A piece of copper weighing 0.2 kg was placed in 0.4 kg of water at 20 ° C at a temperature of –8 ° C. At what temperature will thermal equilibrium be established?
mw = 0.4 kg.
tv = 20 ° C.
Cw = 4200 J / kg * ° C.
mm = 0.2 kg.
tm = – 8 ° C.
Cm = 400 J / kg * ° C.
Since the temperature of the copper is less than the temperature of the water, the water will give up a certain amount of heat Q to the copper.
Q = Cw * mw * (tv – t).
Q = Cm * mm * (t – tm).
Cw * mw * (tv – t) = Cm * mm * (t – tm) – heat balance equation.
Cw * mw * tv – Cw * mw * t = Cm * mm * t – Cm * mm * tm.
Cw * mw * tv + Cm * mm * tm = Cm * mm * t + Cw * mw * t.
Cw * mw * tv + Cm * mm * tm = (Cm * mm + Cw * mw) * t.
t = (Cw * mw * tv + Cm * mm * tm) / (Cm * mm + Cw * mw).
t = (4200 J / kg * ° C * 0.4 kg * 20 ° C + 400 J / kg * ° C * 0.2 kg * (- 8 ° C)) / (400 J / kg * ° C * 0.2 kg + 4200 J / kg * ° C * 0.4 kg) = 18.7 ° C.
Answer: when thermal equilibrium is established, a temperature of t = 18.7 ° C will be established.
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