Thermostats and mathematics
Thermostats are devices designed to maintain a desired temperature by regulating the heating or cooling systems in various environments, including vehicles and buildings. A thermometer measures temperature, while a thermostat keeps it steady by controlling heat flow. The first electronic thermostats were invented by Warren S. Johnson in 1883, primarily for classroom comfort. In automobiles, thermostats play a crucial role in managing engine temperature, using a wax-based mechanism that opens or closes a valve to regulate coolant flow based on temperature changes.
In buildings, thermostats often employ bimetallic strips, which bend in response to temperature fluctuations, triggering heating or cooling units to activate or deactivate. Modern electronic thermostats can feature advanced functions such as setpoint staging and time-based staging, allowing for more efficient temperature regulation by analyzing variables like current and desired temperatures. Proper placement of thermostats is essential to ensure accurate readings, as incorrect positioning can lead to inefficient heating or cooling cycles. Overall, thermostats are integral to maintaining comfort and efficiency in various settings through mathematical calibration and operational mechanisms.
Thermostats and mathematics
Summary: Thermostats are mathematically calibrated according to physical principles to regulate temperature in a variety of settings.
Thermostats and thermometers are related instruments that perform different tasks. A thermometer measures (“meter”) heat (“thermo”) to determine and display a current temperature. On the other hand, a thermostat is designed to keep the heat (“thermo”) stationary (“stat”) to help maintain a desired temperature. Inventor and college professor Warren S. Johnson produced the first electronic room thermostats in 1883. He installed them in classrooms to keep students more comfortable in cold weather and to minimize outside interruptions. In the twenty-first century, thermostats are most commonly found inside vehicle engines and as a part of residential, commercial, or industrial heating systems—though they can also be found in appliances, like gas stoves.
Automobiles
In an automobile engine, the thermostat helps regulate temperature so that the engine operates properly and efficiently. The thermostat acts as a control valve for the coolant fluid, which flows within an engine and to a separate radiator that helps to cool the hot coolant. When an engine is first started, the thermostat is closed, and the coolant flowing within the engine cycles through only the engine until it warms up to an ideal temperature. The thermostat measures the temperature change using a special type of wax. Initially, the wax is solid but as the temperature of the surrounding coolant increases, the wax melts and expands to allow hot fluid to flow from the engine to the radiator and cooler fluid to flow from the radiator back in to the hot engine. If the engine gets too hot, the thermostat will open more to allow coolant from the radiator to permeate through the engine. On the other hand, if the engine begins to get too cold, the thermostat will begin to close, allowing less coolant into the radiator and more coolant to cycle through the engine to heat it back up. The thermostat is mathematically calibrated to the engine type and will automatically make the needed corrections as the vehicle is in use.
Buildings
A thermostat used to control temperature in a building similarly does not directly heat (or cool) the rooms. In this situation, it controls a heating (or cooling) unit, which is used to help regulate the temperature. In many systems, a bimetallic strip is used to measure the temperature of a room. Metals expand and contract as they heat and cool. Bimetallic strips work because different metals expand and contract at different rates. A strip of steel and a strip of copper (or brass) will be placed together and the ends secured to each other. If the temperature does not change, the strip remains flat. When the temperature changes, the different rate of expansion or contraction will cause the flat strip to develop a curve toward the metal that has changed less. The amount of curvature can be matched mathematically to a specific degree or range of change in temperature, triggering the system to adjust accordingly.
To increase the sensitivity of the thermostat, most bimetallic strips are long and coiled inside the thermostat. The coil loosens or winds more tightly with a change in room temperature. At a certain point, the bimetallic strip’s movements will trigger the heating unit to turn either on or off. Once turned on, the thermostat uses weights or magnets to keep the heating unit from turning off too quickly. Without these devices, the thermostat would create short cycles (turning on and off quickly), which are generally inefficient and could cause a premature failure of the heating unit. Since the bimetallic strip’s movement depends directly on the temperature of the immediately surrounding air, the thermostat should not be placed in a location that would cause an inaccurate reading. One common mistake is placing the thermostat by a heat register, where hot air flowing out will trigger the thermostat to turn the heating unit off before the rest of the room has acclimated.
Electronic Variations
More advanced thermostats frequently use electronic rather than electromechanical sensors and may have more than a simple on-off setting. Setpoint staging uses one type of heating process, or stage, when the room temperature is within two degrees of the thermostat setting and another when the difference is greater than two degrees from the thermostat setting. Time-based staging activates a secondary stage or unit after the first stage runs for a predetermined amount of time, indicating that the room is colder or hotter than some preset value. Multistage thermostats analyze variables such as the current room temperature, the desired temperature, and the amount of time it takes for a space to warm or cool one degree to determine mathematically when to use a second heating stage.
Bibliography
Automatic and Programmable Thermostats. Merrifield, VA: Energy Efficiency and Renewable Energy Clearinghouse, 1997.
Brumbaugh, James E. Audel HVAC Fundamentals, Heating Systems, Furnaces and Boilers. 4th ed. Hoboken, NJ: Wiley, 2007.
Cleveland, Cutler J., et al. Dictionary of Energy. Expanded ed. Oxford, England: Elsevier, 2009.
Miles, Victor Chesney. Thermostatic Control; Principles and Practice. London: Newnes, 1965.