The correct option is B on gas is 0.5×105 J
Heat is absorbed by system {gas}, ΔQ=+8×105 J
work done by system, ΔW=+6.5×105 J
According to the 1st law of thermodynamics
ΔQ=ΔU+ΔW
8×105=ΔU+6.5×105
⇒ΔU=+1.5×105J ........(1)
For the second process,
Heat absorbed by the system ΔQ′=+105 J
Again using First law,ΔQ=ΔU+ΔW
We write that,
ΔQ′=ΔU+ΔW′
ΔU will stay the same as initial and final states of gas is same.
Now, From the data given in the question and (1)
105=1.5×105+ΔW′
ΔW′=−0.5×105 J
(negative sign indicates work is being done on the gas).
Thus, option (b) is the correct answer.