Refer to the Carnot cycle of an ideal gas shown in the figure. Let `W_(ararrb), W_(brarrc), W_(crarrd)` and `W_(drarra)` represent the work done by the system during the processes `ararrb, brarrc, crarrd` and `drarr a` respectively. Consider the following relations

(1) `W_(ararrb) + W_(brarrc) + W_(crarrd)+W_(drarra) gt 0`
(2) `W_(ararrb) + W_(brarrc) + W_(crarrd)+W_(drarra) lt 0`
(3) `W_(ararrb) + W_(crarrd) gt 0`
(4) `W_(brarrc) +W_(drarra) = 0`
Which of the above relation is/are true?

Options

A. 1 and 3 only
B. 3 and 4 only
C. 1, 3 and 4 only
D. 2, 3 and 4 only

Answer

C

Explanation

`a rarr b rarr` isothermal expansion (`W_(ararrb) rarr` +ve)
`brarrc rarr` adiabatic expansion (`W_(brarrc) rarr` +ve)
`c rarr d rarr` isothermal compression (`W_(crarrd)rarr` -ve)
`d rarr a rarr` adiabatic compression (`W_(drarra) rarr` -ve)
For expansion process `rarr W rarr` +ve
For compression process `rarr W rarr` -ve
Total work should be +ve (as process is clockwise) and `W_(brarrc)= -W_(drarra) implies W_(brarrc)+W_(drarra) = 0`.