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An ideal mono...

Question

An ideal monoatomic gas is taken through the theromodynamic 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?

U_{A} = U_{D}

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U_{B} = U_{A}

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U_{B} = U_{C}

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U_{C} > U_{D}

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Solution

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

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