Entropy of a system decreases .........

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

An ideal gas in a cylinder is separated by a piston in such a way that the entropy of one part is $S_{1}$ and that of the other part is $S_{2}$. Given that $S_{1} > S_{2}$. If the piston is removed,then the total entropy of the system will be:

State the Clausius statement of the second law of thermodynamics.

$A$ solid body of constant heat capacity $1 \ J/^oC$ 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 same amount of heat.
$(ii)$ Sequentially keeping in contact with $8$ reservoirs such that each reservoir supplies same amount of heat.
In both the cases,the body is brought from initial temperature $100^oC$ to final temperature $200^oC$. The entropy change of the body in the two cases respectively is :

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