1.

One mole of an ideal monoatomic gas is caused to go through the cycle shown in figure. Then, the change in the internal energy is expanding the gas from a to `c` along the path `abc` is:A. `3P_(0)V_(0)`B. `6 RT_(0)`C. `4.5 RT_(0)`D. `10.5 RT_(0)`

Answer» Correct Answer - D
`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)`


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