# To what temperature was a steel cutter weighing 0.15 kg heated during quenching, if, after lowering it into an aluminum

To what temperature was a steel cutter weighing 0.15 kg heated during quenching, if, after lowering it into an aluminum vessel weighing 0.10 kg, containing 0.60 kg of machine oil at 15 ° C, the oil was heated at 48 ° C?

The change in the internal energy of the cutter is determined by the formula Qr = Cs * mr (t1-t2), where Cs is the specific heat capacity of steel, mr is the mass of the cutter, t1 and t2 are the initial and final temperatures, respectively.
Changes in the internal energies of the vessel and oil are recorded in a similar way.
According to the law of conservation of energy, we get:
Qr = Qm + Qa, where Qm and Qa are changes in the energies of the oil and the vessel.
Then we get:
Cs * mr (t1-t2) = Cm * m (t2-t3) + Ca * ma (t2-t3) where t3 is the initial oil temperature
from here we easily find t1.

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