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

$A$ 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,

Find the change in the entropy in the following process: $100 \, g$ of ice at $0^{\circ}C$ melts when dropped in a bucket of water at $50^{\circ}C$. (Assume the temperature of the water does not change). The result is in $cal/K$.

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

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.

“Heat cannot by itself flow from a body at lower temperature to a body at higher temperature” is a statement or consequence of