You have been hired by a venture capitalist to evaluate a concept engine proposed by an inventor, who claims that the engine consumes 100 MW at a temperature of 500 K, rejects 20 MW at a temperature of 300 K, and delivers 50 MW of mechanical work. Does this claim violate the first law of thermodynamics, the second law, both, or neither?

It violates neither of them

Explanation:

first law of thermodynamics, also known as Law of Conservation of Energy, states that energy can neither be created nor destroyed; energy can only be transferred or changed from one form to another.

As we can see, 100MW work and temp of 500K was initial.

Now, the summation of output and lost work and temp = 70MW and 300k, do it doesn't violates first law.

The Second Law of Thermodynamics says that processes that involve the transfer or conversion of heat energy are irreversible, from the question, it is irreversible.

chemical properties of thing

they should be similar or the same