A mass of `8g` of oxygen at the pressure of one atmosphere and at temperature `27^(@)C` is enclosed in a cylinder fitted with a frictionless piston. The following operations are performed in the order given (Specific heat fo oxygen `c_(V) = 670 J//kgK`, Molecular mass of oxygen `=32 gm//"mole"`, one atm `= 1.013 xx 10^(5)N//m^(2)` and `R = 25//3 J//"mole"-K)`
(a) the gas is heated at constant pressure to `127^(@)C`,
(b) then it is compressed isothermally to its initial volume and
(c ) finally it is cooled to its initial temperature at constant volume.

Options

A. Find the heat absorbed by the gas during operation (a) ?
B. Find work done by the gas in case (a)?
C. Find the work done on the gas in case (b)?
D. Find the heat extracted from the gas in case (c )?

Answer

A, B, C, D

Explanation

for enclosed gas number of moles
`n = (8)/(32) = (1)/(4)` mole
From gas equation for process (a)
`(P_(0)V_(i))/(T_(i)) = (P_(0)V_(f))/(T_(f)) rArr (V_(i))/(V_(f)) = (300)/(400) = (3)/(4)`

(1) Heat absrobed by the gas during operation 'a'
`Q = nC_(P)DeltaT =(1)/(4) [(670)/(1000)xx32+(25)/(3)] xx 100 = (893@)/(12)J`
(2) Work done by the gas in case 'a'
`W = nR DeltaT = (1)/(4) xx (25)/(3) xx 100 = (625)/(3) J`
(3) Work done by the gas in case 'b'
`W = nRT log_(e) ((V_(f))/(V_(i))) = (1)/(4) (25)/(3) xx 400 ln (4//3)`
`= (2500)/(3) ln (4//3)`
(4) Heat extracted form the gas in case 'c'
`Q = nC_(v) DeltaT = (1)/(4) xx (670)/(1000) xx32 xx 100 = 536 J`