A thermodynamic system is taken from an initial state I with internal energy U_(i)=100 J to the final state f along two different paths iaf and ibf, as schematicallly shown in the figure. The work donw by the system along the paths af, ib and bf are W_(af)=200 J,W_(ib)=50J and W_(bf)=100 J respectively.the heat supplied to the system along the path iaf, ib and bf are Q_(iaf)Q_((jb) and Q_(bf) repsectively.If the internal energy of the system in the state b is U_(b) =200 J and Q_(iaf) =500J, the ratio Q_(bf)//Q_(jb)is In the figure a container is shown to have a movable(without friction) piston on top. The container and the piston are all made of perfectly insualting material allowing no heat transfer between outside and inside the container The container is divided int to two compartments by a rigid partition made of a themally conducting material that allows slow tranfer of heat.The lower compartment of the container is filled with 2 moles of an ideal monatiomic gas at 700 K and the upper compartment is filled with 2 moles of an ideal diatomic gas at 400 K.The heat capacitites per mole of na ideal monatomic gas are C_(v)=(3)/(2)R,C_(p)=(5)/(2)r, and those for an ideal diatomic gas are C_(v)=(5)/(2)r,c_(p)=(7)/(2)R.