/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 6 One of the hottest temperatures ... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

One of the hottest temperatures ever recorded on the surface of Earth was \(134^{\circ} \mathrm{F}\) in Death Valley, CA. What is this temperature in Celsius degrees? What is this temperature in Kelvin?

Short Answer

Expert verified
The temperature is approximately 56.67\text{°C} in Celsius and 329.82 K in Kelvin.

Step by step solution

01

Convert Fahrenheit to Celsius

Use the formula to convert Fahrenheit (\text{°F}) to Celsius (\text{°C}): \[ C = \frac{5}{9}(F - 32) \] Insert the given Fahrenheit temperature (134\text{°F}) into the formula: \[ C = \frac{5}{9}(134 - 32) \]
02

Calculate the Celsius Temperature

Perform the arithmetic inside the parentheses first: \[ 134 - 32 = 102 \] Then multiply by the fraction: \[ C = \frac{5}{9} \times 102 \] Finally, calculate the product to find the Celsius temperature.
03

Convert Celsius to Kelvin

To convert Celsius to Kelvin, use the formula: \[ K = C + 273.15 \] Insert the Celsius temperature found in step 2 into this formula to find the Kelvin temperature.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

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

Fahrenheit to Celsius
Understanding how to convert temperatures from Fahrenheit to Celsius is an essential skill in science and everyday life, especially for those who travel frequently or engage in scientific studies. The formula \( C = \frac{5}{9}(F - 32) \) is the key to transforming Fahrenheit \( (\text{\degree F}) \) into Celsius \( (\text{\degree C}) \).

Here's how it works: first, subtract 32 from the Fahrenheit temperature, which adjusts the scale starting point from 32 \( (\text{\degree F}) \) in Fahrenheit to 0 \( (\text{\degree C}) \) in Celsius. Next, multiply this number by \( \frac{5}{9} \) to correct for the scale difference where each Celsius degree is larger than each Fahrenheit degree. To illustrate, the scorching Earth surface temperature of 134\degree F from our original problem would be converted as follows: \[ C = \frac{5}{9}(134 - 32) = \frac{5}{9} \times 102 = 56.67\text{\degree C} \]. This simple mathematical transformation facilitates temperature comparisons and studies across different regions and scientific disciplines.
Celsius to Kelvin
Once we've converted our temperature into Celsius, we can then translate it into Kelvin, which is necessary for scientific endeavors, including physics and chemistry that utilize the International System of Units (SI). The relationship between Celsius and Kelvin is straightforward: \[ K = C + 273.15 \].

The Kelvin scale is an absolute thermodynamic temperature scale where 0 K is the point of absolute zero, the temperature where all thermal motion ceases in the classical description of thermodynamics. Unlike Celsius, where 0 is the freezing point of water, 0 K represents the absence of all heat. Adding 273.15 to the Celsius measurement allows us to convert to this absolute scale.

For instance, using the temperature we calculated earlier 56.67\text{\degree C}, converting into Kelvin would be: \[ K = 56.67 + 273.15 = 329.82 \text{K} \]. It's a seamless shift, but fundamental for scientists who rely on precise and standard temperature measurements across all domains.
Thermodynamic Temperature Scales
Diving deeper into the realm of thermodynamics, we encounter various temperature scales, each with its significance. The most commonly used scales are Fahrenheit, Celsius, and Kelvin. Fahrenheit is often used in the United States for weather and cooking, Celsius is widely applied across the world for similar everyday applications, and Kelvin, which is vital for thermodynamic equations and scientific calculations.

The Celsius scale is based on the properties of water, with 0 \( (\text{\degree C}) \) marking the freezing point, and 100 \( (\text{\degree C}) \) the boiling point under standard atmospheric pressure.

The Kelvin scale, on the other hand, as an absolute scale, ties directly into the laws of thermodynamics and provides a uniform measurement for scientific analysis. In fact, temperature in thermodynamics is solely and officially measured in Kelvin because of its absolute nature, allowing for calculations that pertain to the fundamental nature of heat, energy, and molecular activity.

Understanding each scale’s origin and application greatly enhances the ability to navigate and convert between them for varied practical and scientific purposes.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A certain \(50.0-\mathrm{Hz}\) AC power line radiates an electromagnetic wave having a maximum electric field strength of \(13.0 \mathrm{kV} / \mathrm{m}\). (a) What is the wavelength of this very low frequency electromagnetic wave? (b) What is its maximum magnetic field strength?

The gauge pressure in your car tires is \(2.50 \times 10^{5} \mathrm{N} / \mathrm{m}^{2}\) at a temperature of \(35.0^{\circ} \mathrm{C}\) when you drive it onto a ferry boat to Alaska. What is their gauge pressure later, when their temperature has dropped to \(-40.0^{\circ} \mathrm{C} ?\)

An \(L C\) circuit containing a \(1.00\) -pF capacitor oscillates at such a frequency that it radiates at a 300 -nm wavelength. (a) What is the inductance of the circuit? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

What is the atmospheric pressure on top of Mt. Everest on a day when water boils there at a temperature of \(70.0^{\circ} \mathrm{C} ?\)

Atmospheric pressure atop Mt. Everest is \(3.30 \times 10^{4} \mathrm{N} / \mathrm{m}^{2} .\) (a) What is the partial pressure of oxygen there if it is \(20.9 \%\) of the air? (b) What percent oxygen should a mountain climber breathe so that its partial pressure is the same as at sea level, where atmospheric pressure is \(1.01 \times 10^{5} \mathrm{N} / \mathrm{m}^{2} ?\) (c) One of the most severe problems for those climbing very high mountains is the extreme drying of breathing passages. Why does this drying occur?

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.