A block of iron ore A of mass m = 350 kg and specific heat capacity...
A block of iron ore A of mass m = 350 kg and specific heat capacity C = 460 kJ/(kg·K) obeys the constitutive relations where T is temperature. The block of metal is initially at temperature T1 = 700 K and it is placed in a perfectly-sealed, constant-pressure container B containing 64 kg of air initially at 320 K and atmospheric pressure 101.3 kPa. The air in container B can be modeled as a perfect gas with specific heat capacity at constant pressure Cp = 1.0 kJ/(kg.K) and gas constant R = 0.287 kJ/(kg K).
Energy E: E2 − E1 = mC (T2 − T1)
Entropy S: S2 − S1 = mC ln (T2/T1)
(a) Find the initial volume of air in container B. If the only allowable interaction is a heat interaction between iron block A and the air in container B, find the final temperature of block A and of the air in container B, the entropy generated by irreversibility, the final volume of the air in container B, the energy transferred from the ore to the air, and the energy received from the ore by the air.
(b) Determine the adiabatic availability of the combination of block A and the air in container B, the final temperatures of the ore A and air in container B, the final volume of the air in container B, the energy transferred from the ore to the air, and the energy received from the ore by the air.
(c) If block A and the air in container B are also allowed to interact with the local reservoir R which is at temperature TR =298 K, what is the maximum temperature that the air in container B can reach while interacting with block A and reservoir R? What is the final volume of the air in container B? What is the energy transferred from the ore in this case? What is the energy received by the air in this case? [Hint: write the equations you would use to solve the problem, formulate into one equation as a function of final temperature of air, and solve the equation graphically or numerically]
(d) What is the available energy of the ore and air in their initial state?
(e) In a practical application only 30% of the available energy is extracted. What is the entropy generated by irreversibility?
Homework Answers
This is a simple question of thermodynamics and simply solved by
using Ideal Gas equation, Energy transfer formula and Entropy
formula. 
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A block of iron ore A of mass m = 350 kg and specific heat
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