The heat output of a particular engine is $7.5 \times 10^{3} \mathrm{~J}$ per cycle, and the net work out is $4.0 \times 10^{3} \mathrm{~J}$ per cycle. (a) The heat input is (1) less than $4.0 \times 10^{3} \mathrm{~J},$ (2) between $4.0 \times 10^{3} \mathrm{~J}$ and $7.5 \times 10^{3} \mathrm{~J},$ (3) greater than $7.5 \times 10^{3} \mathrm{~J}$ Explain. (b) What is the heat input and thermal efficiency of the engine?