Question

The pressure in the tyre of a car is four times the atmospheric pressure at 300 K. If this tyre suddenly bursts, its new temperature will be $( \gamma = 1.4 )$

• A. $300 ( 4 ) ^ { 1.4 / 0.4 }$
• B. $300 \left( \frac { 1 } { 4 } \right) ^ { - 0.4 / 1.4 }$
• C. $300 ( 2 ) ^ { - 0.4 / 1.4 }$
• D. $300 ( 4 ) ^ { - 0.4 / 1.4 }$

Answer 1

Answer: (D)

$300 ( 4 ) ^ { - 0.4 / 1.4 }$

Answer 2

For adiabatic process $\frac { T ^ { \gamma } } { P ^ { \gamma - 1 } } =$constant

⇒$\frac { T _ { 2 } } { T _ { 1 } } = \left( \frac { P _ { 1 } } { P _ { 2 } } \right) ^ { \frac { 1 - \gamma } { \gamma } }$⇒$\frac { T _ { 2 } } { 300 } = \left( \frac { 4 } { 1 } \right) ^ { \frac { ( 1 - 1.4 ) } { 1.4 } }$⇒$T _ { 2 } = 300 ( 4 ) ^ { - \frac { 0.4 } { 1.4 } }$