# Are sudden adiabatic expansions reversible or irreversible? (Tyre burst problems)

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?

• Yes you are right, bursting of tire should be considered irreversible. Jun 25 at 8:25
• 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. Jun 25 at 8:37
• 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. Jun 25 at 10:51