Two reversible heat engine \(\mathrm{E}_{1}\) and \(\mathrm{E}_{2}\) are arranged in series between a hot reservoir at temperature \(\mathrm{T}_{1}\) of \(600 \mathrm{~K}\) and a cold reservoir at temperature \(\mathrm{T}_{2}\) of \(300 \mathrm{~K}\). Engine \(\mathrm{E}_{1}\) receives \(500 \mathrm{~kJ}\) of heat from a reservoir at \(T_{1}\). Presuming both engines have equal thermal efficiency, determine-the temperature at which heat is rejected by \(\mathrm{E}_{1}\) and received by \(\mathrm{E}_{2}\), the thermal efficiency of each engine, work done by engine \(\mathrm{E}_{1}\) and \(\mathrm{E}_{2}\), and heat rejected by \(\mathrm{E}_{2}\) to a cold reservoir.