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6.1.4: Temperature and Time

  • Page ID
    88382
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    6.1.4 Learning Objectives

    • Perform arithmetic calculations on temperature and time
    • Convert from one unit of measure to another unit of measure.
    • Solve application problems using each form of measurement.

    Definition: Time, Temperature

    Temperature is used to describe the level of heat or cold of an object or environment.

    Time is used to describe the amount of existence between events.

    Some of the common units (along with their abbreviations) for temperature and time are listed in the following table.

    Unit Conversion Table
    Temperature Fahrenheit (\(^\circ F\))\(=\dfrac{9}{5}\)\(^\circ\)C\( +32\)
    Kelvin (K)\(=\)\(^\circ\)C\( +273.15\)
    Celsius (\(^\circ\)C)\(=\dfrac{5}{9}(\)\(^\circ\)F\( -32)\)
    Celsius (\(^\circ\)C)\(=\)K\(-273.15\)
    Time 1 minute (min) = 60 seconds (sec)
    1 hour ( hr) = 60 minutes
    1 day (da) = 24 hours
    1 week (wk) = 7 days
    1 year (yr)= 52 weeks

    Example 1

    Convert 73\(^\circ\)F to Celsius.

    Solution

    To convert from Fahrenheit to Celsius, we need the equation ( \(^\circ\)C)\(=\dfrac{5}{9}\) \(^\circ\)F\( -32)\). Substitute in the given value for Fahrenheit to find the answer. Round to the nearest degree.

    ( \(^\circ\)C)\(=\dfrac{5}{9}\)\(^\circ\)F\( -32\)(=

    \dfrac{5}{9}\(73^\circ F\)- 32

    =\dfrac{5}{9} \times 41=\dfrac{41 \times 5}{9}=23.7\approx 24^\circ F

    Thus, 73\(^\circ\)F\(\approx 24^\circ\)C\)

    Example 2

    Convert 3763 K to Fahrenheit.

    Solution

    First we need to covert to Celsius, then we can convert to Fahrenheit. Round to two decimal places.

    ( \(^\circ\)C)\(=\)K\(-273.15=3763+273.15=3489.85\) \(^\circ\)C

    ( \(^\circ\)F)\(=\dfrac{9}{5}\) \(^\circ\)C\( +32=\dfrac{9}{5}3489.85 +32=\dfrac{9\times 3489.85}{5} +32=6281.73+32=6313.73^\circ\)F

    Thus, 3763 K\(=6313.73^\circ\)F

    Example 3

    Convert 2,016 hr to weeks.

    Solution

    Looking in the unit conversion table under time, we see that \(\text{1 wk = 7 da}\) and that \(\text{1 da = 24 hr}\). To convert from hours to weeks, we must first convert from hours to days and then from days to weeks. We need two unit fractions.

    The unit fraction needed for converting from hours to days is \(\dfrac{1 \text{ da}}{24 \text{ hr}}\). The unit fraction needed for converting from days to weeks is \(\dfrac{\text{1 wk}}{\text{7 da}}\).

    \(\begin{array} {rcll} {\text{2,016 hr}} & = & {\dfrac{\text{2,016 hr}}{1} \cdot \dfrac{\text{1 da}}{\text{24 hr}} \cdot \dfrac{\text{1 wk}}{\text{7 da}}} & {\text{Divide out common units.}} \\ {} & = & {\dfrac{\text{2,016 } \cancel{\text{hr}}}{1} \cdot \dfrac{\text{1 } \cancel{\text{da}}}{\text{24 } \cancel{\text{hr}}} \cdot \dfrac{\text{1 wk}}{\text{7 } \cancel{\text{da}}}} & {} \\ {} & = & {\dfrac{2,016 \cdot 1 \text{ wk}}{24 \cdot 7}} & {\text{Simplify}} \\ {} & = & {\text{12 wk}} & {} \end{array}\)

    Thus, \(\text{2,016 hr = 12 wk}\).

    Example 4

    Your employer tracks your accumulated vacation time in hours. You want to take a two week vacation and have accumulated 412 hours of paid time off. Do you have enough hours for your vacation?

    Solution

    To solve this we need to covert 412 hours to weeks.

    The unit fraction needed for converting from hours to days is \(\dfrac{1 \text{ da}}{24 \text{ hr}}\). The unit fraction needed for converting from days to weeks is \(\dfrac{\text{1 wk}}{\text{7 da}}\).

    \(\begin{array} {rcll} {\text{412 hr}} & = & {\dfrac{\text{412 hr}}{1} \cdot \dfrac{\text{1 da}}{\text{24 hr}} \cdot \dfrac{\text{1 wk}}{\text{7 da}}} & {\text{Divide out common units.}} \\ {} & = & {\dfrac{\text{412 } \cancel{\text{ hr}}}{1} \cdot \dfrac{\text{1 } \cancel{\text{ da}}}{\text{24 } \cancel{\text{ hr}}} \cdot \dfrac{\text{1 wk}}{\text{7 } \cancel{\text{ da}}}} & {} \\ {} & = & {\dfrac{412 \cdot 1 \text{ wk}}{24 \cdot 7}} & {\text{Simplify}} \\ {} & = & {\text{2.5 wk}} & {} \end{array}\)

    Thus, \(\text{412 hr = 2.5 wk}\).

    Yes, you have enough time for a 2.5 week vacation.

    Try It Now 1

    Make the following conversions. If a fraction occurs, convert it to a decimal rounded to two decimal places.

    1. Convert 32\(^{\circ}\)C to \(^{\circ}\)F
    2. Convert 1732\(^{\circ}\)F to K
    3. Convert 52 min to hours.
    Answer
    1. 89.6\(^{\circ}\)F
    2. 1217.59 K
    3. 0.87 hr

    This page titled 6.1.4: Temperature and Time is shared under a not declared license and was authored, remixed, and/or curated by Leah Griffith, Veronica Holbrook, Johnny Johnson & Nancy Garcia.

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