Asphere made of pure iron has a 4.50-inch diameter. it is kept in a freezer at 0.00 o f before it is placed into a hot oil bath at 220 o f. data iron sphere and oil bath density (lbm/ft3 ) 491 and 66.6 respectively heat capacity (btu/lbmo f) 0.107 and 0.000652 respectively thermal conductivity (btu/h-fto f) 52.0 and 0.151 respectively convective heat transfer coefficient (btu/h-ft2 - o f) n/a and 15.6 respectively(a) can lumped capacitance be used to evaluate t(t)? (b) regardless of your answer to (a), assume that lumped capacitance is valid and determine the temperature of the sphere 10.0 minutes after it is placed in the bath. (c) what is the maximum diameter pure iron sphere where lumped capacitance can be used (i. e., bi < 0.1)?