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 -44.14 C and a boiling point of 337.82 C.

Question

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 -44.14 C and a boiling point of 337.82 C. What is the range of temperatures in degrees Fahrenheit for which this substance is not in a liquid​ state? (Hint: C=5/9(F−32) Express the range as an inequality.

Let x represent the temperature in degrees Fahrenheit. What is the range of temperatures for which this substance is not in a liquid​ state?

​(Type an inequality or a compound inequality. Simplify your answer. Use integers or decimals for any numbers in the expression. Round to three decimal places as​ needed.)

Answer 1

melting= -44.14C

boiling= 337.82C

-44.14C <liquid< 337.82C

C=5/9 (F-32)

We have to solve two equations, one for melting and one for boiling, by plugging in their values instead of C in the formula C=5/9 (F-32), and then express it as an inequality: melting in F < x < boiling in F.

for melting:

-44.14=5/9 (F - 32) distribute

-44.14=5/9 F - 160/9 multiply both sides by 9

-397.26= 5F - 160 add 160 on both sides

-237.26=5F divide both sides by 5

-47.452= F

F= -47.452

for boiling:

337.82=5/9 (F - 32) distribute

337.82=5/9 F - 160/9 multiply both sides by 9

3040.38= 5F - 160 add 160 on both sides

3200.38=5F divide both sides by 5

640.076= F

F= 640.076

Final result, expressed as the inequality from above:

-47.452F < x < 640.076F

Answer 2

So Kassidi F.,

Interestingly phrased question. You should be able to figure out that the substance is a solid from 0K to (273.15-44.14)K and a gas from (337.82+273.15) K on upwards. But (assuming you can convert to degrees F by multiplying degrees C ranges by 9/5), how can you set a minimum bound on that range set? And, WHY WOULD THE MINIMUM RANGE THEN NOT BE INFINITE?

Now you get to the nitty-gritty! Since it does have a melting point, and the solid is more stable than a liquid, you definitely have the solid range as a minimum. But, what to do about the gaseous range?

Here's why the solid range is your answer. After a substance vaporizes, it may start to decompose at some higher temperature. But you don't know what that higher temperature is (or how to interpret decomposition rates, even if some are supplied)! But, the *conservative* estimation of it is, it starts to decompose at the vaporization temperature.

It's of note that not all solids can be melted successfully to liquids, either. Some things may sublime instead at normal pressure, or a solid may start to decompose as it approaches a melting point -- either to a different solid crystal structure, or into decomposition byproducts. This is not uncommon for organic materials (think of sugar caramelizing in a fry pan), and in order to set a "melting point" for such materials, they must be rapidly heated through the melting point. It may even be necessary to detect the melting point instrumentally (by differential scanning calorimetry, and computer calculations) rather than visually.

-- Cheers, --Mr. d.