100 kJ of energy is transferred from a heat reservoir at 1000 K to a heat reservoir at 500 K. The ambient temperature is 300 K. The loss of available energy due to heat transfer process is

Option 2 : 30 kJ

__Concept:__

According to Gouy-Stodola theorem, the loss of available energy (Irreversibility) is given by To(ΔS)gen

where To 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 = 100 kJ and T1 = 1000 K, T2 = 500 K

Then, \({({\rm{\Delta }}S)_{gen}} = \frac{{100}}{{500}} - \frac{{100}}{{1000}} = 0.1\;kJ/K\)

∴ Loss of available energy = To(ΔS)gen = 300 × 0.1 = 30 kJ