A piston of mass M is hung from a massless spring whose restoring force law goes as F =- kx ^3 , where k is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts, where the bottom part is filled with ' n ' moles of an ideal gas. An external work is done on the gas isothermally (at a constant temperature T) with the help of a heating filament (with negligible volume) mo

Step-by-step solution

Using WET Total energy supplied = gravitational potential energy + spring potential energy + work done by gas aligned & Mg (L₁-L₀ )+ _ L₀ ^ L₁ k^3 d x+n R T n & [ L₁ ~A ~L ₀ ~A ]+ W _ ext =0 & ~K 4 [ x ^4 ]_ L ₀ ^ L ₁ + Mg ( L ₁- L ₀ )+ _ L ₀ ^ L ₁ k x^3 d x+n R T n aligned aligned & [ L₁ L₀ ]+ W _ ext =0 & k 4 ( ~L ₁^4- L ₀^4 )+ Mg ( L ₁- L ₀ )+ nRT n & [ L ₁ ~L ₀ ]+ W _ ext =0 & ~W _ ext = k 4 ( ~L ₁^4- L ₀^4 )+ Mg ( L ₁- L ₀ )+ nRT n [ L ₁ ~L ₀ ] aligned