An ideal gas is enclosed in a cylinder having cross sectional area A. The piston of mass M has its lower face inclined at `theta` to the horizontal. The lower face of the piston also has a hemispherical bulge of radius r. The atmospheric pressure is `P_(0)`.
(a) Find pressure of the gas.
(b) The piston is slowly pulled up by a distance x. During the process the piston is always maintained in equilibrium by adding heat to the gas. [It means if the piston is left at any stage it will stay there in equilibrium]. Find change in temperature of the gas. Number of mole of the gas in the cylinder is one.

Answer

(a)`P_(0)+(Mg)/(A) " " (b) ((P_(0)A+Mg)x)/(R )`