Question:
Which one of the following is a first-order instrument?
Which one of the following is a first-order instrument?
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Any bare sensing element (like a bare thermocouple or bare thermometer) typically acts as a first-order system. As soon as you add a thermowell, sheath, or covering, it introduces a secondary thermal lag, transforming it dynamically into a second-order system.
Updated On: Jul 9, 2026
- U-tube type mercury manometer
- Bimetallic thermometer with covering
- Vapour pressure thermometer without any covering
- Mercury thermometer with covering
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The Correct Option is C
Solution and Explanation
Concept:
In process dynamics and control, instruments are categorized by their dynamic response behavior based on the differential equation that models them.
• A first-order instrument contains a single energy storage element and is governed by a first-order linear differential equation. It does not exhibit oscillatory behavior.
• A second-order instrument contains two energy storage elements (like mass and springiness, or thermal capacities separated by resistance) and can exhibit underdamped, critically damped, or overdamped behaviors.
Step 1: Reviewing the options systematically.
• U-tube type mercury manometer: Liquid column movement involves kinetic energy storage (mass acceleration) and potential energy storage (gravity/head difference). This leads to an oscillatory second-order system.
• Thermometers with coverings: Adding a protective well or covering introduces an extra layer of thermal resistance and capacitance. The heat must first transfer to the covering (first capacity) and then to the internal fluid (second capacity), creating a cascading second-order response.
• Vapour pressure thermometer without any covering: Lacking any protective layer, heat transfers directly across a single thermal resistance into a single fluid pool capacity. This direct storage configuration matches a pure first-order system. Hence, option (C) is a standard first-order instrument.
• A first-order instrument contains a single energy storage element and is governed by a first-order linear differential equation. It does not exhibit oscillatory behavior.
• A second-order instrument contains two energy storage elements (like mass and springiness, or thermal capacities separated by resistance) and can exhibit underdamped, critically damped, or overdamped behaviors.
Step 1: Reviewing the options systematically.
• U-tube type mercury manometer: Liquid column movement involves kinetic energy storage (mass acceleration) and potential energy storage (gravity/head difference). This leads to an oscillatory second-order system.
• Thermometers with coverings: Adding a protective well or covering introduces an extra layer of thermal resistance and capacitance. The heat must first transfer to the covering (first capacity) and then to the internal fluid (second capacity), creating a cascading second-order response.
• Vapour pressure thermometer without any covering: Lacking any protective layer, heat transfers directly across a single thermal resistance into a single fluid pool capacity. This direct storage configuration matches a pure first-order system. Hence, option (C) is a standard first-order instrument.
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