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The question is as follows:

A block of $500.0\ \mathrm g$ of an unknown metal is boiled for a while in water, before it is immediately put up in an insulating beaker with $1.00\ \mathrm{ kg}$ of water at room temperature ($20.0^\circ \mathrm C$). The lid is put on. After waiting for 5.00 minutes and stirring gently, you observe that the temperature is stable at $22.0^\circ\mathrm C$ in the beaker. We first assume that the beaker does not absorb any heat, and that no heat was lost to the surroundings. What is the specific heat capacity of the metal?

I tried many different approaches such as: $Q_{\text{out}} = Q_{\text{in}}$, and then solved for the specific heat but I only got the wrong answer.

The correct answer to the question is $215\ \mathrm{J/K}$.

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  • $\begingroup$ In regular examples that I find in my book and on the internet the metal is boiled to some specified temperature but in this question it only states that it was boiled for a while. Which I find very strange. $\endgroup$ Sep 24, 2021 at 8:21

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I think that 'boiled' means that the water is at 100C.

The water in the beaker gains energy of $$E=ms\Delta \theta = 1 \times 4,200 \times 2 = 8,400J$$

The metal loses energy of $$E=ms\Delta \theta = 0.5 \times s \times 78 = 39 s$$

Equating these gives the specific heat capacity of the metal is $215 J K^{-1}$.

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  • $\begingroup$ Thank a lot, it helped. $\endgroup$ Sep 24, 2021 at 8:42
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    $\begingroup$ Hey Blitzer. Please do not to provide full solutions to homework problems. Just a few hints on how to solve the problem is recommended. $\endgroup$
    – joseph h
    Sep 24, 2021 at 9:13
  • $\begingroup$ You are quite right @Joseph. Sorry - I forgot the rules! $\endgroup$
    – Blitzer
    Sep 25, 2021 at 10:53

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