A piece of metal with a mass of 1.6 kg, specific heat of 200 J/kg C, and initial

Question

A piece of metal with a mass of 1.6 kg, specific
heat of 200 J/kg C, and initial temperature
of 100C is dropped into an insulated jar that
contains liquid with a mass of 3.7 kg, specific
heat of 1000 J/kg C, and initial temperature
of 0C. The piece of metal is removed after
5 s, at which time its temperature is 20C.
Find the temperature of the liquid after the
metal is removed. Neglect any effects of heat
transfer to the air or to the insulated jar.
Answer in units of C.

B.)

Find the average rate at which heat is trans-

ferred while the piece of metal is in the liquid.

Answer in units of J

Explanation / Answer

This problem has a nce twist. Usually we write a single equation once everything settles down, but here there wasn't a chance to come to equilibrium. For A, let's find how much heat energy the metal lost, then give that to the liquid and see what temperature this heat energy would heat the liquid to. Metal loses: 1.6kg*200J/kg C*(100C-20C) = 25600J This energy is what the liquid gains Heat Energy Gained = mass liquid*specific heat liquid*(final temp - initial temp) final temp = Heat Energy Gained/[mass liquid*specific heat liquid] - initial temp final temp = 25600J/[3.7kg*1000J/kgC] - 0C = 6.9 C So, the temperature of the liquid after the water was removed is: 6.9C B 25600J of energy were transfered in 5s, so the average transfer is 25600J/5s = 5120 J/s of course more heat would be transfered in the first second,when the metal was hotter, than in the final second, when the metal was cooler, but this is the average

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