College

Math Extension: Atmospheric Pressure

**Conversion Factors:**
- 10 mm = 1 cm
- 2.54 cm = 1 inch
- 29.92 inHg = 1 atmosphere
- 1 mile = 1.6 km

1. Convert 44 mmHg to inHg.

2. Convert 72 inHg into atmospheres.

3. Convert 0.83 atmospheres into two other units of pressure.

4. The stratosphere extends from 10 km above the ground to 50 km. How many miles thick is the stratosphere?

Answer :

Sure! Let's solve each part of the question step-by-step:

1. Convert 44 mmHg to inHg:

To convert millimeters of mercury (mmHg) to inches of mercury (inHg), we can follow these steps:
- First, convert mm to cm. Since 10 mm equals 1 cm, we divide 44 mm by 10, which equals 4.4 cm.
- Next, convert cm to inches. Since 2.54 cm equals 1 inch, we divide 4.4 cm by 2.54, which gives approximately 1.732 inches of mercury.

So, 44 mmHg is approximately 1.732 inHg.

2. Convert 72 inHg into atmospheres:

To convert inches of mercury to atmospheres, use the conversion factor that 29.92 inHg equals 1 atmosphere.
- Divide 72 inHg by 29.92 to get the result in atmospheres.
- This gives approximately 2.406 atmospheres.

3. Convert 0.83 atmospheres into two other units of pressure:

- To convert atmospheres to mmHg, we use the fact that 1 atmosphere equals 29.92 inHg. Since each inch of mercury can be converted to mmHg using the original two conversions (2.54 cm in an inch and 10 mm in 1 cm), 1 atmosphere ultimately equals 760 mmHg.
- Therefore, multiply 0.83 atmospheres by 760 mmHg to get approximately 630.773 mmHg.

For the conversion to inHg,
- Multiply 0.83 atmospheres by 29.92 inHg to get approximately 24.834 inHg.

4. Calculate the thickness of the stratosphere in miles:

The stratosphere extends from 10 km to 50 km above the ground.
- First, find the thickness in kilometers by subtracting 10 km from 50 km, which gives 40 km.
- To convert kilometers to miles, use the conversion factor that 1 mile equals 1.6 kilometers.
- Divide 40 km by 1.6 to get 25 miles.

So, the stratosphere is approximately 25 miles thick.