Initially inside a rigid cylinder there is a certain amount of mass M of superheated water vapor at T$1=250\backslash$deg C and p$1=1$MPa with its initial specific internal energy u$1.$ The circular lids of the cylinder are adiabatic, while the side wall is not. A metal coil is placed that absorbs the heat from the cylinder until the substance inside it reaches a final temperature T$2=125\backslash$deg C and a specific internal energy u$2.$ The volume of the cylinder is $0\mathrm{.}23275$ m$^3$

a$)$ If there is no loss of energy when the coil absorbs heat, express the heat expelled by the substance as a function of M$,$ u$1,$ u$2.$

b$)$ Find the specific volume v$1$ and the specific energy u$1$

c$)$ Find the mass M

d$)$ The value of the heat expelled by the substance if the quality in the final state is x$2=0\mathrm{.}3011$