A vertical thermally insulated cylinder of volume `V` contain `n` moles of an ideal monoatomic gas under a weightless piston. A load of weight `W` is placed on the piston as a result of which the piston is displaced. If the initial temp of the gas is `300K`, area of piston is `A` and atmospheric pressure `P_(0)`. (take `W=P_(0)A`). Determine the value of final temperature of the gas

Options

A. `375K`
B. `425K`
C. `475K`
D. `515K`

Answer

A

Explanation

Let `T_(1)` and `T_(2)` be the initial and final temperature then
`P_(0)V=nRT_(1)`……….i
`(P_(0)+W/A)(V-Ah)=nRT_(2)`…….ii
Where `h` is the displacement of piston.
Also, work done on gase `=/_\U`
`Wh=nC_(v)/_\T=3/2nR(T_(2)-T_(1))`......iii
From equation i, ii and iii
`2/3Wh=(WV)/A-Wh-P_(0)Ab`
or , `Ah=(WV)/(P_(0)A+55/3/W)`
`T_(2)=(P_(0)+W/A)(V-(Wv)/(P_(0)A+5/3W))`
`T_(2)=5/3T_(1)=5/4xx300=5xx75K`