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

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

Step-by-step 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 = (T_h - T_c)/(T_h)`

=>
`\eta = (500 - 300)/(500)`

=>
`\eta = 0.4`

Generally the thermal efficiency of the engine is

`\eta_t = (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

`(Q - Q_l)/(Q) \le 0.4`

=>
`(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`