An inventor claims to have developed a work-producing steady flow device which e

Question

An inventor claims to have developed a work-producing steady flow device which employs steam as the working fluid. The claim states that, for conditions shown on Figure 1, the device accepts 1200kW of heat from a reservoir at 700 degrees celsius, rejects heat at an unspecified rate to a reservoir at 40 degrees celsius, and delivers 1500kW of mechanical power. Would you advise considering a patent application for the device? Specifically, show numerically whether or not the device violaes the Second Law of Thermodynamics.

Explanation / Answer

Q1 = 1200 KW

W = 1500 KW

T1 = 700 C = 973 K

T2 = 40 C = 313 K

max efficiency = = 1- T2/T1 = 1 - 313/973 = 0.678

Now actual efficiency = W/Q = 1500 / 1200 = 1.25

Hence, what the inventor has invented has an efficiency greater than 1

Hence, it would be advisable to have a patent of such a design..

THERMODYNAMICALLY, this is not possible. the max efficiency of any device cannot be greater than 1

and in this case max efficiency is limited to 0.678

HEAT REJECTED:

by first law

W + Q2 = Q1, where Q2 = heat rejected

1500 + Q2 = 1200

Q2 = - 300 KW

Now, = - § (dQ/t)

= - [Q1/T1 + Q2/T2]

= - [1200 /973 - 300/313]

= - 0.274 Kj/K
here entropy change is < 0. which is not possible by 2nd law thermpo.

hence system is not feasible.

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