Question

An ideal gas is allowed to expand both reversible and irreversibly in an isolated system. If `T_(i)` is the initial temperature and `T_(f)` is the final temperature, which of the following statements is correct:
A. `(T_(f))_("irrev") gt (T_(f))_("rev)`
B. `T_(f) gt T_(i)` for reversible process but `T_(f) = T_(i)` for irreversible process
C. `(T_(f))_("rev") = (T_(f))_("irrev")`
D. `T_(f) = T_(i)` for both reversible and irreversible processes

Answer 1

Correct Answer - A
In isolated system the expansion of gas is carried out adiabatically. Since heat exchange between system and surrounding is not possible i.e., `q=0` and secondary `w_(rev)` is always greater than `w_(irr)` therefore for reversible process there must be comparatively higher decreases in internal energy i.e, `Delta U` for reversible process will be more negative. Hence final temperature in reversible process will be smaller than irreversible process.
`:. (T_(f))_("irrev") gt (T_(f))_(rev)`