An inventor claims to have devised a heat engine for use in space vehicles that operates with a nuclear$-$fuel$-$ generated energy source whose temperature is $510$ K and a sink at $270$ K that radiates waste heat to deep space. He also claims that this engine produces $4\mathrm{.}1$ kW while rejecting heat at a rate of $15,000$ kJ$/$h$.$ Is this claim valid? Support your answer with appropriate calculations.