Steel spheres 3 in. in diameter heated to 700°F are to be cooled by immersion in an oil bath at 125°F. If there is negligible thermal resistance between the oil and the steel surfaces, 

(a) Calculate the average temperature of the spheres 10 s and 1 and 6 min after immersion. 

(b) How long would it take for the unaccomplished temperature change to be reduced to 1 percent of the initial temperature difference? The steel has the same thermal properties as in Prob. 10.5.

Prob. 10.5

A long steel rod 1 in. in diameter is initially at a uniform temperature of 1.200°F. It is suddenly immersed in a quenching bath of oil at 150°F. In 4 min its average temperature drops to 250°F. How long would it take to lower the temperature from 1,200 to 250°F 

(a) If the rod were 2¹/₂ in. in diameter. 

(b) If it were 5 in. in diameter? For steel. k=26 Btu/ft-h-°F; ρ = 486 lb/ft³: C_p = 0.11 Btu/lb-°F.