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An ideal gas is allowed to expand both r...

An ideal gas is allowed to expand both reversibly and irreversibly in an isolated system. If `T_i` is the initial temperature and `T_f` is the final temperature, which of the following statement is correct ?

A

`T_(f) gt T_(i)` for reversible process but `T_(f)=T_(i)` for irreversible process

B

`(T_(f))_(rev)=(T_(f))_(irrev)`

C

`T_(f)=T_(i)` for both reversible processes

D

`(T_(f))_(irrev) gt (T_(t))_(rev)`

Text Solution

Verified by Experts

The correct Answer is:
D
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 is reversible process will be smaller than irreversible process.
`:. (T_(f))_(irrev) gt(T_(f))_(rev)`
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