Question

An ideal monoatomic gas is taken thorough the thermodynamic states $ A\to B\to C\to D $ via the paths shown in the figure. If $ {{U}_{A}},{{U}_{B}},{{U}_{C}} $ and $ {{U}_{D}} $ represent the internal energy of the gas in states A, B, C and D respectively, then which of the following is not true?

• A. $ {{U}_{B}}={{U}_{A}} $
• B. $ {{U}_{B}}<{{U}_{A}} $
• C. $ {{U}_{B}}={{U}_{C}} $
• D. $ {{U}_{C}}>{{U}_{D}} $

Answer 1

Answer: (A)

Internal energy of a gas
$ U=\frac{3}{2}nRT $
where, R is constant.
Thus, for a given number of moles of the same gas
$ U\propto T $
From the graphs, we conclude that
$ {{U}_{A}}={{U}_{D}} $
$ {{U}_{B}}={{U}_{C}} $
$ {{U}_{B}}>{{U}_{A}} $
$ {{U}_{C}}>{{U}_{D}} $