Question

A power cycle operating between hot and cold reservoirs at 500 K and 300 K, respectively, receives 1000 kJ by heat transfer from the hot reservoir. The magnitude of the energy discharged by heat transfer to the cold reservoir must satisfy

Answer 1

Answer:

The value is $Q_l \ge 600\ k J$

Explanation:

From the question we are told that  

   The temperature of  hot is  $T_h = 500 \ K$

   The temperature of cold is  $T_c = 300 \ K$

   The energy received is  $E = 1000 \ kJ = 1000 *10^{3 } \ J$

Generally the maximum thermal  efficiency of the engine is mathematically represented as

     $\eta = \frac{T_h - T_c}{T_h}$

=> $\eta = \frac{500 - 300}{500}$

=> $\eta = 0.4$

Generally the thermal  efficiency of the engine is  

   $\eta_t = \frac{Q - Q_l}{Q}$

Here  $Q_l$ is the heat energy rejected

Generally the thermal efficiency must be less than or equal to the maximum thermal  efficiency

So

       $\frac{Q - Q_l}{Q} \le 0.4$

=>    $\frac{1000 *10^{3} - Q_l}{1000 *10^{3} } \le 0.4$

the change in inequality sign is because $1000*10^{3}$  which was dividing started multiplying

=>    $Q_l \ge 1000*10^{3} - 400*10^{-3}$

=>  $Q_l \ge 600*10^{3} \ J$

=>  $Q_l \ge 600\ k J$