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11.Thermodynamics
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Air is filled in a motor tube at ${27^o}C$ and at a pressure of $8$ atmospheres. The tube suddenly bursts, then temperature of air is $[{\rm{Given}}\,\,\gamma \,{\rm{of}}\,{\rm{air}} = \,1.5]$
A
${27.5^o}C$
B
${75^o}K$
C
$150\,K$
D
${150^o}C$
Solution
(c) $\frac{{{T_2}}}{{{T_1}}} = {\left( {\frac{{{P_2}}}{{{P_1}}}} \right)^{\frac{{\gamma – 1}}{\gamma }}}$
$ \Rightarrow \frac{{{T_2}}}{{{T_1}}} = {\left( {\frac{1}{8}} \right)^{\frac{{1.5 – 1}}{{1.5}}}} = {\left( {\frac{1}{8}} \right)^{\frac{1}{3}}} = \frac{1}{2}$
$ \Rightarrow {T_2} = \frac{{{T_1}}}{2} = \frac{{300}}{2} = 150K$.
Standard 11
Physics
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