Answer:
The value is [tex]P_e = 31275.2 \ W[/tex]
Explanation:
From the question we are told that
The efficiency of the carnot engine is [tex]\eta[/tex]
The efficiency of a heat engine is [tex]k = \frac{3}{4} * \eta[/tex]
The operating temperatures of the carnot engine is [tex]T_1 = 65 ^oC =338 \ K[/tex] to [tex]T_2 = 435 ^oC = 708 \ K[/tex]
The rate at which the heat engine absorbs energy is [tex]P = 44.0 kW = 44.0 *10^{3} \ W[/tex]
Generally the efficiency of the carnot engine is mathematically represented as
[tex]\eta = [ 1 - \frac{T_1 }{T_2} ][/tex]
=> [tex]\eta = [ \frac{T_2 - T_1}{T_2} ][/tex]
=> [tex]\eta = 0.3856[/tex]
Generally the efficiency of the heat engine is
[tex]k = \frac{3}{4} * 0.3856[/tex]
=> [tex]k = 0.2892[/tex]
Generally the efficiency of the heat engine is also mathematically represented as
[tex]k = \frac{W}{P}[/tex]
Here W is the work done which is mathematically represented as
[tex]W = P - P_e[/tex]
Here [tex]P_e[/tex] is the heat exhausted
So
[tex]k = \frac{P - P_e}{P}[/tex]
=> [tex]0.2892 = \frac{44*10^{3} - P_e}{44*10^{3}}[/tex]
=> [tex]P_e = 31275.2 \ W[/tex]
