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

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

Can the whole of heat be converted into work?

$A$ 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 :

$A$ hot piece of copper at $100^{\circ} C$ is dropped into a pond at $30^{\circ} C$. The copper cools down to $30^{\circ} C$,while the pond remains at its initial temperature due to its large size. Then,

Which limitation of a heat engine is imposed by the second law of thermodynamics?