You are designing a system to cool an insulated silver plate of dimensions 2.00 cm × 2.00 cm × 0.50 cm. One end of a thermally insulated copper wire (diameter D = 2.50 mm and length L = 15.0 cm) is dipped into a vat of liquid nitrogen (T = 77.2 K), and the other end is attached to the bottom of the silver plate.

(a) If the silver plate starts at room temperature (72.0 °F), what is the initial rate of heat flow between the plate and the liquid nitrogen reservoir?

(b) Assuming the rate of heat flow calculated in part (a), estimate the temperature of the silver plate after 30.0 seconds.