Question

Assertion: A process of expansion of an ideal gas which is isothermal as well as adiabatic must be a free-expansion process.
 Reason: A reversible isothermal process can also be adiabatic only at $\text{T}=0$ and an irreversible isothermal process can also be adiabatic at $\text{T}\ne 0$
A.Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B.Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C.Assertion is correct but Reason is incorrect
D.Assertion is incorrect but Reason is correct

Answer 1

Hint: Free expansion is one the few cases in which we see adiabatic and isothermal processes going on at the same place and same time. In case of adiabatic expansion, there is no exchange of heat outside the system, and as there is no exchange of heat or energy hence we can say that the temperature of the gas inside the chamber or the cylinder is constant throughout.

Complete step by step answer:
To solve this question, we need to have knowledge about free expansion, isothermal process. Free expansion is one the few cases in which we see adiabatic and isothermal processes going on at the same place and same time. There is no exchange of energy inside and outside the system walls because the whole system is insulated.
A process in which gas is allowed to expand in vacuum and this happens so quickly that no heat leaves or enters the system this type of process is also known as adiabatic process and because this happens so fast the gas does not cross the system boundaries, hence no work is done by the system or on the system, then the expansion is called the free expansion.
Isothermal thermal systems are defined as by the change in particular systems where the temperature will remain constant. Isothermal expansion gives $\mathrm{\Delta }\text{T}=0$ . When the vacuum gas expands it leads to the free expansion of gas. In the case of an ideal gas the rate of free expansion is zero, that is total work done is zero, that is work done is zero. The value of zero is the result regardless of whether the process is reversible or irreversible. A process of expansion of an ideal gas which is isothermal as well as adiabatic must be a free-expansion process. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Hence, Option B is correct.

Note:
The stopper material used must ensure that no leakage of temperature occurs inside the cylinder. . Some of the reversible cases of isothermal expansion include converting ice from its solid-state to the liquid state as water, dehydrogenation and hydrogenation in milling a chemical and more. Examples for an irreversible condition include work that is done against the friction, Joule's heating effect, magnetic hysteresis and so on.