A high-altitude balloon is filled with 1.41 $\times 10^{4}$ L of hydrogen at a temperature of $21^{o} C$ and a pressure of 745 Torr. What is the volume of the balloon at a height of 20km, where the temperature is - $48^{o} C$ and the pressure is 63.1 Torr.

1.274 \times 10^{5}

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1.66 \times 10^{5}

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1.66 \times 10^{4}

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None of these

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Solution

The correct option is A $1.274 \times 10^{5}$ L
$\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}} \frac{745 \times 1.41 \times 10^{4}}{273 + 21} = \frac{63.1 \times V_{2}}{273 - 48} \frac{1050.45 \times 10^{4}}{294} = \frac{63.1 \times V_{2}}{225} V_{2} = \frac{1050.45 \times 10^{4} \times 225}{294 \times 63.1} = 1.274 \times 10^{5} L$

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A high-altitude balloon is filled with 1.41×104 L of hydrogen at a temperature of 21oC and a pressure of 745 Torr. What is the volume of the balloon at a height of 20km, where the temperature is -48oC and the pressure is 63.1 Torr.

The correct option is A 1.274×105LP1V1T1=P2V2T2745×1.41×104273+21=63.1×V2273−481050.45×104294=63.1×V2225V2=1050.45×104×225294×63.1=1.274×105L

A high-altitude balloon is filled with 1.41 $\times 10^{4}$ L of hydrogen at a temperature of $21^{o} C$ and a pressure of 745 Torr. What is the volume of the balloon at a height of 20km, where the temperature is - $48^{o} C$ and the pressure is 63.1 Torr.