An engine operating between $150\,^{\circ}C$ and $25\,^{\circ}C$ takes $500\,J$ of heat from a higher temperature reservoir. If there are no frictional losses,the work done by the engine is.....$J$.

One mole of an ideal gas expands adiabatically and reversibly from its initial pressure to half of its initial pressure. What will be the value of $\Delta S$ in $J \ K^{-1} \ mol^{-1}$? $[\ln 2 = 0.693$ and $R = 8.314 \ J \ mol^{-1} \ K^{-1}]$

The enthalpy of vaporization of water is $186.5 \, kJ \, mol^{-1}$. What is the entropy of vaporization in $kJ \, K^{-1} \, mol^{-1}$?

At $298 \, K$ and $1 \, atm$ pressure,the entropies of $H_2(g)$,$Cl_2(g)$,and $HCl(g)$ are $130.6$,$223$,and $186.7 \, J \, K^{-1} \, mol^{-1}$ respectively. What is the entropy change for the reaction $H_2(g) + Cl_2(g) \rightarrow 2HCl(g)$ in $J \, K^{-1} \, mol^{-1}$?

When a solid melts reversibly,which of the following occurs?

Given that $\Delta H = 0$ for the mixing of two gases,explain whether the diffusion of these gases into each other in a closed container is a spontaneous process or not?