You are performing an analysis of a new metalic alloy created in your research l

Question

You are performing an analysis of a new metalic alloy created in your research lab. You place a 22.5 kg block of this new metal initially at a temperature 17 oC in a rigid insulated box. 0.10 kg of steam at 100 oC is piped into the box and then the box is sealed so that no heat can be transfered in or out. When the system comes to equilibrium, the temperature is 74 oC.

What is the specific heat of the metal? Give your answer in J/(kg oC) (or equivalently J/(kg K)), and give your answer to at least 3 significant digits.

Explanation / Answer

Mass of the metal M = 22.5 kg

Mass of the steam m = 0.10 kg

Temperature of the metal tm = 170 C

Temperature of the steam ts = 1000 C

Final temperature T = 740 C

Since the system is insulated, no heat is lost to surroundings then

heat lost by steam(Q1) = heat gained by metal(Q2)

Heat lost by steam(Q1) = m * L + m * Ss * ts

Where L = 2.26 * 106 J/kg

            Ss = 4.2 * 103 J/kg K

Now Q1 = 0.10 * 2.26 * 106 + 0.10 * 4.2 * 103 * (1000 - 740)

                 = 236920 J

Heat gained by metal(Q2) = M*Sm* tm where Sm is specific heat of the metal

                                Q2           = 22.5 * (74 - 17) * Sm

                                                = 1282.5 * Sm

Now Q1 = Q2

So, 236920 = 1282.5 * Sm

            Sm   = 236920/1282.5 = 184.73294 J/kg K or J/kg 0C

So the specific heat of the metal Sm = 184.73294 j/kg K

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