(1) Method A: Consider the egg as a closed system
Take the egg as a system. It is a closed system since no mass
flow in or out of the egg. The entropy balance for a closed system is:
Rearranging the above equation gives the expression of the entropy generation.
That is,
The first two terms on the
right hand side of the above equation corresponds to the entropy change
in the system, and the third term is the entropy
transfer by heat.
The entropy change in the system:
The egg is approximated as an incompressible substance. With constantspecificheat
assumption, its entropy change can be determined from
ΔS = S_{2 } S_{1 }= mC_{ave}ln(T_{2}/T_{1})
where 1 denotes the initial state
and 2 denotes the final state. Hence,
T_{1} = 10 ^{o}C = 283 K
T_{2} = 100 ^{o}C = 373 K
The mass of the egg is
m = Vρ = 4/3(3.14)(0.03)^{3}(1000)
= 0.113 kg
The average specific heat is given as 3.4 kJ/(kgK). Substituting
all the data into the expression of entropy change yields
S_{2 } S_{1 }= 0.113(3,400)
ln(373_{}/283_{}) = 106.1 J/K
The entropy transfer to the egg by heat:
The egg is cooked from 10^{o}C to 100^{o}C in 100^{o}C
water. Assume the boundary of the egg remains 100^{o}C during
the whole process and hence the entropy transfer to the egg by
heat transfer can be determined by
where Q is the heat transferred to the egg from the surrounding water,
and T is 100^{o}C. Q can be determined by the energy balance
of the egg.
Q  W = U_{2}  U_{1
} Q = mc_{ave} (T_{2}  T_{1})
= 0.113(3,400)(100
 10) = 34,578 J
Substituting Q and T to the expression of entropy transfer gives,
Q/T = 34,578/(373) = 92.7 J/K
After calculating the entropy change in the system and the entropy
transfer by heat, the entropy generation can be determined.
It is
S_{gen} = (S_{2}  S_{1})  Q/T
= 106.1  92.7 = 13.4 J/K
