Abstract
We devised a method to control the temperature of a liquid bath as low as $-100^{\circ}C$ using the duty cycle control of a solenoid valve. The solenoid valve controls the flow of liquid nitrogen that we used as a cryogen in this system. By controlling the duty cycle of a solenoid valve using feedback from the measured temperature of the liquid bath, we were able to achieve temperature stability within ${\pm}19mK$ around $-100^{\circ}C$. We also demonstrated that by taking average values of the temperature readings for sequence of measurements from more than one thermometer, it is possible to use this system for the calibration of thermometers within 3 mK. This system and the control method can be used for the precise temperature control in the range between $0^{\circ}C$ and $-100^{\circ}C$, where commercially available precision baths are much expensive and hard to be built in customized configurations.
