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Encountered Question:

The tube of the tyre of a car is filled with air at $\pu{27^\circ C}$ and $\pu{2 atm}$ pressure. If the tube suddenly bursts, the final temperature of the air will be ($γ_\textrm{air}=1.5$) ____.

Approach here:

Given: $T_1 = \pu{27 K}+ \pu{273K}=\pu{300K}$ ,$P_ 1 = \pu{2atm}$

in the process

$T_1^γP_1^{γ−1} = T_2^γ​P_2^{γ−1}$

gives

$T_2 = (2^{-1/3}) \pu{300 K}= \pu{240 K}$

Q: The pressure inside a tyre is 4atm at 27C. If the tyre bursts suddenly, the new temperature will be $(\gamma = \frac75)$_____.

Ans: $300(4)^{-2/7}$

Source

The above approach is correct if we assume reversible process but as bursting is very fast we should assume it is an irreversible process, hence $\Delta U = W_\textrm{on system}$ gives

$\frac{f}{2}nR(T_2-T_1) = -P_{ext}(V_2-V_1)$

Putting values gives $T=\pu{250 K}$.

So, why do we assume tyre bursting is a reversible process OR are above sources incorrect?

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    $\begingroup$ Yes you are right, bursting of tire should be considered irreversible. $\endgroup$ Jun 25 at 8:25
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    $\begingroup$ Yes, the sources aren't correct. The first source is actually quite faulty and unreliable and in the second source it seems by seeing the webpage that the source is a website of physics (targeting IITJEE), also, in physics that is asked in IITJEE, every thermodynamic process is taken to be reversible one , that is why they assumed the process to be reversible adiabatic . But as @NisargBhavsar pointed out, the process should be irreversible adiabatic. $\endgroup$
    – ecneics
    Jun 25 at 8:37
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    $\begingroup$ Thanks I will add answer soon and feel free to answer if you have better possible answer. $\endgroup$
    – Jay
    Jun 25 at 9:11
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    $\begingroup$ The adjective sudden does not fit well the noun equilibrium, which is a required state along paths of reversible processes. By other words, reversible system processes are those, where a closed cycle of system states can by achieved by the closed cycle of the environment state, so the closed path $\Delta S_tot=0$. ( Not to be confused with other meaning of reversibility as 2 way process.). In the first sense it is the opposite to what @ecneics said: Truly reversible process does not exist, as intermediate process states are not in true equilibrium, unless the process takes infinite time. $\endgroup$
    – Poutnik
    Jun 25 at 10:51
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    $\begingroup$ The second approach actually assumes that the expansion is irreversible, against the constant pressure of the surrounding atmosphere, and gets the right answer. $\endgroup$ Jun 25 at 15:34
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Conclusion from comments:

  1. Sources are incorrect.
  2. Second approach is correct assuming expansion is irreversible against the constant pressure of the surrounding atmosphere and hence gets the right answer.
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