be the temperature in Kelvin at the boiling point?
  3. If the substance's boiling point changed to 400°C, what would the new temperature range in Fahrenheit be?
  4. How does pressure affect the boiling point and melting point of a substance?
  5. What happens to the physical state of a substance at temperatures between its melting point and boiling point?

Tip: Understanding temperature conversions is crucial when working with scientific data, especially when dealing with different measurement systems.

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Math Problem Analysis

Mathematical Concepts

Temperature conversions
Scientific measurement systems

Formulas

Celsius to Fahrenheit conversion: F = (9/5 * C) + 32

Theorems

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Suitable Grade Level

Advanced High School