# How can the $PV^{\gamma}$ equation be used here? If it can't be used then how do you solve this problem?

A motor tyre has a pressure of $$3$$ atm at a temperature of $$27^\circ C$$ If the tyre suddenly bursts what is the resulting temperature?
First of all, I believe this is not a quasi-static process and by "suddenly" i dont think there is any equillibrium maintained. This question is given as a homework problem under the section of Applications of the First Law of Thermodynamics. There was a solution on some other website to a very similar problem but they use the $$PV^{\gamma}=constant$$ equation and also the equation for ideal gas. But I dont see how they are able to use it since this is not a quasi-static process.

• Well, the question arises whether the process is quasistatic (i.e. reversible) or not? What do you think? Based on the formula you've given in the problem, what kind of process does it look to you? And, does that process necessarily have to be a quasistatic one? Jun 22, 2020 at 13:40
• based on the formula it is an adiabatic process, and to apply the equation which i meant i thought the process needs to be necessarily quasistatic. Jun 22, 2020 at 14:11
• Well, if the process is happening suddenly, then it's not quasistatic, is it? The reason is that, adiabatic processes can be irreversible as well, as a sudden 'bursting' of tires involves no heat exchange. This is an example of an irreversible adiabatic process. Jun 22, 2020 at 14:58
• See this for the difference between a reversible and a quasistatic process: Quasistatic vs Reversible. Also, read these sites to understand what I am talking about:1. 2. Jun 22, 2020 at 17:08
• thank you, i finally did get what you mean and this problem should be assumed as a quasi-static irreversible adiabatic process. Jun 23, 2020 at 10:12

• heat up? i got a lower temperature value on applying the $PV^{\gamma}=constant$ equation. Jun 22, 2020 at 13:48