Can the whole of heat be converted into work?

State the Clausius statement of the second law of thermodynamics.

$A$ solid body of constant heat capacity $1\,J/^{\circ}C$ is being heated by keeping it in contact with reservoirs in two ways:
$(i)$ Sequentially keeping in contact with $2$ reservoirs such that each reservoir supplies the same amount of heat.
$(ii)$ Sequentially keeping in contact with $8$ reservoirs such that each reservoir supplies the same amount of heat.
In both cases, the body is brought from an initial temperature $100^{\circ}C$ to a final temperature $200^{\circ}C$. The entropy change of the body in the two cases respectively is:

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

$N_{2}$ 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 $J/K$)

$Assertion :$ When a glass of hot milk is placed in a room and allowed to cool,its entropy decreases.
$Reason :$ Allowing a hot object to cool does not violate the second law of thermodynamics.