Nitrogen gas (N_2) at 600 kPa, 21 degree C enters an insulated control volume op

Question

Nitrogen gas (N_2) at 600 kPa, 21 degree C enters an insulated control volume operating at steady state with no work done. Half of the nitrogen exits the device at 100 kPa and 82 degree C and the other half exits at 100 kPa and -40 degree C. The effects of kinetic and potential energy are negligible. Assume that nitrogen is an ideal gas with constant specific heats, find out whether the operation of this device can satisfy the First-law of Thermodynamics and whether the device can operate as described?

Explanation / Answer

according to steady state energy equation

h1+KE1+PE1+Q=h2+KE2+PE2+W
here, KE=PE=Q=W=0

therefore according to 1st law of thermodynamics h1 must be equal to h2

initial enthalpy at 600kPa and 100oC is 268.532 kJ/kg (from property table of nitrogen)
enthalpy at 100kPa and 82oC is 356.152  kJ/kg

enthalpy at 100kPa and -40oC is 207.04 kJ/kg

since final state is equally divided, the average of both are taken
therefore final enthalpy h2 =(356.152+207.04)/2 =281.596 kJ/kg
here h1 and h2 are not equal, therefore this device does not satisfy First law of thermodynamics

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