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Hydrogen becomes a liquid at \(20.27 \mathrm{~K}\). What is this temperature in (a) \({ }^{\circ} \mathrm{C}\) ? (b) \({ }^{\circ} \mathrm{F}\) ?

Short Answer

Expert verified
20.27 K is -252.88 °C and -423.18 °F.

Step by step solution

01

Convert Kelvin to Celsius

The formula to convert Kelvin to Celsius is \text{°C} = K - 273.15. Here, K is 20.27 K.So,\[ \text{°C} = 20.27 - 273.15 \]\[ \text{°C} = -252.88 \]
02

Convert Celsius to Fahrenheit

The formula to convert Celsius to Fahrenheit is \text{°F} = (\text{°C} \times \frac{9}{5}) + 32. Using °C = -252.88:\[ \text{°F} = (-252.88 \times \frac{9}{5}) + 32 \]\[ \text{°F} = -423.18 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Kelvin to Celsius
When converting temperatures from the Kelvin scale to the Celsius scale, the formula is quite straightforward: \[ \text{°C} = \text{K} - 273.15 \]
Kelvin is an absolute temperature scale, meaning it starts from absolute zero, the lowest temperature theoretically possible.
To convert a Kelvin temperature to Celsius, subtract 273.15 from the Kelvin value.
For Hydrogen, which becomes a liquid at 20.27 K, the conversion would be:
\[ \text{°C} = 20.27 \text{~K} - 273.15 = -252.88 \text{~°C} \]
So, 20.27 K is equivalent to -252.88 °C.
Celsius to Fahrenheit
To convert temperatures from the Celsius scale to the Fahrenheit scale, use the formula: \[ \text{°F} = (\text{°C} \times \frac{9}{5}) + 32 \]
This formula first multiplies the Celsius temperature by 9/5 to adjust the scale, then adds 32 to shift the temperature to the Fahrenheit scale.
Using the Celsius temperature of -252.88 °C, we convert it as follows:
\[ \text{°F} = (-252.88 \times \frac{9}{5}) + 32 = -423.18 \text{~°F} \]
So, -252.88 °C is equivalent to -423.18 °F. This shows the much lower perception of the same temperature in different scales.
Temperature Scales
Understanding different temperature scales helps in various scientific and daily applications.
Let's briefly go over the three commonly used scales: Kelvin, Celsius, and Fahrenheit.

**Kelvin Scale**
- The Kelvin scale is an absolute temperature scale starting from absolute zero (0 K).
- It is mainly used in scientific contexts.

**Celsius Scale**
- The Celsius scale, based on water's freezing (0 °C) and boiling points (100 °C) under standard atmospheric pressure, is widely used in most of the world.
- It is part of the metric system.

**Fahrenheit Scale**
- The Fahrenheit scale, used primarily in the United States, defines 32 °F as the freezing point and 212 °F as the boiling point of water.
- Each degree Fahrenheit is an increment of 1/180th of the difference between the freezing and boiling points of water under standard conditions.

Understanding these scales and how to convert between them assists students in grasping how temperature is measured and compared globally.

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Most popular questions from this chapter

A recipe calls for heating the oven to \(425^{\circ} \mathrm{F}\). If you are vacationing in Europe and the oven only has temperature marked in \({ }^{\circ} \mathrm{C}\), to what temperature do you preheat the oven? What is this temperature in \(\mathrm{K}\) ?

A Mexican restaurant has the reputation of serving the hottest salsa in town. In order to maintain this standard, the restaurant must use a minimum of \(8.41 \%\) by mass of cayenne pepper. If the restaurant just received a \(3.26-\mathrm{kg}\) shipment of cayenne pepper, how many pounds of salsa can it make?

A solution is prepared by dissolving \(283.4\) grams of potassium dichromate in \(650.0\) grams of water. (a) What is the percent potassium dichromate in the solution? (b) If 275 . grams of the solution are poured into a beaker, how many grams of potassium dichromate are introduced into the beaker? (c) How many grams of the solution are required to obtain \(15.0\) grams of potassium dichromate?

As a solid substance is heated, its volume increases, but its mass remains the same. Sketch a graph of density versus temperature showing the trend you expect. Briefly explain.

U.S. quarters are composed of \(91.67 \%\) copper and \(8.33 \%\) nickel. The mass of a quarter is \(5.670 \mathrm{~g}\). (a) Write out the dimensional analysis factors that can be derived from the two percentages given above. Be sure to include units. (b) If the U.S. mint buys \(3.0\) tons of copper for making quarters, how many quarters can it make?

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