An ideal monoatomic gas is taken through the thermodynamic states `AtoBtoCtoD` via the paths shown in the figure. `U_(A),U_(B),U_(C)andU_(D)` represent the internal energies of the gas in the states A, B, C and D respectively. Which is the wrong statement from the following ?

Options

A. `U_(C)gtU_(D)`
B. `U_(B)=U_(C)`
C. `U_(B)ltU_(A)`
D. `U_(A)=U_(D)`

Answer

C

Explanation

The internal energy of a gas depends only upon the temperature.
`thereforeU_(A)=U_(D)` at temperature T
Similarly, `U_(B)=U_(C)` at temperature 2T
These are correct statements.
`U_(C)` is at temperature 2T and `U_(D)` is at temperature T.
`thereforeU_(C)gtU_(D)` is also correct.
But `U_(B)` at `2TltU_(A)` at T is wrong.