Carbon monoxide is carried around a closed cyclic processes `abc`, in which `bc` is an isothermal process, as shown in Fig. The gas absorbs `7000 J` of heat as its temperature is increased from `300 K` to `1000 K` in going from `a` to `b`. The quantity of heat ejected by the gas during the process `ca` is

Options

A. `4200 J`
B. `500 J`
C. `9000 J`
D. `9800 J`

Answer

D

Explanation

`(Delta Q)_(ab) = + 7000 = mu C_(v) (1000 - 300)`
For the process ca:
`T_(a) = 300 K, T_(c ) = T_(b) = 1000 K`
`(Delta Q)_(ca) = mu C_(P) (300 - 1000) = - mu C_(P) xx 700`
`= - mu (C_(V) + R) 700`
For carbon monoxide :
`T_(a) = 300 K, T_(c) = T_(v) = 1000 K`
`(Delta Q)_(ca) = mu C_(P) (300 - 1000) = - mu C_(P) xx 700`
`= - mu (C_(V) + R) 700`
For carbon monoxide :
`gamma = (7)/(5)`
`C_(V) = (R )/(gamma - 1) = (R )/((7)/(5) - 1) = (5 R)/(2)`
Hence, form Eq. (i)
`7000 = mu (5 R)/(2) xx 700` or `mu R = (20)/(5) = 4`
`(Delta Q)_(ca) = - (700 + 4 xx 700) = - 9800 J`
Negative sign shows that heat is ejected.