A stream of liquid water enters a boiler and emerGes from the boiler as steam. This steam is mixed with a second stream of steam and the mixed steam is fed to a turbine. It emerges from the turbine as a VLE mixture with a quality of 0.96. The entire process operates at steady state.

Question

An engineer draws a control volume that contains the boiler, the turbine and the mixing point. Which of the following is an energy balance that is both correct for this system and consistent with the sign conventions established in this book?
A. 0= m ?_(1,in) H ?_(1,in)+ m ?_(2,in) H ?_(2,in)- (m ?_(1,in)+m ?_(2,in) ) H ?_out+W ?_s+ Q ?
B. W ?_s+ Q ?= m ?_(1,in) H ?_(1,in)+ m ?_(2,in) H ?_(2,in)- m ?_out H ?_out
C. ?-W ??_s= m ?_(1,in) H ?_(1,in)+ m ?_(2,in) H ?_(2,in)- m ?_out H ?_out
D. m ?_(1,in)+m ?_(2,in) ?=m ??_out
E. All of the above.

Answer 1

A. Correct.
B. Incorrect. This expression of the energy balance does not agree with the sign convention we are using. Review Section 1.4.3 and the energy balance itself in Section 3.3.
C. Incorrect. The heat term is missing. The function of a boiler is to add heat and cause a phase change from liquid to vapor.
D. Incorrect. This is a material or mass balance, not an energy balance.
E. Incorrect. Only one of these answers the question.

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