An ideal gas can be expended from an initial state to a certain volume through two different processes
(i) `pV^(2)=` constant and (ii) `p=KV^(2)` where K is a positive constant. Then

Options

A. Final temperature in (i) will be greater then in (ii)
B. Final temperature in (ii) will be equal to (i)
C. Total heat given to the gas in (i) case is given then in (ii)
D. Total heat given to the gas in (ii) case is greater than in (i)

Answer

D

Explanation

From equation PV=nRT
`P_(C) lt P_(B), V_(C)=V_(B)` and `T_(B) gt T_(C)`
`W_(AB) gt W_(AC) , (T_(B)-T_(A)) gt T_(C)-T_(A)`
so by ist law
`Q=DeltaU+W`
`Q=1/2 nRT Delta T+W`
`Q_(AB) gt Q_(AC)`