A system goes from A to B via two processes I and II as shown in the figure. If $\Delta \mathrm{U}_{1}$ and $\Delta \mathrm{U}_{2}$ are the changes in internal energies in the processes I and II respectively, the

(A) $\Delta \mathrm{U}_{1}=\Delta \mathrm{U}_{2}$

(B) relation between $\Delta \mathrm{U}_{1}$ and $\Delta \mathrm{U}_{2}$ can not be determined

(C) $\Delta \mathrm{U}_{2}>\Delta \mathrm{U}_{1}$

(D) $\Delta \mathrm{U}_{2}<\Delta \mathrm{U}_{1}$

JEE Main · 2005 · 08 May 2005 · Offline · Heat & Thermodynamics

A system goes from A to B via two processes I and II as shown in the figure. If

Δ U_{1}

and

Δ U_{2}

are the changes in internal energies in the processes I and II respectively, the

(A) $Δ U_{1} = Δ U_{2}$ ✓ Correct
(B)relation between $Δ U_{1}$ and $Δ U_{2}$ can not be determined
(C) $Δ U_{2} > Δ U_{1}$
(D) $Δ U_{2} < Δ U_{1}$

Answer: (A)

Solution

Internal energy is a state function, fixed once the end states are fixed. Both processes start at

A

and finish at

B

, so although the paths differ, and the heat and work along them differ, the change in internal energy is the same for the two:

Δ U_{1} = Δ U_{2}

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option

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