An ideal monoatomic gas is taken thorough the thermodynamic states A→ B→ C→ D via the paths shown in the figure. If UA,UB,UC and UD represent the internal energy of the gas in states A, B, C and D respectively, then which of the following is not true?

Question

An ideal monoatomic gas is taken thorough the thermodynamic states A→ B→ C→ D via the paths shown in the figure. If UA,UB,UC and UD represent the internal energy of the gas in states A, B, C and D respectively, then which of the following is not true? (A)  UB=UA  (B)  UB<UA  (C)  UB=UC  (D)  UC>UD

Tardigrade Admin · Accepted Answer

Internal energy of a gas U=(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 UA=UD UB=UC UB>UA UC>UD

Q. 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?

$U_{B} = U_{A}$

$U_{B} < U_{A}$

$U_{B} = U_{C}$

$U_{C} > U_{D}$

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

Q. An ideal monoatomic gas is taken thorough the thermodynamic states A→B→C→D via the paths shown in the figure. If UA​,UB​,UC​ and UD​ represent the internal energy of the gas in states A, B, C and D respectively, then which of the following is not true?

UB​=UA​

UB​<UA​

UB​=UC​

UC​>UD​