Certain devices require a constant temperature environment for proper oper- ation. Examples are gyroscopes, accelerometers and crystals used as frequency standards. A particular temperature control system for this purpose uses electrical heaters, exterior thermal insulation and a thermostat for maintaining the temper- ature at 1700F ± 10F. The thermostat turns the heater on when the temperature drops to 1690F and turns it off at 1710F. The heater consists of a 3 ohm resistor supplied by a 28 volt source where 1 watt=3.4 Btu/hr. The heat capacity of the device is 0.1 Btu/0F . Heat is lost to the environment by conductive heat transfer, the constant of the process being 3.6 Btu/0F/hour.

1. Prepare completely labeled block diagram of the control system.
2. Sketch the variation of the device temperature vs. time through a complete control cycle, for environmental temperature of 700F and −200F, taking the initial temperature to be that of the environment.
3. What is the lowest environmental temperature for which the desired tem- perature can be maintained?