Explanation:
When a system undergoes a sudden change under condition that no exchange of heat takes place between the system and surroundings, then such a process is called adiabatic. So, a tyre bursting suddenly an adiabatic process.
\(p^{1-\gamma} T^{\gamma}=\text { constant }\)
where, \(\gamma\) is ratio of specific heats, \(p\) is pressure and \(T\) is temperature.
\(\therefore \,\,\,\,{\left( {\frac{{{p_2}}}{{{p_1}}}} \right)^{\gamma - 1}} = {\left( {\frac{{{T_2}}}{{{T_1}}}} \right)^\gamma }\)
\( \Rightarrow \,\,\,\,\,{\left( {\frac{1}{2}} \right)^{0.4}} = {\left( {\frac{{{T_2}}}{{300}}} \right)^{1.4}}\)
\(\therefore 0.4\left[ {\log 1 - \log 2} \right]\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1.4\left[ {\log {T_2} - \log 300} \right]\)
\( \Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{T_2} = 246.1\,\,\,K\)