State the Kelvin-Planck statement of the second law of thermodynamics.

The graphs below show the entropy versus energy $U$ of two systems $1$ and $2$ at constant volume. The initial energies of the systems are indicated by $U_{1, i}$ and $U_{2, i}$,respectively. The graphs are drawn to the same scale. The systems are then brought into thermal contact with each other. Assume that,at all times,the combined energy of the two systems remains constant. Choose the most appropriate option indicating the energies of the two systems and the total entropy after they achieve equilibrium.

$A$ 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 :

Water of mass $m$ gram is slowly heated to increase the temperature from $T_1$ to $T_2$. The change in entropy of the water,given specific heat of water is $1 \ J \ g^{-1} \ K^{-1}$,is

When $1\, kg$ of ice at $0^\circ C$ melts to water at $0^\circ C,$ the resulting change in its entropy,taking latent heat of ice to be $80\, cal/g,$ is ...... $cal/K$.

The entropy of a thermodynamic system does not change when this system is used for: