Question

$\Delta U$ will be zero for which processes?
(A) Cyclic process
(B) Isothermal expansion
(C) Isochoric process
(D) Adiabatic process

Answer 1

Hint: Try to understand each term given in the options. Recollect the first law of thermodynamics. The difference in internal energy of the system is zero when there is no temperature change.

Complete step by step answer:
-According to the first law of thermodynamics, in basic terms, energy is neither gained nor lost when a substance is converted from one form to another.
-First law of thermodynamics has many definitions. One of the statements is, the total internal energy of an isolated system is constant that is, $\Delta U=0$.
-Mathematically, the first law is given as, $\Delta U=q+W$ where $\Delta U$ is the change in internal energy of the system, q is the heat supplied to the system and W is the work done on the system by the surroundings.
-Let’s see what happens to the first law of thermodynamics when work is carried out under different conditions.
-In the isothermal process, temperature is kept constant so change in temperature when work is done on the system is zero. The internal energy of the system depends on temperature. So, $\Delta U=0$.
-In adiabatic process, no heat is supplied to the system externally. So, q=0. The system uses internal energy of the system to do the work. Therefore, $\Delta U=W$
-In an isochoric process, volume is kept constant. So, $\Delta V=0$. In this case, work is not done on the system. Therefore, internal energy will be equal to heat absorbed in the system but since, work is not involved at all, we can say that, $\Delta U=0$.
-In cyclic process, there is formation of intermediates which ultimately form the same reactant and the cycle repeats. So, we can say that there is no work done in the system and internal energy of the system remains constant. Therefore, change in internal energy is zero. Hence, $\Delta U=0$.
-Therefore, the correct options are (A) Cyclic process, (B) Isothermal expansion and (C) Isochoric process.
So, the correct answer is “Option A, B and C”.

Note: Remember for an isothermal process, $\Delta T=0$. For an isochoric process, $\Delta V=0$. For an adiabatic process, q=0. For an isobaric process, $\Delta P=0$. In a cyclic process, a series of intermediates are formed which ultimately give back the original reactant and this process gets repeated like Krebs’ cycle.