Question: Choose the correct option for free expansion of an ideal gas under adiabatic condition is A) 𝑞 = 0 ,    𝑊 = 0 ,    Δ 𝑇 = 0 B) 𝑞 = 0 ,    𝑊 = 0 ,    Δ 𝑇 ≠ 0 C) 𝑞 = 0 ,    𝑊 = 0 ,    Δ 𝑇 < 0 D) 𝑞 = 0 ,    𝑊 = 0 ,    Δ 𝑇 > 0.

              Solution :-    Correct option : (1)

In  a free expansion,

P_ext = 0 — (1)

then,
W = PΔV
= 0 (ΔV)

W = 0 — (2)

Since, it is an adiabatic process, Heat is constant –

q = 0 — (3)

acc. to first law of thermodynamics,

ΔU = q + W

ΔU = 0 + 0

ΔU = 0 — (4)

if  ΔU = 0 , then

ΔT = 0 — (5).

Hence, option (1) is the correct answer

In adiabatic free expansion of an ideal gas,  the gas expands into a vacuum within an insulated container, resulting in no heat transfer and no work done.

Types of Thermodynamic processes:

1. Isothermal process                                           2.Adiabatic process                                                 3. Isochoric process                                                 4. Isobaric process

1. Isothermal process :The thermodynamic process which is carrying outtemperature is constant is called isothermal process. In this process  although heat enters (or) leaves the system, the temperature of the system remains constant through out the process.

In an isothermal process, The change of temperature (dT = 0) is constant.

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(ii) Adiabatic process:-
A process in which no heat enters (or) leaves the system during any step of the process is known as adiabatic process.

In an adiabatic process, heat change (dq = 0) is constant.

(iii) Isobaric process:-
A process during which pressure of the system remains constant throughout the reaction is called “Isobaric process”. (dp = 0).

(iv) Isochoric Process:
A process in which volume of the system remains constant throughout the studies.

For an isochoric process ΔV = 0.

 Another thermodynamic process is cyclic process,

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Cyclic process:-
A process during which the system comes to its initial state through a number of different processes is called cyclic process.

For a cyclic process change in internal energy(ΔU ) = 0 and change in enthalpy( ΔH) = 0. Δ (state function) = 0, Δ (path function) ≠ 0