A heat engine absorbs \(250 \mathrm{~kJ}\) of heat from a source at \(310 \mathrm{~K}\). The heat engine produces a work to the tune of \(65 \mathrm{~kJ}\), discarding \(110 \mathrm{~kJ}\) of heat to a thermal reservoir at \(312 \mathrm{~K}\) and \(80 \mathrm{~kJ}\) of heat to another reservoir at \(270 \mathrm{~K}\). Does this engine violate the second law of thermodynamics?