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 21.5 kg block of this new metal initially at a temperature 16 degree C in a rigid insulated box. 0.25 kg of steam at 100 degree C 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 70 degree C. What is the specific heat of the metal? Give your answer in J/(kg degree C) (or equivalently J/(kg K)), and give your answer to at least 3 significant digits. Do not include units in your answer.

Explanation / Answer

using principle of caloriemetry

heat gained by block = heat lost by steam

mb*Sb*dTb = (ms*Lv)+(ms*Sw*dTs)

mb = 21.5 kg and ms = 0.25 kg

Sb =? and Sw specific heat of water = 4186 J/kg*K

dTb is the change in temparature of the block = 70-16 = 54 C

dTs is the change in temparature of the steam = 100-70 = 30 C

Lv is the latent heat of vapourisation = 2264.76*1000 J/kg

then mb*Sb*dTb = (ms*Lv)+(ms*Sw*dTs)

21.5*Sb*54 = (0.25*2264.76*1000)+(0.25*4186*30)

specific heat capacity of block is 514.71 J/kg-K

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