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  4. A tyre pumped to a pressure 3.375 atm at 27° C suddenly bursts. What is the final temperature (γ=1.5) ?

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Q. A tyre pumped to a pressure $3.375\, atm$ at $27^{\circ} C$ suddenly bursts. What is the final temperature $(\gamma=1.5)$ ?

Thermodynamics

Solution:

$T_{1}^{1-\gamma} P_{1}^{1-\gamma}=T_{2}^{\gamma} P_{2}^{1-\gamma}$
or $\left(\frac{T_{1}}{T_{2}}\right)^{\gamma}=\left(\frac{P_{1}}{P_{2}}\right)^{\gamma-1}$
$=\left(\frac{300}{T_{2}}\right)^{3 / 2}=\left(\frac{3.375}{1}\right)^{3 / 2-1}$
or $T_{2}=\frac{300}{(3.375)^{1 / 3}}$
$=200\, K =-73^{\circ} C$