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Chapter 11: Problem 28

The planet Mercury's surface temperature varies from \(700 \mathrm{K}\) during the day to \(90 \mathrm{K}\) at night. What are these values in \({ }^{\circ} \mathrm{C}\) and \({ }^{\circ} \mathrm{F}\) ?

Short Answer

Expert verified
The day temperature on Mercury is \(700 \mathrm{K}\), \(426.85 \,{ }^{\circ} \mathrm{C}\), or \(800.33 \,{ }^{\circ}\mathrm{F}\). The night temperature on Mercury is \(90 \mathrm{K}\), \(-183.15 \,{ }^{\circ} \mathrm{C}\), or \(-297.67\,{ }^{\circ}\mathrm{F}\).

Step by step solution

01

Convert Kelvin to Celsius

The formula to convert Kelvin to Celsius is \(C = K - 273.15\). Apply this formula to both the day and night temperatures on Mercury. For the day temperature: \(C = 700 \mathrm{K} - 273.15 = 426.85 \,{ }^{\circ}\mathrm{C}\). For the night temperature: \(C = 90 \mathrm{K} - 273.15 = -183.15 \,{ }^{\circ}\mathrm{C}\)
02

Convert Celsius Temperatures to Fahrenheit

The formula to convert Celsius to Fahrenheit is \( F = C \times \frac{9}{5} + 32 \). Use this formula for both the daytime and nighttime Celsius temperatures. For the day: \( F = 426.85 \,{ }^{\circ} \mathrm{C} \times \frac{9}{5} + 32 = 800.33 \,{ }^{\circ}\mathrm{F} \). For the night: \( F = -183.15 \,{ }^{\circ} \mathrm{C} \times \frac{9}{5} + 32 = -297.67\,{ }^{\circ}\mathrm{F} \)
03

Consolidate the Results

Summarize the temperatures for Mercury in Kelvin, Celsius, and Fahrenheit. The day temperature is \(700 \mathrm{K}\), \(426.85 \,{ }^{\circ} \mathrm{C}\), or \(800.33 \,{ }^{\circ}\mathrm{F}\). The night temperature is \(90 \mathrm{K}\), \(-183.15 \,{ }^{\circ} \mathrm{C}\), or \(-297.67\,{ }^{\circ}\mathrm{F}\).

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Key Concepts

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

Kelvin to Celsius conversion
Understanding how to convert temperatures from Kelvin to Celsius is essential in physics and chemistry. Kelvin is the standard unit of temperature in the scientific community, primarily used because it starts at absolute zero, the point where molecular motion stops. The formula to convert Kelvin to Celsius is straightforward: subtract 273.15 from the Kelvin temperature.

For example, if you have a temperature of 700 K, as seen on Mercury during the day, you convert it to Celsius by using the formula: - Subtract 273.15 from 700, resulting in 426.85掳C. - Conversely, a nighttime temperature of 90 K converts to -183.15掳C. This conversion is simple yet extremely useful for understanding temperatures in more familiar units, especially when dealing with data from beyond our Earth.
Celsius to Fahrenheit conversion
Once you have a temperature in degrees Celsius, you may often need to convert it to Fahrenheit, especially if you're working in a region or field that uses the Imperial system. The conversion formula is: multiply the Celsius temperature by \( \frac{9}{5} \) and then add 32.

Applying this to Mercury's daytime and nighttime temperatures:
  • Daytime: Multiply 426.85掳C by \( \frac{9}{5} \), then add 32, giving you 800.33掳F.
  • Nighttime: Multiply -183.15掳C by \( \frac{9}{5} \), then add 32, resulting in -297.67掳F.
Converting to Fahrenheit can make it easier to grasp for those familiar with the Fahrenheit scale, often used in daily weather reports.
Temperature on Mercury
Mercury, being the closest planet to the Sun, has extreme temperature fluctuations. Its lack of atmosphere causes drastic temperature variations from day to night.

During the day, temperatures can soar up to 700 K (426.85掳C), making Mercury's surface extremely hot. This is unlike any surface temperatures we experience on Earth. At night, without an atmosphere to retain heat, the temperature can plummet to 90 K (-183.15掳C), much colder than any temperature found naturally on Earth.
These extremes are a result of Mercury's thin atmosphere, which cannot trap heat like Earth's atmosphere does. Understanding these conditions is crucial for planning scientific missions and studies of other planetary bodies in our solar system.

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Most popular questions from this chapter

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