Instrument order identification: which of the following is not a second-order instrument?

Introduction / Context: The “order” of an instrument refers to the order of the differential equation describing its dynamic response. Many mechanical/thermal instruments behave as first- or second-order systems depending on construction details such as protective covers, wells, or multiple elastic elements.

Given Data / Assumptions:

• A bare mercury-in-glass thermometer has a single dominant thermal capacitance/resistance pair.
• Adding coverings/wells introduces additional lags, often elevating the effective order.
• Composite pressure devices with multiple elastic elements can behave as second order.

Concept / Approach: A bare mercury-in-glass thermometer is classically modelled as a first-order system: one time constant dominates heat transfer from the fluid to the bulb and mercury. When a protective covering or thermowell is added, extra thermal resistance/capacitance can create effectively second-order behaviour. Complex pressure gauges with bellows/tank arrangements similarly produce second-order responses.

Step-by-Step Solution:

Verification / Alternative check: Standard instrumentation texts model bare thermometers as first-order, adding a second lag for wells/covers.

Why Other Options Are Wrong:

Common Pitfalls: Assuming all thermometers behave identically regardless of mounting; installation affects instrument dynamics.

Final Answer: Bare mercury-in-glass thermometer