Question

Air is filled ina motor car tube at ${27}^{o}C$ temperature and $2atm$ pressure. If the tube suddenly bursts then the final temperature will be [given $(1/2{)}^{2/7}=0.82$]

• A. $642K$
• B. $563K$
• C. $300K$
• D. $246K$

Answer 1

The correct option is D $246K$

For an adiabatic process:
$P^{1-\gamma }{T}^{\gamma }=constant$
Initial pressure and temperatures are:
2atm and 300K respectively.
After the explosion the final pressure is 1atm
$P_1^{1-\gamma }{T}_1^{\gamma }=P_2^{1-\gamma }{T}_2^{\gamma }$
For air, majority of the gas is nitrogen which is diatomic
Hence $\gamma =\frac{7}{2}$

$\left(2atm{)}^{1-\left(7/2\right)}\right(300{)}^{\left(7/2\right)}=\left(1atm{)}^{1-\left(7/2\right)}\right(T_2^{\left(7/2\right)})$
i.e. We get $T_2=246K$