One mole of an ideal gas at temperature `T_(1)` expands slowly according to the law `(P)/(V)`= constant. Its final temperature is `T_(2)`. The work bone by the gas is

Options

A. `R (T_(2) - T_(1))`
B. `(R//2) (T_(2) - T_(1))`
C. `(R//4) (T_(2) - T_(1))`
D. `PV (T_(2) - T_(1))`

Answer

B

Explanation

b. `W = int_(V_(1))^(V_(2)) P dV = int_(V_(1))^(V_(2)) KV dV`
`( :' (p)/(V) = ` constant)
`:. W = (1)/(2) k (V_(2)^(2) - V_(1)^(2))`
`PV = RT`
But `p = KV`
`:. KV^(2) = RT`
or `K (V_(2)^(2) - V_(1)^(2)) = R (T_(2) - T_(1))`
`:. W = (R )/(2) (T_(2) - T_(1))`