An ideal gas goes from State A to state B via three different process as indicate in the `P-V` diagram.

If `Q_(2), Q_(3)` indicates the heat absorbed by the gas along the three processes and `DeltaU_(1), DeltaU_(2), DeltaU_(3)` indicates the change in internal energy along the three processes respectively, then

Options

A. `Q_(1)gtQ_(2)gtQ_(3)` and `DeltaU_(1)=DeltaU_(2)=DeltaU_(3)`
B. `Q_(3)gtQ_(2)gtQ_(1)` and `DeltaU_(1)=DeltaU_(2)=DeltaU_(3)`
C. `Q_(1)=Q_(2)=Q_(3)` and `DeltaU_(1)=DeltaU_(2)=DeltaU_(3)`
D. `Q_(3)gtQ_(2)gtQ_(1)` and `DeltaU_(1)gtDeltaU_(2)gtDeltaU_(3)`

Answer

A

Explanation

For all process `1,2,and 3`
`DeltaU=U_(B)-U_(A)` is the same
`:. DeltaU_(1)=DeltaU_(2)=DeltaU_(3)`
`Now, Q = DeltaU+W`
Now `W` = work done by the gas
`:. Q_(1) gt Q_(2) = Q_(3)`.