`A` gas is found to obey the law `P^(2)V`= constant. The initial temperature and volume are `T_(0)` and `V_(0^(@))` If the gas expands to a volume `3V_(0)`, then

Options

A. final temperature become `sqrt3 T_(0)`
B. internal energy of the gas will increase
C. final temperature becomes `(T_(0))/(sqrt3)`
D. internal energy of the gas decrease.

Answer

A, B

Explanation

`P^(2)V=` constant `(n^(2)R^(2)T^(2))/(V^(2)).V=` constant
`P=(nRT)/(V)implies(T^(2))/(V)=` constant
`(T_(o)^(2))/(V^(o))=(T^(2))/(3V_(o))impliesT=sqrt3T_(o)TalphasqrtV` here `V` increases
`:. T` increases hence internal energy increases