3.0 m 25℃ 1.0 atm H2 air density 1.22 kg/m3 He

3.0 m 25℃ 1.0 atm H2 air density 1.22 kg/m3 He

 

 

Balloons are still used to deploy sensors that monitor meteorological phenomena and the chemistry of the atmosphere. It is possible to investigate some of the technicalities of ballooning by using the perfect gas law.

Suppose your balloon has a radius of 3.0 m and that it is spherical.

a) What amount of H2 (in moles) is needed to inflate it to 1.0 atm in an ambient temperature of 25℃ at sea level?

b) What mass can the balloon lift (the payload) at sea level, where the density of air is 1.22 kg/m3?

c) What would be the payload if He were used instead of H2?

 

 

 

기구의 부피 = 구의 부피(V)

V = (4/3)πr^3

= (4/3) (π) (3.0 m)^3

= 113.097 m3

= 113 m3

= 113000 L

 

 

 

a)

PV = nRT 로부터,

( 참고 https://ywpop.tistory.com/3097 )

 

n = PV / RT

= [(1.0) (113000)] / [(0.08206) (273.15 + 25)]

= 4618.62 mol

= 4.62×10^3 mol

---> 필요한 H2의 몰수

 

 

 

b)

(4.62×10^3 mol) (2.02 g/mol)

= 9332.4 g

= 9.33 kg

---> H2의 질량

= 기구의 질량

 

 

 

113 m3 × (1.22 kg/m3)

= 137.86 kg

= 138 kg

---> 공기의 질량

 

 

 

138 kg – 9.33 kg

= 128.67 kg

= 129 kg

---> H2 기구가 들어 올릴 수 있는 질량

 

 

 

c)

(4.62×10^3 mol) (4.00 g/mol)

= 18480 g

= 18.5 kg

---> He의 질량

 

 

 

138 kg – 18.5 kg

= 119.5 kg

= 120. kg

---> He 기구가 들어 올릴 수 있는 질량

 

 

 

 

[키워드] 기구가 들어 올릴 수 있는 질량 기준, 수소 대신 헬륨 기준