The pressure in monoatomic gas increases linearly from ` =4xx10^(5) Nm^(-2)` to ` 8xx10^(+5) Nm^(-2)` when its volume increases from `0.2m^(3)` to `0.5m^(3)`. Calculate .
(i) Work done by the gas ,
(ii) Increase in the internal energy,
(iii) Amount of heat supplied,
(iv) Molar heat capacity of the gas `R= 8.31J mol^(-1) K^(-1)`

Explanation

The change in internal energy of a gas is given by
`Delta U = mu C _(V) Delta T= (mu R Delta T)/( (gamma -1))= ((P_(F)V_(F) -P_(I)V_(I)))/((gamma -1 ))`
As the gas is monatomic `gamma = (5//3)`
So, `Delta U = (10 ^(5) (8xx 0.5 -4 xx 0.2))/([(5//3)-1])`
`=3/2 xx 10^(5)(4-0.8).`
i.e., ` Delta U =4.8 xx10^(5) J`