Can the whole of heat be converted into work?

Which of the following statements is correct for any thermodynamic system?

Write an example in which the first law of thermodynamics is allowed but is never observed.

Why is a heat engine never $100\%$ efficient?

The fundamental limitation to the coefficient of performance of a refrigerator is given by

$N_{2}$ gas is heated from $300\, K$ to $600\, K$ through an isobaric process. Find the change in entropy of the gas. $(n = 1\, \text{mole})$ (in $J/K$)