A device used to measure the surface temperature of an object to within a spatial resolution of approximately 50 nm is shown in the schematic. It consists of an extremely sharp-tipped stylus and an extremely small cantilever that is scanned across the surface. The probe tip is of circular cross section and is fabricated of polycrystalline silicon dioxide. The ambient temperature is measured at the pivoted end of the cantilever as T_∞ = 25°C and the device is equipped with a sensor to measure the temperature at the upper end of the sharp tip, T_sen. The thermal resistance between the sensing probe and the pivoted end is R, = 5 X 10⁶ K/W.

(a) Determine the thermal resistance between the surface temperature and the sensing temperature.

(b) If the sensing temperature is T_sen = 28.5°C, determine the surface temperature.

T- 25C Cantilever T. Stylus- Surface d= 100 nm Air Tan L= 50 nm