Dynamic classification: Which of the following is a first-order temperature-measuring instrument when used bare (no protective well or significant air gap)?

Introduction / Context:
Dynamic response characterizes how quickly an instrument follows temperature changes. Many common thermometers can be approximated by first-order systems under typical conditions.

Given Data / Assumptions:

• “Bare” means minimal additional thermal resistance or capacitance (no well, minimal air gap).
• Small temperature excursions; linear approximation valid.

Concept / Approach:
A mercury-in-glass thermometer commonly behaves as a first-order system with a single dominant thermal time constant due to lumped thermal mass and film resistance. Bimetal and vapor-pressure systems can introduce more complex mechanics or distributed effects that deviate from a simple first-order approximation in many practical setups.

Step-by-Step Solution:
Model mercury bulb and glass stem as lumped capacity.Heat transfer to the bulb primarily via convection → single resistance.This yields a first-order differential equation: τ dθ/dt + θ = K * input.Hence, the “bare” mercury-in-glass thermometer is the canonical first-order instrument among the options.

Verification / Alternative check:
Textbook treatments frequently use mercury-in-glass thermometers to introduce first-order dynamics and time constant identification by step tests.

Why Other Options Are Wrong:

• Bimetallic elements can show nonlinearities and mechanical hysteresis; not always well-modeled as a simple first-order system.
• Vapor-pressure thermometers involve bulb, capillary, and Bourdon/elastic element, often producing more complex dynamics.
• “All of these” overgeneralizes beyond typical first-order approximations.

Common Pitfalls:
Assuming every temperature device is first-order; added wells and protective lags can produce multi-time-constant behavior.

Final Answer:
Mercury-in-glass thermometer (bare)