JEE Main · 2006 · 30 Apr 2006 · Offline · Chemical Thermodynamics

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) $(T_{f})_{irrev} > (T_{f})_{rev}$ ✓ Correct
(B) $T_{f} > T_{i}$ 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: (A)

Solution

In an isolated system no heat is exchanged, so the gas does its expansion work entirely at the expense of its own internal energy and must cool. A reversible expansion extracts the maximum possible work, so it lowers the internal energy most and produces the largest temperature drop; an irreversible expansion against a smaller opposing pressure does less work and cools the gas less. The final temperature after the irreversible path is therefore the higher of the two,

(T_{f})_{irrev} > (T_{f})_{rev}

JEE Main · 2006 · 30 Apr 2006 · Offline · Single correct option

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JEE Main · 2006 · 30 Apr 2006 · Offline · Chemical Thermodynamics

Solution

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