First slide

Different type of processes

Question

A tyre pumped to a pressure 3.375 atm at $27^{0} C$ suddenly bursts. What is the final temperature ( $γ =$ 1.5)?

Moderate

A

$27^{0} C$
B

$- 27^{0} C$
C

$0^{0} C$
D

$- 73^{0} C$

Solution

${T^{γ}}_{1} {P^{1 - γ}}_{1} = {T_{2}}^{γ} {P_{2}}^{1 - γ}$
or ${(\frac{T_{1}}{T_{2}})}^{γ} = {(\frac{P_{1}}{P_{2}})}^{γ - 1} = {(\frac{300}{T_{2}})}^{\frac{3}{2}} = {(\frac{3.375}{1})}^{\frac{3}{2} - 1}$
or $T_{2} = \frac{300}{{(3.375)}^{\frac{1}{3}}} = 200 K \Rightarrow t_{1} - 73^{0} C$

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