One mole of an ideal mono-atomic gas is caused to go through the cycle shown in the figure below. Then the change in the internal enegry in expanding the gas from `a` to `c` along the path `abc` is:

Options

A. `3P_(0)V_(0)`
B. `6 RT_(0)`
C. `4.5 RT_(0)`
D. `10.5 RT_(0)`

Answer

D

Explanation

`Pv= nRT` at point `C`
`2P_(0)xx4V_(0)=1xxRT_(c)`
`T_(c )=[(8P_(0)V_(0))/(R )]`
at point a
`P_(0)V_(0)=1xxRT_(0)`
`T_(0)=(P_(0)V_(0))/(R ) , T_(c )=8T_(0)`
change in internal energy `=[ nC_(v)dT]`
For path `a` to `b=1xx(3)/(2)Rxx[3T_(0))=(9)/(2)RT_(0)`
For path `b` to `c=1xx(3)/(2)Rxx[4T_(0)]=6T_(0)R`
Total change `=(9)/(2)RT_(0)+6RT_(0)=(21RT_(0))/(2)=10.5 RT_(0)`
So total change in internal energy
`Delta U =10.5 RT_(0)`