A steel cutter, heated to t 82C, is immersed for quenching in 4kg of water, t of which is 10C.

A steel cutter, heated to t 82C, is immersed for quenching in 4kg of water, t of which is 10C. The weight of the cutter is 400g. To what temperature the cutter will cool.

Given: t1 (cutting tool heating temperature for hardening) = 820 ºС; m2 (mass of water) = 4 kg; t2 (water temperature) = 10 ºС; m2 (chisel weight) = 400 g (0.4 kg).

Constants: Cc (specific heat capacity of carbon steel) = 468 J / (kg * K); Sv (specific heat capacity of water) = 4200 J / (kg * K).

We determine the temperature to which the steel cutter will cool from the equality:

Сс * m1 * (t1 – t) = Cв * m2 * (t – t2).

468 * 0.4 * (820 – t) = 4200 * 4 * (t – 10).

153504 – 187.2t = 16800t – 168000.

16987.2t = 321504 and t = 18.93 ºС.