Answer:
The value is [tex]\eta _2 = 0.57[/tex]
Explanation:
From the question we are told that
The temperature of the heat source is [tex]T_s = 1000 \ K[/tex]
The amount of power transferred is [tex]P_s = 1000 \ kW = 1000 *10^{3} \ W[/tex]
The work produced is [tex]W = 400 \ kW[/tex]
The temperature of the environment [tex]T_e = 300 \ K[/tex]
Gnerally the Carnot efficiency of the system is mathematically represented as
[tex]\eta_c = 1 -\frac{T_e}{T_s}[/tex]
=> [tex]\eta_c = 1 -\frac{300}{1000}[/tex]
=> [tex]\eta_c = 0.7[/tex]
Generally the first law efficiency of the system is mathematically represented as
[tex]\eta _1 = \frac{W}{P_s}[/tex]
=> [tex]\eta _1 = \frac{400}{1000}[/tex]
=> [tex]\eta _1 = 0.40[/tex]
Generally the second law efficiency of the system is mathematically represented as
[tex]\eta _2 = \frac{\eta_1}{\eta_c}[/tex]
=> [tex]\eta _2 = \frac{0.4}{0.7}[/tex]
=> [tex]\eta _2 = 0.57[/tex]
