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Chapter 12: Problem 3

On the moon the surface temperature ranges from \(375 \mathrm{K}\) during the day to \(1.00 \times 10^{2} \mathrm{K}\) at night. What are these temperatures on the (a) Celsius and (b) Fahrenheit scales?

Short Answer

Expert verified
Daytime: 101.85掳C, 215.33掳F; Nighttime: -173.15掳C, -279.67掳F.

Step by step solution

01

Understanding the conversion formulas

To convert Kelvin to Celsius, use the formula: \[ C = K - 273.15 \]To convert Celsius to Fahrenheit, use the formula:\[ F = \frac{9}{5}C + 32 \]
02

Convert daytime temperature to Celsius

Starting with the daytime temperature on the moon.Given: \( K = 375 \)Using the formula \( C = K - 273.15 \), we calculate:\[ C = 375 - 273.15 = 101.85 \]Thus, the daytime temperature in Celsius is \( 101.85^{\circ}C \).
03

Convert daytime temperature to Fahrenheit

Using the Celsius temperature calculated in Step 2, apply the formula:\[ F = \frac{9}{5}C + 32 \]\[ F = \frac{9}{5}(101.85) + 32 \]\[ F = 183.33 + 32 = 215.33 \]Therefore, the daytime temperature in Fahrenheit is \( 215.33^{\circ}F \).
04

Convert nighttime temperature to Celsius

Now convert the nighttime temperature on the moon.Given: \( K = 1.00 \times 10^{2} \)Convert to Celsius using:\[ C = 1.00 \times 10^{2} - 273.15 \]\[ C = 100 - 273.15 = -173.15 \]Thus, the nighttime temperature in Celsius is \( -173.15^{\circ}C \).
05

Convert nighttime temperature to Fahrenheit

Using the Celsius temperature from Step 4, apply the Celsius-to-Fahrenheit formula:\[ F = \frac{9}{5}C + 32 \]\[ F = \frac{9}{5}(-173.15) + 32 \]\[ F = -311.67 + 32 = -279.67 \]Therefore, the nighttime temperature in Fahrenheit is \( -279.67^{\circ}F \).

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Key Concepts

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

Kelvin to Celsius
The conversion from Kelvin to Celsius is quite straightforward and essential for understanding temperature scales in the scientific community. The Kelvin scale is the base unit for temperature in the International System of Units (SI), and it doesn't go into negative values, making it useful for absolute temperature measurements. To convert a temperature from Kelvin to Celsius, simply subtract 273.15 from the Kelvin temperature. This adjustment accounts for the offset between the two scales. For example, on the moon, the daytime temperature is 375 K. By applying the conversion formula:
  • Convert Kelvin to Celsius: \[ C = K - 273.15 \]
  • Apply to the moon's daytime temperature: \[ C = 375 - 273.15 = 101.85 \]
This means the surface temperature during the moon's day is 101.85掳C.
Celsius to Fahrenheit
Celsius and Fahrenheit are two of the most commonly used temperature scales, especially in everyday scenarios. Understanding how to convert between these scales is useful for interpreting temperature data from different sources. The formula to convert a temperature from Celsius to Fahrenheit is:
  • Convert Celsius to Fahrenheit: \[ F = \frac{9}{5}C + 32 \]
  • For the moon's daytime temperature of 101.85掳C: \[ F = \frac{9}{5}(101.85) + 32 = 215.33 \]
This gives us the Fahrenheit equivalent, showing how differently temperature is expressed in this scale. Fahrenheit is used primarily in the United States, while Celsius is more commonly used worldwide.
Moon Temperature Range
The moon experiences dramatic temperature swings due to its lack of atmosphere, which means it cannot retain heat. During the lunar day, temperatures can soar to 375 K. At night, it plummets to just 100 K. Converting these temperatures gives a clearer picture:
  • Daytime (375 K): 101.85掳C or 215.33掳F
  • Nighttime (100 K): -173.15掳C or -279.67掳F
These extreme temperatures challenge conventional materials and engineering, making lunar exploration and habitation complex. Understanding these swings is essential for anyone planning to work or live on the moon.

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Most popular questions from this chapter

A steel bicycle wheel (without the rubber tire) is rotating freely with an angular speed of \(18.00 \mathrm{rad} / \mathrm{s}\). The temperature of the wheel changes from \(-100.0 \mathrm{to}+300.0^{\circ} \mathrm{C} .\) No net external torque acts on the wheel, and the mass of the spokes is negligible. (a) Does the angular speed increase or decrease as the wheel heats up? Why? (b) What is the angular speed at the higher temperature?

You are sick, and your temperature is 312.0 kelvins. Convert this temperature to the Fahrenheit scale.

Dermatologists often remove small precancerous skin lesions by freezing them quickly with liquid nitrogen, which has a temperature of \(77 \mathrm{K}\). What is this temperature on the (a) Celsius and (b) Fahrenheit scales?

At a fabrication plant, a hot metal forging has a mass of \(75 \mathrm{kg}\) and a specific heat capacity of \(430 \mathrm{J} /\left(\mathrm{kg} \cdot \mathrm{C}^{\circ}\right) .\) To harden it, the forging is immersed in \(710 \mathrm{kg}\) of oil that has a temperature of \(32^{\circ} \mathrm{C}\) and a specific heat capacity of \(2700 \mathrm{J} /\left(\mathrm{kg} \cdot \mathrm{C}^{\circ}\right) .\) The final temperature of the oil and forging at thermal equilibrium is \(47^{\circ} \mathrm{C}\). Assuming that heat flows only between the forging and the oil, determine the initial temperature of the forging.

During an all-night cram session, a student heats up a one-half liter \(\left(0.50 \times 10^{-3} \mathrm{m}^{3}\right)\) glass (Pyrex) beaker of cold coffee. Initially, the temperature is \(18^{\circ} \mathrm{C},\) and the beaker is filled to the brim. A short time later when the student returns, the temperature has risen to \(92^{\circ} \mathrm{C} .\) The coefficient of volume expansion of coffee is the same as that of water. How much coffee (in cubic meters) has spilled out of the beaker?
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