State the Clausius statement of the second law of thermodynamics.

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

On a hot day,a cup full of ice water placed on a table heats up,while a cup of hot tea on the same table cools down. Explain the reason.

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.

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