Question

On the surface of the earth at $1atm$ pressure, a balloon filled with $H_2$ gas occupies $500mL$. This volume is $5/6$ of its maximum capacity. The balloon is left in air. It starts rising. The height above which the balloon will burst if temperature of the atmosphere remains constant and the pressure decreases $1mm$ for every $100cm$ rise of height is:

• A. $120m$
• B. $136.67m$
• C. $126m$
• D. $100m$

Answer 1

The correct option is C $126m$

Given:

$P_1=1atm=760mmofHg$

$V_1=500ml$

Solution:

Let Maximum capacity $V_2$= x

According to question ,

$500=\frac{5}{6}\times x$

$\Rightarrow x=500\times \frac{6}{5}$

$\Rightarrow x=600$

From the ideal gas law ,

$P_1{V}_1=P_2{V}_2$

$\Rightarrow 760\times 500=P_2\times 600$

$\Rightarrow P_2=760\times \frac{500}{600}$

$\Rightarrow P_2=633.33mmofHg$

Change in pressure = $P_2-P_1$

$\Rightarrow Changeinpressure=760-633.33$

$\Rightarrow Changeinpressure=126.67mmofHg$

It is given that for each 1 mm decrease, rise = 100 cm

Therefore, Height = 100 × 126.67 cm

$\Rightarrow$ Height = 126.67 m

Hence, option C is correct and the answer is 126.67m.