Calculate the efficiency of a cycle consisting of isothermal, isobaric and isochoric lines, if in the isothermal process, the volume of the ideal gas with the adiabatic exponent $\mathrm{\gamma }$,

(a) increases $n$-fold,

(b) decreases $n$-fold.

An ideal gas with the adiabatic exponent $\mathrm{\gamma }$, goes through a cycle within which the absolute temperature varies $\mathrm{\tau }$-fold. Find the efficiency of this cycle.

A weightless piston divides a thermally insulated cylinder into two equal parts. One part contains one $\mathrm{mole}$ of an ideal gas, with adiabatic exponent $\mathrm{\gamma }$, the other is evacuated. The initial gas temperature is $T_0$. The piston is released and the gas fills the whole volume of the cylinder. Then, the piston is slowly displaced back to the initial position. Find the increment of the internal energy and the entropy of the gas, resulting from these two processes.

Find the capillary pressure

(a) in mercury droplets, of diameter, $d=1.5 \mathrm{\mu m}$, 

(b) inside a soap bubble, of diameter, $d=3.0 \mathrm{mm}$, if the surface tension of the soap water solution is, $\alpha =45 \mathrm{mN} {\mathrm{m}}^{-1}$.