MCQ Detailed View

In atmospheric physics, pressure decreases with increasing altitude because the density of air becomes lower as we move away from Earth's surface. The scale height (H) is a scientific term used to describe the characteristic height over which atmospheric pressure decreases by a factor of e, where e is the mathematical constant approximately equal to 2.71828.

Mathematically, the relationship between atmospheric pressure and height is given by the barometric formula:

P(h)=P0 e−h/HP(h) = P_0 \, e^{-h/H}P(h)=P0e−h/H

Where:

• 
  

  $P(h)$ = atmospheric pressure at height $h$

  
  


• 
  

  P0P_0P0 = atmospheric pressure at sea level

  
  


• 
  

  $H$ = scale height (typically around 8 to 9 km for Earth's atmosphere)

  
  


• 
  

  $e$ = base of natural logarithms (2.71828)

  
  

The scale height depends on:

1. 
   

   Temperature (T): Higher temperatures increase scale height because air expands when heated.

   
   


2. 
   

   Molecular mass (M): A lighter gas (like hydrogen) gives a larger scale height.

   
   


3. 
   

   Gravitational acceleration (g): Stronger gravity compresses the atmosphere, reducing scale height.

   
   

For Earth, the average scale height is about 8.5 kilometers, meaning that every 8.5 km you ascend, the air pressure drops to about 36.8% (1/e) of its value at the starting level. At higher altitudes, the air becomes thinner, making breathing more difficult.

The other options are incorrect:

• 
  

  Average height, Mean height, and Standard height are not scientific terms used in atmospheric physics for this concept. The universally accepted term is Scale Height (H).

  
  

This concept is fundamental in meteorology, aerospace engineering, planetary science, and environmental studies, as it explains how pressure and density change with height on Earth and other planetary atmospheres.

The correct answer is Scale height (H), as it is the defined term for the altitude at which atmospheric pressure decreases by a factor of e.