4. In the manufacturing of ball bearings, the components, such as the ball, are hardened through a process of heating and then rapid cooling or “quenching” by submersion in oil or water bath. The temperature of the ball as a function of time, T), in the bath may be estimated as follows: where t is the time in the bath, in seconds, Ti, is the initial ball temperature; To, the oil temperature, and τ is
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