Question
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 statements is correct?
A.
$${\left( {{T_f}} \right)_{rev}} = {\left( {{T_f}} \right)_{irrev}}$$
B.
$${T_f} = {T_i}$$ for both reversible and irreversible processes
C.
$${\left( {{T_f}} \right)_{irrev}} > {\left( {{T_f}} \right)_{rev}}$$
D.
$${T_f} > {T_i}$$ for reversible process but $${T_f} = {T_i}$$ for irreversible process
Answer :
$${\left( {{T_f}} \right)_{irrev}} > {\left( {{T_f}} \right)_{rev}}$$
Solution :
NOTE : In a reversible process the work done is greater than in irreversible process. Hence the heat absorbed in reversible process would be greater than in the latter case. So
$${T_f}\left( {rev.} \right) < {T_f}\left( {irr.} \right)$$