Atmospheric pressure

Why atmospheric pressure changes with altitude:

• Atmospheric pressure is caused by the weight of the air column above.
• Higher altitude → less air above → smaller weight of air → lower atmospheric pressure.
• At the top of a high mountain the atmospheric pressure is significantly less than at sea level.

Crushed can experiment: Remove air from inside a metal can (e.g. by boiling water to fill it with steam, then sealing and cooling it). The steam condenses, lowering the internal pressure. Atmospheric pressure on the outside then crushes the can inward.

Suction cup: Pressing a suction cup expels air. The lower internal pressure means atmospheric pressure holds the cup firmly against the surface.

Drinking through a straw: Sucking lowers the pressure inside the straw. Atmospheric pressure acting on the surface of the liquid pushes it up the straw.

A mercury barometer consists of a glass tube (closed at the top, open at the bottom) filled with mercury and inverted in a trough of mercury.

• Atmospheric pressure acts on the mercury surface in the trough.
• This pressure supports a column of mercury of height \( h \) in the tube.
• The space above the mercury in the closed tube is a near-vacuum (very low pressure).
• At sea level: \( h \approx 760\,\text{mm Hg} = 76\,\text{cm Hg} \).

\[ P_\text{atm} = h\rho g = 0.760 \times 13\,600 \times 10 = 103\,360\,\text{Pa} \approx 100\,\text{kPa} \]

A U-tube manometer measures the pressure of a gas relative to atmospheric pressure:

• One arm is connected to the gas supply; the other is open to the atmosphere.
• If the gas pressure is greater than atmospheric, the liquid level on the gas side is lower.
• The difference in liquid levels \( h \) gives the gauge pressure (excess above atmospheric): \( \Delta P = h\rho g \).