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Inside the earth and the sun. (a) Geophysicists have estimated that the temperature at the center of the earth's core is \(5000^{\circ} \mathrm{C}\) (or more), while the temperature of the sun's core is about 15 million \(\mathrm{K}\). Express both of these temperatures in Fahrenheit degrees.

Short Answer

Expert verified
Earth's core is 9032°F, Sun's core is 26,999,520.33°F.

Step by step solution

01

Understand Temperature Conversion Formulas

The goal is to convert the given temperatures from Celsius and Kelvin to Fahrenheit. The formula to convert Celsius to Fahrenheit is:\[F = \frac{9}{5}C + 32\]To convert Kelvin to Fahrenheit, use the following formula:\[F = \frac{9}{5}(K - 273.15) + 32\]
02

Convert Earth's Core Temperature to Fahrenheit

Given that the temperature at the center of the Earth's core is \(5000^{\circ}\, C\). Applying the Celsius to Fahrenheit conversion formula:\[F = \frac{9}{5} \times 5000 + 32 = 9000 + 32 = 9032^{\circ}F\]
03

Convert Sun's Core Temperature to Fahrenheit

Given that the temperature at the center of the Sun's core is \(15\, million\, K\). First, express this in numeric form: \(15\,000,000\, K\). Apply the Kelvin to Fahrenheit conversion formula:\[F = \frac{9}{5}(15\,000,000 - 273.15) + 32 \]Simplifying this:1. Calculate \(15\,000,000 - 273.15 = 14\,999,726.85\)2. Apply the formula: \(F = \frac{9}{5} \times 14\,999,726.85 + 32\) \(= 26,999,488.33 + 32\) \(= 26,999,520.33^{\circ}F\)

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Key Concepts

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

Celsius to Fahrenheit
When we want to convert temperatures from Celsius to Fahrenheit, we use a straightforward formula: \(F = \frac{9}{5}C + 32\). This conversion is essential for comparing temperatures in countries where Fahrenheit is used or for scientific calculations that require different units. The formula tells us to first multiply the Celsius temperature by \(\frac{9}{5}\) and then add 32 to the result. This will give us the temperature in Fahrenheit.
  • Celsius is the metric system's base unit for temperature.
  • Fahrenheit is commonly used in the United States.
Understanding this conversion helps in comparing temperatures and predicting weather conditions, especially when traveling or studying environments that experience various temperature scales.
Kelvin to Fahrenheit
Converting from Kelvin to Fahrenheit involves a slightly more complex formula since Kelvin measures absolute temperature without negative numbers. The formula is \(F = \frac{9}{5}(K - 273.15) + 32\). In this formula:
1. Subtract 273.15 from the Kelvin temperature. This adjusts for zero Kelvin being absolute zero, which is equivalent to -273.15°C.2. Multiply the result by \(\frac{9}{5}\), which changes it to the Fahrenheit base scale.3. Add 32, the final step, to convert to the Fahrenheit scale.

Kelvin is commonly used in scientific contexts, while Fahrenheit is used for everyday applications. Knowing how to switch from Kelvin to Fahrenheit is crucial for interpreting data from scientific reports or labs.
Geophysics Temperatures
Geophysics involves studying Earth's physical properties and processes. One significant aspect is understanding temperature variations in different layers of the planet. Temperatures deep within the Earth, such as the core, influence geological activities.
  • The Earth's core temperature is essential for understanding magnetic field generation.
  • High temperatures at the core affect convection currents within the mantle.
  • These temperatures are crucial for assessing volcanic activity and tectonic movements.
By learning about geophysics temperatures, scientists can better predict natural disasters and understand the planet's evolution.
Earth Core Temperature
The Earth's core temperature is estimated to be around \(5000^{\circ} C\). This incredibly high temperature is a result of heat generated from radioactive decay and residual heat from Earth's formation. Such temperatures can be converted into Fahrenheit using the formula for Celsius to Fahrenheit: \(F = \frac{9}{5} \times 5000 + 32 = 9032^{\circ}F\).

The core's temperature impacts:
  • The behavior of materials (e.g., rock becomes semi-liquid at these temps).
  • Generation of Earth's magnetic field through dynamo action.
  • The surface geological phenomena driven by heat transfer from the core to the crust.
Understanding these factors is crucial for geologists and climatologists in studies related to Earth's internal structure and dynamics.
Sun Core Temperature
The core temperature of the Sun is about 15 million Kelvin. This temperature is the driving force behind the sun's nuclear fusion, where hydrogen atoms fuse to form helium, releasing massive amounts of energy. To express this temperature in Fahrenheit, use the Kelvin to Fahrenheit formula. Initially, express 15 million Kelvin as a number (15,000,000 K). Performing the conversion gives us approximately \(26,999,520.33^{\circ}F\).

The implications of such astronomical temperatures include:
  • Understanding stellar processes and lifecycle of stars.
  • Predicting solar phenomena such as solar flares and their impact on Earth.
  • Studying energy propagation from the core to the Sun's surface.
Knowing the core temperature helps astrophysicists model and predict solar behaviors, which is vital for our understanding of the solar system.

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Most popular questions from this chapter

A \(15.0 \mathrm{~g}\) bullet traveling horizontally at \(865 \mathrm{~m} / \mathrm{s}\) passes through a tank containing \(13.5 \mathrm{~kg}\) of water and emerges with a speed of \(534 \mathrm{~m} / \mathrm{s}\). What is the maximum temperature increase that the water could have as a result of this event?

(a) While vacationing in Europe, you feel sick and are told that you have a temperature of \(40.2^{\circ} \mathrm{C}\). Should you be concerned? What is your temperature in \({ }^{\circ} \mathrm{F}\) ? (b) The morning weather report in Sydney predicts a high temperature of \(12^{\circ} \mathrm{C}\). Will you need to bring a jacket? What is this temperature in \({ }^{\circ} \mathrm{F}\) ? (c) A friend has suggested that you go swimming in a pool having water of temperature \(350 \mathrm{~K}\). Is this safe to do? What would this temperature be on the Fahrenheit and Celsius scales?

Convert the following Kelvin temperatures to the Celsius and Fahrenheit scales: (a) the midday temperature at the surface of the moon \((400 \mathrm{~K}) ;\) (b) the temperature at the tops of the clouds in the atmosphere of Saturn \((95 \mathrm{~K}) ;\) (c) the temperature at the center of the sun \(\left(1.55 \times 10^{7} \mathrm{~K}\right)\)

A carpenter builds an exterior house wall with a layer of wood \(3.0 \mathrm{~cm}\) thick on the outside and a layer of Styrofoam insulation \(2.2 \mathrm{~cm}\) thick on the inside wall surface. The wood has a thermal conductivity of \(0.080 \mathrm{~W} /(\mathrm{m} \cdot \mathrm{K}),\) and the Styrofoam has a thermal conductivity of \(0.010 \mathrm{~W} /(\mathrm{m} \cdot \mathrm{K})\). The interior surface temperature is \(19.0^{\circ} \mathrm{C}\). and the exterior surface temperature is \(-10.0^{\circ} \mathrm{C}\). (a) What is the temperature at the plane where the wood meets the Styrofoam? (b) What is the rate of heat flow per square meter through this wall?

The blood plays an important role in removing heat from the body by bringing this heat directly to the surface where it can radiate away. Nevertheless, this heat must still travel through the skin before it can radiate away. We shall assume that the blood is brought to the bottom layer of skin at a temperature of \(37^{\circ} \mathrm{C}\) and that the outer surface of the skin is at \(30.0^{\circ} \mathrm{C}\). Skin varies in thickness from \(0.50 \mathrm{~mm}\) to a few millimeters on the palms and soles, so we shall assume an average thickness of \(0.75 \mathrm{~mm}\). A \(165 \mathrm{lb}, 6 \mathrm{ft}\) person has a surface area of about \(2.0 \mathrm{~m}^{2}\) and loses heat at a net rate of \(75 \mathrm{~W}\) while resting. On the basis of our assumptions, what is the thermal conductivity of this person's skin?

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