Question

A balloon is 3m in diameter and is filled with 5 kg of N2. Find the specific volume of the gas in the balloon. Express it in both m/kg and in m/kmol. Answers: about 3 and 80, respectively Find the weight of the gas in the balloon, expressed in N. Assume g = 9.8 m/s. Answer: about 50 a. b.

Answer 1

The the specific volume and weight are 79.16m³/k mol and 49 N.

Step-by-step explanation:

Given that,

Diameter = 3 m

Mass of N₂ = 5 kg

We need to calculate the volume of balloon

Using formula of volume

`V= (4)/(3)\pi r^3`

`V= (4)/(3)\pi *{(d)/(2)}^3`

`V= (4)/(3)\pi *((3)/(2))^3`

`V=14.137\ m^3`

We need to calculate the specific volume in the balloon

`Specific\ volume=(Volume)/(mass)`

`Specific\ volume=(14.137)/(5)`

`Specific\ volume=2.8274\ m^3/kg`

Now, Molar mass of N₂ gas is 0.028 kg/mol

Now, Specific volume of N₂ gas in the balloon is

`Specific\ volume =0.028*2.8274=0.0791672\ m^3/mol`

`Specific\ volume =79.16m^3/kmol`

(b). We need to calculate the weight of the gas in the balloon

Weight of the balloon is dependent on the mass of the gas.

The weight of the gas is given by

`W = mg`

`W = 5*9.8`

`W = 49\ N`

Hence, The the specific volume and weight are 79.16m³/k mol and 49 N.