An inventor claims to have built a machine that operates as follows: 100 kg/min

Question

An inventor claims to have built a machine that operates as follows: 100 kg/min of steam at T = 400degreeC and P = 5bar enters the machine. 100 kg/min of saturated liquid water at 40degreeC leaves the machine. 50,000 kJ/min of shaft work is produced by the system. There is no heat exchange with the surroundings. An undisclosed amount of nitrogen enters the process at 315K and 1 bar, and the same amount of nitrogen leaves at 300K and 1 bar. Assume the N2 is an ideal, diatomic gas. Kinetic and potential energy of all entering and leaving streams is negligible. This is a steady state process that can continue as described indefinitely. Without knowing anything else about how this machine works, what can you say about the feasibility of the inventor's claim?

Explanation / Answer

Solution:

Given:

P1= 5 bar

T1= 400C

m1=100kg/min

T2=40C

m2=100kg/min

W=50000 kg/min

Q=0

KE = 0 ; PE =0

If the given machine is feasible them it should satisfy steady equation of flow.

Steady Flow equation says

H1 + KE + PE + Q = H2 + KE + PE + W (where H is enthalpy)

H1 = H2 + W as KE, PE & Q is zero

m1CpT1 = m1CpT2 + W

100x1.005x673 = 100x1.005x313 + W

67636.5 = 31456.5 + W

W =36180 kJ/min

Max work coming using steady equation is 36180 kJ/min

But Work available at shaft mention is 50000kJ/min therefore given mention is not feasible.

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