A block of iron ore A of mass m = 10 kg and specific heat capacity C = 460 kJ/(kg·K) obeys the constitutive relations Energy E: E2 − E1 = mC (T2 − T1)Entropy S: S2 − S1 = mC ln (T2/T1) where T is temperature. The block of metal is initially at temperature T1 = 700 K and it is inthe vicinity of a thermodynamic reservoir R, which is at temperature T0 = 298 K and pressurep0 = 101.3 kPa. a) What is the maximum amount of work that can be extracted adiabatically from the metal blockin its initial state (known as the adiabatic availability Psi_1)? b) What is the maximum amount of work that can be extracted adiabatically from the combinationof the metal block A and reservoir R? (known as the available energy, or exergy, Omega_1)? c) Evaluate the energy and entropy changes of system A and reservoir R in part (b). Fournumerical values are required. d) Draw three separate energy-entropy diagrams, one for system A, one for the reservoir R,and one for the combined system AR. Draw on these diagrams the initial and final states of theinteraction described in part (b). e) In a practical application we only manage to extract half the available energy computer inpart (b), while the final temperature of system A becomes equal to that of the reservoir. Whatis the amount of entropy generated by irreversibility? f) How would you define the first law efficiency of the process in part (e)? Evaluate this efficiency. g) How would you define the second law efficiency (effectiveness) of the process in part (e)?Evaluate this efficiency. h) Evaluate the energy and entropy changes of system A and reservoir R in part (e). Four valuesare required. Compare these values with those of part (c) and with the entropy generated byirreversibility. i) Draw on the diagrams of part (d) the final states of the systems A, R and AR in part (e).
A block of iron ore A of mass m = 10 kg and specific heat capacity C = 460 kJ/(kg·K) obeys the constitutive relations
Energy E: E2 − E1 = mC (T2 − T1)
Entropy S: S2 − S1 = mC ln (T2/T1)
where T is temperature. The block of metal is initially at temperature T1 = 700 K and it is in
the vicinity of a
p0 = 101.3 kPa.
a) What is the maximum amount of work that can be extracted adiabatically from the metal block
in its initial state (known as the adiabatic availability Psi_1)?
b) What is the maximum amount of work that can be extracted adiabatically from the combination
of the metal block A and reservoir R? (known as the available energy, or exergy, Omega_1)?
c) Evaluate the energy and entropy changes of system A and reservoir R in part (b). Four
numerical values are required.
d) Draw three separate energy-entropy diagrams, one for system A, one for the reservoir R,
and one for the combined system AR. Draw on these diagrams the initial and final states of the
interaction described in part (b).
e) In a practical application we only manage to extract half the available energy computer in
part (b), while the final temperature of system A becomes equal to that of the reservoir. What
is the amount of entropy generated by irreversibility?
f) How would you define the first law efficiency of the process in part (e)? Evaluate this efficiency.
g) How would you define the second law efficiency (effectiveness) of the process in part (e)?
Evaluate this efficiency.
h) Evaluate the energy and entropy changes of system A and reservoir R in part (e). Four values
are required. Compare these values with those of part (c) and with the entropy generated by
irreversibility.
i) Draw on the diagrams of part (d) the final states of the systems A, R and AR in part (e).
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