The heat transfer coefficient for hydrogen flowing over a sphere is to be determined by observing the temperature–time history of a sphere fabricated from pure copper. the sphere, which is 20.0 mm in diameter, is at 80°c before it is inserted into the gas stream having a temperature of 27°c. a thermocouple on the outer surface of the sphere indicates 50°c 97 s after the sphere is inserted into the hydrogen.

find
(a) what is the value of the specific heat of the copper at the average temperature of the process, in j/kg·k?
(b) what is the value of the lumped thermal capacitance of the sphere, in j/k?
(c) solve for the thermal time constant, in sec.