Question

A Carnot cycle operates between the temperature limits of 300 K and 2000 K, and produces 600 kW of net power. The rate of entropy change of the working fluid during the heat addition process is

Answer 1

Correct Answer - Option 3 : 0.353 kW/K

Concept:

The rate of heat addition is expressed as, 

\(\dot Q = \frac{{{\rm{W}}{{\rm{T}}_{\rm{H}}}}}{{{{\rm{T}}_{\rm{H}}}{\rm{\;}} - {\rm{\;}}{{\rm{T}}_{\rm{L}}}}}\)

The rate of entropy generation during heat addition is, 

\({\dot S_{{\bf{gen}}}} = \frac{{{\bf{\dot Q}}\;}}{{{{\bf{T}}_{\bf{H}}}}} = \frac{{\bf{W}}}{{{{\bf{T}}_{\bf{H}}}\; - \;{{\bf{T}}_{\bf{L}}}}}\)

Calculation:

Given:

T_L = 300 K, T_H = 2000 K, W = 600 kW

\({\dot S_{{\rm{gen}}}} = \frac{{\rm{W}}}{{{{\rm{T}}_{\rm{H}}}{\rm{\;}} - {\rm{\;}}{{\rm{T}}_{\rm{L}}}}} = \frac{{600}}{{2000 - 300}} = 0.353{\rm{\;kW}}/{\rm{K}}\)

The rate of entropy change of the working fluid during the heat addition process is 0.353 kW/K.