Answer to Question #134634 in Mechanics | Relativity for Jessica

Question

A clown at a birthday party has brought along a helium cylinder, with which he intends to fill balloons. When full, each balloon contains 0.00210 m3 of helium at an absolute pressure of 1.20 x 10^5 Pa. The cylinder contains helium at an absolute pressure of 2.30 x 10^7 Pa and has a volume of 0.00360 m3. The temperature of the helium in the tank and in the balloons is the same and remains constant. What is the maximum number of people who will get a balloon?

Answer 1

Let us determine the ratio of amount of helium in the tank and the balloon. We may write the equation of the ideal gas

for the tank

$P_0V_0=\nu_0 RT$

and for the balloon

$P_1V_1=\nu_1 RT$

So

$\dfrac{\nu_0}{\nu_1} = \dfrac{P_0V_0}{P_1V_1}=\dfrac{2.30\cdot10^7\cdot0.00360}{1.20\cdot10^5\cdot0.00210}\approx 328.6. \\$

This amount is quite large, but it is not surprising, because the pressure in a tank is more than 100 times larger than the pressure in a balloon.