Three moles of an ideal monoatomic gas per form a cyclic as shown in the figure. The gas temperature in different states are: `T_(1) = 400 K, T_(2) = 800 K, T_(3) = 2400 K and T_(4) = 1200 K`. The work done by the gas during the cyclic is

Options

A. `10 kJ`
B. `20 kJ`
C. `5 kJ`
D. `8.3 kJ`

Answer

B

Explanation

In the curve 1-2 and 3-4, we find that the pressure is directly proportional to temperature . So that volume remains unchanged, i.e., gas does not work
The work done during the isobaric processes 2-3 and 1-4 are follow:
`W_(2-3)=P_(2)(V_(3)-V_(2))`
`W_(1-4) =P_(1)(V_(1)-V_(4))`
Total work done
`=P_(2)(V_3-V_2)+P_(1)(V_1-V_(4))`
`:. W_(T)=3RT_(2)+3RT_(1)-3RT_(4)`
`:. W_(T) = 3RT[T_(1)+T_(3)-T_(2)-T_(4)]`
`=3R[400+200-800-1200]`
`=3Rxx800=20xx1^3J`
`=20kJ`.