Three moles of an ideal monoatomic gas perform a cycle shown in figure. The gas temperatures 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 cycle is :

Options

A. (a)`5 kj`
B. (b)`10 kj`
C. (c)`15 kj`
D. (d)`20 kj`

Answer

D

Explanation

we are given 3 moles of monatomic gas
`T_1 = 400 K, " "T_2 = 800 K `
`T_3 = 2400 K," "T_4 = 1200 K`
Process 1 to 2 : Isochoric
Process 2 to 3 : Isobaric
Process 3 to 4: Isochoric
Process 4 to 1 : Isobaric
Let `T_1 = T_0 = 400 K, P_1 = P_0` and ` V_1 = V_0`
(i) Process 1 to 2 is isochoric, so `V_2 = V_1 = V_0` and ` T_2 = T_1` (given ) `rArr P_1 = 2P_1 = 2P_0`
(ii) Process 2 to 3 is isobaric, So `P_3 = P_2 = 2P_0` and `T_3 3 T_2 `(given ) `rArr " "V_3 = 3V_2 = 3V_0`
(iii) Process 3 to 4 is isobhoric, so `V_4 = V_4 = 3V_0 ` and `T_4 = T_3 /2`(given ) `rArr " "P_4 = P_3/2 = P_0`
Now, we know the pressure and volume at each of the 4 points. So we can draw P-V diagram. Work done = W = Area under P-V curve
` = 3 P_0 V_0`
but at state 1
`P_0 V_0 = n RT_0 (3R) (400) = 1200 R rArr W = 3 (L 200 R ) = 3600 R`