Question

A weather balloon has a volume of 175 L when filled with hydrogen at a pressure of 1.000atm.
Calculate the volume of the balloon when it rises to a height of 2000m, where the atmosphere
pressure is 0.8000 atm. Assume the temperature is constant.

Answer 1

P1=1 atm                          P2=0.8000 atm
V1=175 L               V2=?

P1/V1=P2/V2
1/175=0.8000/V2
175*0.800=V2
V2=140 L

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Answer 2

Volume of the balloon when it rises to 2000 m is 218.75 L.

Explanation:

Given:

Volume of balloon $V_{1}$ = 175 L = 175000 $cm^{3}$

Pressure at the ground level $P_{1}$ = 1000 atm

We know, according to Ideal Gas law,

                                                  ⇒ PV = nRT

Temperature is constant throughout the process.

                                                 ⇒ PV = constant

At, 200 m height, new pressure   $P_{2}$ = 0.8 atm

So,

⇒ $V_{1}$ x $P_{1}$ =  $V_{2}$ x  $P_{2}$

                        ⇒ $V_{2}$ = $\frac{ 175000}{0.8}$

                         ⇒ $V_{2}$ = 218750 $cm^{3}$

                          ⇒ $V_{2}$ = 218750 L