Under what conditions does the isothermal exp | vedclass

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(C) Free expansion is defined as the expansion of a gas into a vacuum $(P_{ext} = 0)$.
For an ideal gas,the internal energy $(U)$ is a function of te

Vedclass · Accepted Answer

The gas is ideal and expands against a vacuum.

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(C) Free expansion is defined as the expansion of a gas into a vacuum $(P_{ext} = 0)$.
For an ideal gas,the internal energy $(U)$ is a function of temperature only,i.e.,$U = f(T)$.
In an isothermal process,the temperature remains constant $(\Delta T = 0)$,therefore $\Delta U = 0$.
According to the first law of thermodynamics,$\Delta U = q + w$.
Since $w = -P_{ext} \Delta V$ and $P_{ext} = 0$,the work done $(w)$ is $0$.
Thus,for an ideal gas undergoing isothermal expansion against a vacuum,$\Delta U = 0$ and $w = 0$,which implies $q = 0$ (adiabatic process).
Therefore,the condition for free expansion is that the gas expands against a vacuum,and for an ideal gas,this process is both isothermal and adiabatic.

Under what conditions does the isothermal expansion of a gas become a free expansion process?

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