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Death Valley holds the record for the highest recorded temperature in the United States. On July 10,1913 , at a place called Furnace Creek Ranch, the temperature rose to \(134^{\circ} \mathrm{F}\). The lowest U.S. temperature ever recorded occurred at Prospect Creek Camp in Alaska on January 23,1971 , when the temperature plummeted to \(-79.8^{\circ} \mathrm{F}\). (a) Convert these temperatures to the Celsius scale. (b) Convert the Celsius temperatures to Kelvin.

Short Answer

Expert verified
The highest recorded temperature in Celsius is \(56.67^{\circ}C\) and in Kelvin is \(329.82K\). The lowest recorded temperature in Celsius is \(-62.11^{\circ}C\) and in Kelvin is \(211.04K\).

Step by step solution

01

Convert Fahrenheit to Celsius

First, we'll convert the temperatures from Fahrenheit to Celsius using the given formula \( C = \frac{5}{9}(F - 32) \). For highest recorded temperature: \( C = \frac{5}{9}(134 - 32) = 56.67^{\circ}C \) and for lowest recorded temperature: \( C = \frac{5}{9}(-79.8 - 32) = -62.11^{\circ}C \)
02

Convert Celsius to Kelvin

Next, we'll convert these Celsius temperatures to Kelvin using the formula \( K = C + 273.15 \). For the highest recorded temperature: \( K = 56.67 + 273.15 = 329.82K \). For the lowest recorded temperature: \( K = -62.11 + 273.15 = 211.04K \).

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Key Concepts

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

Fahrenheit to Celsius Conversion
Understanding the conversion between Fahrenheit and Celsius is essential for those studying temperature differences within various regions and applications. Our reference points are Dealth Valley's scorching high and Alaska's frigid low. To convert from Fahrenheit to Celsius, we use the formula:
\( C = \frac{5}{9}(F - 32) \).
In this formula, \( F \) represents the Fahrenheit temperature, while \( C \) guides us to the Celsius equivalent. For example, a blistering \( 134^\circ F \) in Death Valley is equivalent to \( 56.67^\circ C \), a figure that is obtained by subtracting 32 from the Fahrenheit value and then multiplying by the fraction \( \frac{5}{9} \). This proportional relationship between the scales helps us comprehend the degree of temperature variation. An interesting note is that at -40 degrees, both Fahrenheit and Celsius scales intersect, meaning -40°F is equal to -40°C.
Celsius to Kelvin Conversion
Once we have the Celsius values from our Fahrenheit conversion, the next step is to understand the relationship between Celsius and Kelvin. This conversion is straightforward. Scientists and researchers use the Kelvin scale as it commences at absolute zero, the theoretically coldest possible temperature.
To obtain Kelvin from Celsius, the formula is simple:
\( K = C + 273.15 \).
Here, \( K \) is the temperature in Kelvin, and \( C \) is the Celsius temperature. When we apply this to the temperatures from Death Valley and Alaska, we find that the searing heat translates to 329.82 K, and the bone-chilling cold converts to 211.04 K. The beauty of this conversion is its linearity, meaning there are no multipliers, just a direct addition of 273.15 to the Celsius temperature.
Temperature Scales
The world employs multiple temperature scales, each valuable for specific applications. The Fahrenheit scale, for example, is commonly used in the United States for weather and cooking temperatures. The Celsius scale, accepted worldwide, is often used in science and by most countries for everyday weather reporting. Kelvin, on the other hand, is the temperature scale of choice for the scientific community, especially in the fields of physics and chemistry. It's important for temperature scales to have fixed points. In Celsius, water freezes at 0°C and boils at 100°C under standard atmospheric pressure, setting a useful scale for everyday life. Fahrenheit sets the freezing point of water at 32°F and its boiling point at 212°F. The Kelvin scale is unique in that it starts at absolute zero, the point where particles theoretically stop moving, and increases incrementally with Celsius.
Thermal Physics
Thermal physics is a branch of physics that deals with heat, temperature, and their relation to energy and work. It involves studying the kinetic theory of gases, thermodynamics, and statistical mechanics. Temperature is a measure of the average kinetic energy of the particles in a substance—the more heat energy present, the faster the particles move, resulting in a higher temperature. This foundational concept is crucial for understanding the behaviors of materials under different conditions and designing everything from engines and refrigerators to climate models. When converting between temperature scales, we are essentially translating the observed kinetic energy of particles into different numeric values that correspond to the chosen scale. For instance, the consideration of absolute zero in Kelvin gives us a point of reference for the lowest possible energy state of a substance.

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Most popular questions from this chapter

The density of helium gas at \(0^{\circ} \mathrm{C}\) is \(\rho_{0}=0.179 \mathrm{~kg} / \mathrm{m}^{3}\). The temperature is then raised to \(T=100^{\circ} \mathrm{C}\), but the pressure is kept constant. Assuming the helium is an ideal gas, calculate the new density \(\rho_{f}\) of the gas.

Long-term space missions require reclamation of the oxygen in the carbon dioxide exhaled by the crew. In one method of reclamation, \(1.00 \mathrm{~mol}\) of carbon dioxide produces \(1.00 \mathrm{~mol}\) of oxygen, with \(1.00 \mathrm{~mol}\) of methane as a by-product. The methane is stored in a tank under pressure and is available to control the attitude of the spacecraft by controlled venting. A single astronaut exhales \(1.09 \mathrm{~kg}\) of carbon dioxide each day. If the methane generated in the recycling of three astronauts' respiration during one week of flight is stored in an originally empty \(150-\mathrm{L}\) tank at \(-45.0^{\circ} \mathrm{C}\), what is the final pressure in the tank?

Gas is confined in a tank at a pressure of \(11.0 \mathrm{~atm}\) and a temperature of \(25.0^{\circ} \mathrm{C}\). If two-thirds of the gas is withdrawn and the temperature is raised to \(75.0^{\circ} \mathrm{C}\), what is the new pressure of the gas remaining in the tank?

The density of gasoline is \(7.30 \times 10^{2} \mathrm{~kg} / \mathrm{m}^{3}\) at \(0^{\circ} \mathrm{C}\). Its average coefficient of volume expansion is \(9.60 \times 10^{-4}\left({ }^{\circ} \mathrm{C}\right)^{-1}\), and note that \(1.00 \mathrm{gal}=0.00380 \mathrm{~m}^{3}\). (a) Calculate the mass of \(10.0 \mathrm{gal}\) of gas at \(0^{\circ} \mathrm{C}\). (b) If \(1.000 \mathrm{~m}^{3}\) of gasoline at \(0^{\circ} \mathrm{C}\) is warmed by \(20.0^{\circ} \mathrm{C}\), calculate its new volume. (c) Using the answer to part (b), calculate the density of gasoline at \(20.0^{\circ} \mathrm{C}\). (d) Calculate the mass of \(10.0\) gal of gas at \(20.0^{\circ} \mathrm{C}\). (e) How many extra kilograms of gasoline would you get if you bought \(10.0\) gal of gasoline at \(0^{\circ} \mathrm{C}\) rather than at \(20.0^{\circ} \mathrm{C}\) from a pump that is not temperature compensated?

The boiling point of liquid hydrogen is \(20.3 \mathrm{~K}\) at atmospheric pressure. What is this temperature on (a) the Celsius scale and (b) the Fahrenheit scale?

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