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Question 5.4: A metallic block of mass M is brought to a temperature T0 an...

A metallic block of mass M is brought to a temperature T_0 and plunged into a calorimeter filled with a mass \acute{M} of water. The system consisting of the metallic block and the water container is considered as isolated. In this process, the water temperature rises from T_i to T_f, the equilibrium temperature. The specific heat of the water per unit mass is c^∗_{\acute{M}} Determine the specific heat per unit mass of the metal c^∗_M in the temperature range used in this experiment. Consider that the water container is made of a material with a negligible specific heat.

Numerical Application:

M = 0.5 kg, \acute{M} = 1 kg, T_0 = 120°C, T_i = 16°C, T_f = 20°C  and  c^∗_{\acute{M}} = 4, 187 J kg^{−1}K^{−1}.

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Since the system consisting of the metallic block and the water is isolated, the variation of internal energy vanishes,

ΔU_{if} = M c^∗_M (T_f − T_0) + \acute{M} c^∗_{\acute{M}} (T_f − T_i) = 0 .

which yields the specific heat of the metal,

c^∗_M = c^∗_{\acute{M}} \frac{\acute{M}}{M} \frac{T_f − T_i}{T_0 − T_f} = 335 J kg^{−1} K^{−1}.

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