29. Volume of alcohol calculation

To calculate the volume of alcohol given its mass and density, we need to first ensure that all units are consistent. The density is given in pounds per gallon (lb/gal), while the mass is in grams (g), and we need to find the volume in liters (L).

Step 1: Convert mass from grams to pounds.

• 1 pound (lb) = 453.59237 grams (g)

$\text{Mass in pounds} = \frac{1587.57 \, \text{g}}{453.59237 \, \text{g/lb}} \approx 3.5 \, \text{lb}$

Step 2: Use the density formula to find the volume in gallons.

• Given that the density is $6.6 \, \text{lb/gal}$, we can use the formula for density:

$\text{Density} = \frac{\text{Mass}}{\text{Volume}} \quad \text{so} \quad \text{Volume} = \frac{\text{Mass}}{\text{Density}}$

$\text{Volume in gallons} = \frac{3.5 \, \text{lb}}{6.6 \, \text{lb/gal}} \approx 0.53 \, \text{gallons}$

Step 3: Convert the volume from gallons to liters.

• 1 gallon = 3.78541 liters

$\text{Volume in liters} = 0.53 \, \text{gal} \times 3.78541 \, \text{L/gal} \approx 2.0 \, \text{L}$

So, the volume of alcohol is approximately 2.0 liters.

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30. Conversion of boiling point of oxygen

Step 1: Convert Celsius to Fahrenheit (°F)

• The formula to convert Celsius to Fahrenheit is:

$°F = (°C \times \frac{9}{5}) + 32$

$°F = (-183 \times \frac{9}{5}) + 32 = -297.4°F$

The boiling point of oxygen in Fahrenheit is -297.4°F.

Step 2: Convert Celsius to Kelvin (K)

• The formula to convert Celsius to Kelvin is:

$K = °C + 273.15$

$K = -183 + 273.15 = 90.15K$

The boiling point of oxygen in Kelvin is 90.15K.

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Would you like more details or have any questions?

Relative Questions:

1. How do different units of density affect volume calculations?
2. What is the process for converting between metric and imperial units?
3. Why is it important to ensure consistent units when performing calculations?
4. Can you explain the difference between mass and weight in the context of these calculations?
5. How would the volume change if the density of alcohol was given in kg/m³?

Tip:

Always ensure unit conversions are accurate to avoid errors in volume, temperature, or other physical quantity calculations.