Question

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

• A. ${27}^{o}C$
• B. $-{27}^{o}C$
• C. $0^{o}C$
• D. $-{73}^{o}C$

Answer 1

Answer: (D)

$-{73}^{o}C$

The given process is adiabatic as no heat transfer is involved. Thus we have
$T_1^{\gamma }{P}_1^{1-\gamma }=T_2^{\gamma }{P}_2^{1-\gamma }$
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 $T_2=(\frac{300}{3.375}{)}^{1/3}=200K=-{73}^{o}C$