Question

A perfectly elastic spherical balloon of 0.2 m diameter was filled with hydrogen at sea level. The diameter of the ball (in m) when it has risen to an altitude where the pressure is 0.65 atm is:

(Assume no change temperature and atmospheric pressure at sea level)

• A. 0.2308
• B. 0.3501
• C. 0.1157
• D. 0.2457

Answer 1

The correct option is A 0.2308

At sea level, the pressure is 1 atm. It drops to 0.65 atm.
The diameter is 0.2 m. The radius will be 0.1 m. It changes to x m.
For an ideal gas $PV=nRT$
Hence, at constant temperature, PV is constant.
$PV=P^{\prime }{V}^{\prime }$
$1\times \frac{4\pi }{3}(0.1{)}^3=0.65\times \frac{4\pi }{3}(x{)}^3$
$x=0.1154$
$2x=0.2308m$
Thus, the diameter changes to 0.2308 m