Gaseous State Test

Result

Gaseous State Test - 4

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Question 1
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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)_rev = (T_f)_irrev

B
T_f = T_i for both reversible and irreversible processes

C
(T_f)_irrev> (T_f)_rev

D
T_f> T_i for reversible process but T_f = T_i for irreversible process

Solution

According to first law of thermodynamics

q=ΔU + w

An isolated system is adiabatic, so q=0.

0 = ΔU + w

⇒w = −ΔU

For reversible expansion, w is positive and hence ΔU is negative.

Since ΔU = Cv×ΔT or we can say that ΔUΔT

This means T_f is less than T_i in both the cases.

For the same expansion of volume, the work done in irreversible process is greater than that in reversible one because the system has to work against friction also. Thus, heat absorbed in reversible process will be greater than that of in irreversible process.

Thus, (T_f)_irrev> (T_f)_rev