Question

On a climb up Mt. Whitney, the atmospheric pressure drops to \(467 \mathrm{mmHg}\). What is the pressure in terms of the following units? a. atm b. torr

Short answer

a. 0.614 atm, b. 467 torr

Step-by-step solution

Convert mmHg to atm

Use the conversion factor between millimeters of mercury (mmHg) and atmospheres (atm). The standard atmospheric pressure is 1 atm which is equal to 760 mmHg. Therefore, to convert 467 mmHg to atm, use the formula: \[ \text{Pressure in atm} = \frac{\text{Pressure in mmHg}}{760} \].

Perform the Calculation for atm

Substitute the given pressure of 467 mmHg into the formula: \[ \text{Pressure in atm} = \frac{467 \ \text{mmHg}}{760 \ \text{mmHg/atm}} \]. Now, calculate the value: \[ \frac{467}{760} \approx 0.614 \text{ atm} \].

Convert mmHg to torr

Use the conversion that 1 mmHg is equal to 1 torr. Therefore, the pressure in torr will be the same numerical value as in mmHg. So, the pressure in torr is: \[ 467 \ \text{torr} \].

Key concepts

Atmospheric Pressure

Atmospheric pressure is the force exerted onto a surface by the weight of the air above that surface in the atmosphere. It is a crucial concept in understanding weather patterns and altitude effects.
As you climb higher, like when hiking up a mountain, the atmospheric pressure decreases. This happens because there is less air above you exerting force.
The standard atmospheric pressure at sea level is defined as 1 atmosphere (atm). This is equivalent to 101,325 Pascals (Pa) in SI units. For easier measurements in everyday scenarios, it is often also represented as 760 millimeters of mercury (mmHg).

Millimeters of Mercury

Millimeters of mercury (mmHg) is a unit of pressure that originated from the way mercury was used in barometers to measure atmospheric pressure.
One mmHg is the pressure exerted by a 1 millimeter high column of mercury at 0°C at the standard acceleration of gravity.
This unit is still widely used in various fields, particularly in medicine. For example, blood pressure readings are often given in mmHg.

Conversion Factors

Conversion factors are used to change one set of units to another, making the comparison or conversion possible and accurate. It's essential to know the correct conversion factors:
- 1 atmosphere (atm) = 760 mmHg
- 1 mmHg = 1 torr.
These factors are used in equations to seamlessly switch between units without changing the resulting measurement's meaning.

ATM

Atmospheres (atm) is a unit of pressure defined by being equal to standard atmospheric pressure at sea level.
This unit is widely used in physical sciences and engineering when discussing pressures relative to atmospheric pressure. For example, scuba divers measure water pressure relative to the surface atmospheric pressure using atm.

Torr

The torr is a unit of pressure that is nearly equal to the mmHg. In fact, 1 torr = 1 mmHg.
It is named after Evangelista Torricelli, who invented the barometer in 1644.
This unit is often used in high-vacuum physics and engineering fields, making it extremely useful for experiments and applications that require precision in low-pressure measurements.