Consider building a space station on Mars. One of the engineering challenges cou

Question

Consider building a space station on Mars. One of the engineering challenges could be the temperature control, because Mars surface temperature can be as low as - 80 degree C at night. If we use an ideal vapor compression cycle discussed in class to build this air conditioning system for a space station, it will be better to use propane. Also since the room temperature is higher than outside temperature, this system resembles a heat pump (see the bottom figure). A heat pump cycle has the same feature as refrigeration cycle, except that the desired quantity is qout instead of qin. To design this heat pump, we use the ideal vapor compression cycle with propane. The T-s diagram is on the right. If the low temperature is -80 degree C and the pump rises pressure to 9bar, find the following quantities: (1) State variables of all four states in T-s diagram (state 1, 2s, 3 and 4). The state variables include pressure, temperature, enthalpy, entropy and quality if a mixture. (2) Work per unit mass consumed by compressor.

Explanation / Answer

1) From therodynamic tables of Propane:

Corresponding to saturated vapor at -80 deg C, we get

P1 = 0.1301 bar, T1 = -80 deg C, h1 = 375.4 kJ/kg-K and s1 = 1.986 kJ/kg-K

Corresponding to superheated Propane at P2s = 9 bar and s2s = s1 = 1.986 kJ/kg-K we get,

P2s = 9 bar, T2s = 64 deg C, h2s = 576.2 kJ/kg, s2s = s1 = 1.986 kJ/kg-K,

Corresponding to sat. liquid at 9 bar, we get

P3 = 9 bar, T3 = 22.82 deg C, h3 = 154.7 kJ/kg and s3 = 0.58 kJ/kg-K

Since process 3-4 is constant enthalpy, h4 = h3 = 154.7 kJ/kg.

Further, P4 = P1 = 0.1301 bar, T4 = T1 = -80 deg C.

h4 = hf + x4*(hg-hf) where hf and hg are enthalpies of sat. liquid and sat. vapor at -80 deg C and x is the quality.

We have, hf = -87 kJ/kg and hg = 375.4 kJ/kg.

So, 154.7 = -87 + x4*(375.4-(-87))

x4 = 0.523

so, s4 = sf + x4*(sg - sf) = -0.408 + 0.523*(1.986-(-0.408)) = 0.844 kJ/kg-K

2) Work by compressor = h2s - h1 = 576.2 - 375.4 = 200.8 kJ/kg

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