Variation of atmospheric pressure, with height from earth is

Options

A. Linear
B. Parabolic
C. Exponential
D. Hyperbolic

Answer

To solve the question regarding the variation of atmospheric pressure with height from the Earth, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: We need to understand how atmospheric pressure changes as we move away from the Earth's surface. The relationship can be described by the equation:
\[ P(h) = P_0 e^{-\frac{mgh}{kT}} \]
where:
- \( P(h) \) is the atmospheric pressure at height \( h \),
- \( P_0 \) is the atmospheric pressure at the Earth's surface,
- \( m \) is the mass of the gas molecules,
- \( g \) is the acceleration due to gravity,
- \( h \) is the height above the Earth's surface,
- \( k \) is the Boltzmann constant,
- \( T \) is the absolute temperature.

2. **Analyze the Equation**: The equation shows that pressure \( P(h) \) decreases exponentially with height \( h \). This means that as you go higher, the pressure drops rapidly.

3. **Identify the Exponential Behavior**: The term \( e^{-\frac{mgh}{kT}} \) indicates that the pressure decreases exponentially as height increases. This is a key characteristic of how gases behave under the influence of gravity.

4. **Conclusion**: From the analysis, we conclude that the variation of atmospheric pressure with height from the Earth follows an exponential decay. Therefore, as height increases, the atmospheric pressure decreases exponentially.

5. **Final Answer**: The correct option for the variation of atmospheric pressure with height from the Earth is option 3 (exponential decrease).