1000 kJ/s of heat is transferred from a constant temperature heat reservoir maintained at 1000 K to a system at a constant temperature of 500 K. The temperature of the surroundings is 300 K. The net loss of available energy as a result of this heat transfer is:

Concept:

According to Gouy-Stodola theorem, the loss of available energy is given by T_o(ΔS)_gen

where T_o is the atmospheric temperature and (ΔS)_gen is the entropy generation due to the heat transfer from one reservoir to another reservoir.

\({({\rm{\Delta }}S)_{gen}} = \oint \frac{{dQ}}{T}\)

\({({\rm{\Delta }}S)_{gen}} = \frac{Q}{{{T_2}}} - \frac{Q}{{{T_1}}}\)

Calculation:

Given, Q = 1000 kJ/s and T₁ = 1000 K, T₂ = 500 K

Then, \({({\rm{\Delta }}S)_{gen}} = \frac{{1000}}{{500}} - \frac{{1000}}{{1000}} = 1\;kJ/Ks\)

∴ Loss of available energy = T_o(ΔS)_gen = 300 × 1 = 300 kJ/s