Question

A mixture of two gases has a total mass of 80 kg. One gas has a specific volume of 0.8 m^3/kg and occupies a volume of 40 m^3. The other gas has a specific volume of 1.4 m^3. How much volume is occupied by the second gas and what is the specific volume of the mixture?

Answer 1

specific volume = 1.025 m³/kg

Step-by-step explanation:

given data

total mass m1 +m2 = 80 kg

specific volume = 0.8 m³/kg

occupies volume v1 = 40 m³

other gas specific volume = 1.4 m³

to find out

How much volume is occupied by the second gas and what is the specific volume of the mixture

solution

we know that density is reciprocal of specific volume and here gas is not interacting

so total specific volume is assume so ratio is total volume to total mass

and

specific volume =
`(1)/(\rho)`

here ρ is density

so ρ1 =
`(1)/(0.8)` = 1.25 kg/m³

and ρ2 =
`(1)/(1.4)` = 0.714 kg/m³

and

so m1 = ρ1v1 = 1.25 × 40 = 50 kg

and m2 = 80 - 50 = 30 kg

so

v2 =
`(m2)/(\rho 2)`

v2 =
`(30)/(0.714)` = 42 m³

so volume occupied by second das = 42 m³

and

specific volume of mixture will be

specific volume of mixture =
`(v1+v2)/(m1+m2)`

specific volume =
`(42+40)/(50+30)`

specific volume = 1.025 m³/kg