One mole of a monoatomic ideal gas undergoes the process `ArarrB` in the given P-V diagram. What is the specific heat for this process?

Explanation

Specific heat
`C=(DeltaQ)/(DeltaT)=(1)/(DeltaT)(DeltaU+W)=C,+(W)/(DeltaT)`
For the given process
`W=4V_(0)(9P_(0))/(2)=18P_(0)V_(0) (because W="area of" P-V "graph")`
Also, `DeltaT=T_(2)-T_(1)`
`((6P_(0))(5V_(0)))/(R)-((3P_(0))V_(0))/(R)=(27P_(0)V_(0))/(R)`
and `C_(v)=(3)/(2)R`
`therefore C=C_(v)+(W)/(DeltaT)=(3R)/(2)+(18P_(0)V_(0))/(((27P_(0)V_(0))/(R)))`
`=(3R)/(2)+(2R)/(3)=(13R)/(6)`