An uninsulated, rigid tank contains 5 kg of steam initially at 40 bars and 180 C

Question

An uninsulated, rigid tank contains 5 kg of steam initially at 40 bars and 180 C.  The air surrounding the tank iis at uniform temperature of 15 C.  After a period of time, the pressure within the tank has been reduced to 9 bars due to heat transfer from the water substance to the air.  Determine:

a) the heat transfer from the steam, in kJ.

b) the entropy change from the steam, in kJ/K.

c) the entropy generation for an enlarged system composed of the steam and the heat transfer region, which includes the tank and the layer of air adjacent to the tank, in kJ/K.

d) Whether the overall process is reversible, irreversible, or impossible.

Explanation / Answer

At 40 bar .. 180 C

enthalpy = 764.70749 KJ/kg
specific volume = 0.0011248626 m3/kg
entropy = 2.1354441361383 KJ/kg

so the final state is ... 9 bar.. specific volume = 0.0011248626 m3/kg..
from steam table we get ...
at 9 bar ...
specific vol at staurated liquid = 0.001121 m3/kg
specific vol at staurated Vapour = 0.215 m3/kg

so quality = (0.0011248626-0.001121) / (0.215 - 0.001121) = 1.80597 * 10^-5

enthalpy at sat. liq = 742.8
enthalpy at sat. vap = 2774
so final enthalpy = (1.80597 * 10^-5 ) * (2774-742.8) + 742.8 = 742.836683 KJ/kg

entropy at sat liq. = 2.095
entropy at sat vap. = 6.623
so final entropy = (1.80597 * 10^-5 ) * (6.623 - 2.095) + 2.095 =2.095082 KJ/kg


a) heat transfer = (initial enthalpy - final)*mass = (764.70749-742.836683)*5 = 109.354035 KJ

b) change in entropy = (final - intial)*mass = (2.095082-2.1354441361383)*5 = - 0.2018106806915 KJ/K

c) change in entropy of surrounding = heat transfered / temperature = 109.354035 / ( 273 + 15 ) = 0.37970151 KJ/K

so the entropy generation for an enlarged system composed of the steam and the heat transfer region, which includes the tank and the layer of air adjacent to the tank
= 0.37970151 - 0.2018106806915 = 0.1778908293085 KJ/k


d) As there is net entropy generation in the system.. so the overall process is irreversible

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