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Question

Calculate the final temperature of the system: A 50.0 gram sample of water initially at 100 °C and a 100 gram sample initially at 22.4 °C are mixed. The specific heat of water is 4.184 J/gC). Record your answer in scientific notation using 3 significant figures.

Answer 1

The final mixing temperature is the weighted average of all the input temperatures weighted by m_iC_i :This is true for any number of substances with different initial temperatures, masses, or specific heats:

T_f = sum of the m_ic_iT_i,initial divided by the sum of the m_ic_i

In this case the c's are all the same and factor out, so you get

T_f = (50g(100 C) + 100g(22.4 C))/(50 + 100 g) (T's weighted with the masses of water)

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