Question

Which of the following pressure gauge operation depends on the variation of the thermal conductivity of a gas at low pressure,

• A. Bourdon tube gauge
• B. Hydrostatic gauge
• C. Pirani gauge
• D. McLeod gauge

Hint:

The Pirani gauge measures low pressures by detecting changes in thermal conductivity, as fewer gas molecules at lower pressures reduce heat loss from a heated filament.

Answer 1

The Correct Option is C

Step 1: Understand the principle of thermal conductivity in pressure measurement.
At low pressures (e.g., in a vacuum), the thermal conductivity of a gas decreases because there are fewer gas molecules to conduct heat. Some pressure gauges operate by measuring this change in thermal conductivity, which correlates with pressure in the low-pressure range. Step 2: Analyze each pressure gauge.
Bourdon tube gauge: A mechanical gauge that measures pressure by the deformation of a curved tube. It does not rely on thermal conductivity; it measures the mechanical response to pressure changes and is typically used for moderate to high pressures (e.g., atmospheric or above).
Hydrostatic gauge: Measures pressure based on the height of a liquid column (e.g., a manometer or barometer). It relies on the hydrostatic pressure principle (\( P = \rho g h \)) and does not involve thermal conductivity.
Pirani gauge: A thermal conductivity gauge used to measure low pressures (e.g., 10\(^{-4}\) to 1 Torr). It consists of a heated filament (wire) in a gas chamber. The filament loses heat to the surrounding gas via conduction, which depends on the gas pressure. At low pressure, fewer gas molecules are present, reducing heat loss, which increases the filament’s temperature and changes its electrical resistance. This resistance change is calibrated to measure pressure, making the Pirani gauge dependent on the thermal conductivity of the gas.
McLeod gauge: Measures low pressures by compressing a known volume of gas to a higher pressure and measuring the resulting pressure with a mercury column. It operates on the principle of Boyle’s law (\( P_1 V_1 = P_2 V_2 \)) and does not rely on thermal conductivity. Step 3: Evaluate the options.
(1) Bourdon tube gauge: Incorrect, as it relies on mechanical deformation, not thermal conductivity. Incorrect.
(2) Hydrostatic gauge: Incorrect, as it uses liquid column height, not thermal conductivity. Incorrect.
(3) Pirani gauge: Correct, as its operation depends on the variation of thermal conductivity of the gas at low pressure. Correct.
(4) McLeod gauge: Incorrect, as it uses gas compression and Boyle’s law, not thermal conductivity. Incorrect.
Step 4: Select the correct answer.
The Pirani gauge’s operation depends on the variation of the thermal conductivity of a gas at low pressure, matching option (3).