Two moles of an ideal mono-atomic gas undergo a cyclic process as shown in the figure. The temperatures in different states are given as `6T_(1) = 3T_(2) = 2T_(4) = T_(3) = 1800 K`. Determine the work done by the gas during the cycle.

Options

A. `-1200R`
B. `1200R`
C. `1575R`
D. `-800R`

Answer

A

Explanation

`6T_(1) = 3T_(2) = 2T_(4)=T_(3) = 1800K`
`T_(1) = 300 K , T_(2)= 600K`
`T_(4) = 900K, T_(3) = 1800K`
`1 rarr 4 and 2 rarr 3` are isochoric process work done = 0.
`W_(12) = P(V_2-V_1) nR(T_2-T_1)`
`=2 xx R(600-300)= 600R`
`W_(341) = P(V_4-V_3)=nR(T_4-T_3)`
`=2xxR(900-1800)=-1800R`
`W_(Total) = 600R - 1800R = -1200R`.