Three moles of an ideal monoatomic gas per form a cyclic as shown in the Fig. 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 curves `1-2` and `3-4` we find that the pressure is directly proportional to temperature. So the volume remains unchanged. i.e., gas does not work .
The work done during the isobaric processes `2-3` and `1-4` are follows:
`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_2)`
`:. W_T = 3RT_3-3RT_2+3RT_1-3RT_4`
Three moles has been given, so
`PV = nRT = 3RT`
`:. W_T = 3RT_(3) -3RT_(2)+3RT_1-3RT_4`
`= 3R[400+2400-800-1200]`
`=3R xx 800 = 20xx1^(3) J = 20kJ` .