One mole of an ideal gas is kept in a rigid vertical cylinder fitted with a light frictionless piston. The space above the piston opens into the atmosphere. The temperature of the gas and the surroundings is \(T\). What work has to be performed on the piston to increase the volume of the gas by a factor of \(\eta\)? Assume the process to be isothermal and quasistatic.
Universal gas constant\(=R\).