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. `- 10 kJ`
B. `- 20 kJ`
C. `- 15 kJ`
D. `- 30 kJ`

Answer

A

Explanation

a. `6T_(1) = 3T_(2) = 2T_(4) = T_(3) = 1800 K`
`T_(1) = 300 K, T_(2) = 600 K`
`T_(4) = 900 K, T_(3) = 1800 K`
`4 rarr 1` and `2 rarr 3` are isochroic process in which work done = 0
`W_(12) = P (V_(2) - V_(1)) = nRT (T_(2) - T_(1))`
`= 2 xx R (600 - 300) = 600 R`
`W_(34) = P (V_(4) - V_(3)) = nRT (T_(4) - T_(3))`
`= 2 xx R (900 - 1800) = - 1800 R`
`W_(T o t a l) = 600 - 1800 R = - 1200 T = - 10000 J`