A balloon of volume V contains an ideal gas at 27 degC and 1.2 atm. It rises to a height where the temperature is -23 degC and the pressure is 0.50 atm. The volume of the balloon there is

JEE Advanced levelSingle correct optionDifficulty 3 of 3ig089

A balloon of volume $V$ contains an ideal gas at $2 7^{\circ} C$ and $1.2 atm$ . It rises to a height where the temperature is $- 2 3^{\circ} C$ and the pressure is $0.50 atm$ . The volume of the balloon there is

\frac{P _{1} V _{1}}{T _{1}} = \frac{P _{2} V _{2}}{T _{2}}

T_{1} = 300 K

T_{2} = 250 K

V_{2} = V \times \frac{1.2}{0.50} \times \frac{250}{300} = V \times 2.4 \times 0.8333 = 2.0 V