The most suitable pressure gauge to measure pressure in the range of 10⁻⁴ to 10⁻³ torr is

Choosing a Pressure Gauge for Low Torr Range

The question asks for the most suitable pressure gauge to measure pressures in the very low range of $1\times 10^{-4}$ torr to $1\times 10^{-3}$ torr. This pressure range falls under the high vacuum or low vacuum classification. Let's examine the given options to determine the best fit.

Analyzing Pressure Gauge Options

- Bellows Gauge: Bellows gauges are mechanical devices often used for measuring moderate vacuum or positive pressures. They rely on the expansion or contraction of a sealed metal bellows. Their typical operating range usually starts from around 1 torr and goes up to higher pressures. They are generally not sensitive or accurate enough for the ultra-low pressure range specified ($10^{-4}$ to $10^{-3}$ torr).
- Barometer: A barometer is specifically designed to measure atmospheric pressure, which is approximately 760 torr at sea level. It is completely unsuitable for measuring low vacuum pressures.
- Strain Gauge: A strain gauge is a sensor whose resistance varies with applied mechanical strain. While strain gauges can be incorporated into pressure transducers (like diaphragm-based pressure sensors), the term "strain gauge" itself does not represent a specific type of gauge suitable for measuring pressures in the $10^{-4}$ to $10^{-3}$ torr range directly. Such transducers are usually capacitance manometers or piezoresistive sensors, which operate differently.
- Pirani Gauge: The Pirani gauge is a thermal conductivity gauge. It works on the principle that the rate of heat loss from a heated filament depends on the thermal conductivity of the surrounding gas. In the low-pressure regime (vacuum), the thermal conductivity of the gas is directly related to the pressure. As pressure decreases, heat loss decreases, and vice versa. Pirani gauges are effective for measuring pressures typically ranging from 10 torr down to $1\times 10^{-4}$ torr or even $1\times 10^{-5}$ torr. This range perfectly encompasses the specified $1\times 10^{-4}$ to $1\times 10^{-3}$ torr requirement.

Conclusion on Suitability

Comparing the options, the Pirani gauge is specifically designed and commonly used for measurements within the low vacuum range, including the specified pressure range of $1\times 10^{-4}$ torr to $1\times 10^{-3}$ torr. The other options are either designed for different pressure ranges (Barometer, Bellows) or are components rather than complete gauge types for this specific application (Strain Gauge).

Therefore, the most suitable pressure gauge for measuring pressure in the range of $1\times 10^{-4}$ to $1\times 10^{-3}$ torr among the given choices is the Pirani gauge.