Four astronauts are in a spherical space station. If, as is typical, each of them breathes about 500 cm3 of air with each breath, approximately what volume of air (in cubic meters) do these astronauts breathe in a year?

Ch 01: Units, Physical Quantities & Vectors

Young & Freedman Calc - University Physics 14th Edition

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Young & Freedman Calc 14th Edition

Ch 01: Units, Physical Quantities & Vectors

문제 20a

1장, 문제 20a

Four astronauts are in a spherical space station. If, as is typical, each of them breathes about 500 cm³ of air with each breath, approximately what volume of air (in cubic meters) do these astronauts breathe in a year?

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First, determine the volume of air each astronaut breathes per breath. This is given as 500 cm³. Convert this volume to cubic meters using the conversion factor: 1 cm³ = 1 × 10⁻⁶ m³.

Calculate the total volume of air each astronaut breathes in one day. Assume an average breathing rate of 12 breaths per minute. Multiply the number of breaths per minute by the number of minutes in a day (60 minutes/hour × 24 hours/day) to find the total number of breaths per day.

Multiply the total number of breaths per day by the volume of air per breath (in cubic meters) to find the daily volume of air each astronaut breathes.

To find the annual volume of air each astronaut breathes, multiply the daily volume by the number of days in a year (365 days).

Finally, calculate the total volume of air breathed by all four astronauts in a year by multiplying the annual volume for one astronaut by four.

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Volume Conversion

Understanding volume conversion is crucial for this problem, as it involves converting the volume of air from cubic centimeters to cubic meters. Since 1 cubic meter equals 1,000,000 cubic centimeters, you need to divide the total volume in cubic centimeters by 1,000,000 to convert it to cubic meters.

Breathing Rate Calculation

To determine the total volume of air breathed in a year, you must calculate the number of breaths taken annually. This involves multiplying the number of breaths per minute by the number of minutes in an hour, hours in a day, and days in a year. This calculation provides the total number of breaths taken by an astronaut in a year.

Multiplication of Volumes

Once you have the number of breaths per year, multiply this by the volume of air per breath to find the total volume of air breathed by one astronaut. Since there are four astronauts, multiply the result by four to get the total volume of air breathed by all astronauts in a year.