Question

A mass of gas has a volume of 4 cubic meters when the temperature is 120 Celsius and the pressure is 25 kPa (gauge). Determine the volume of this mass gas at normal atmospheric conditions (20 Celsius and 101.3 kPa). Select one: a. 4.72 cubic meters b. 1.72 cubic meters c. 3.72 cubic meters

Answer 1

The correct answer is option c.

Step-by-step explanation:

Using An deal gas equation:

`PV=nRT`

V = Volume of the gas at given pressure P and Temperature T.

n= number of moles

`n=(m)/(M)`

m = Mass of the gas

M= Molar mass of the gas

`(PVM)/(mT)=R= constant`

Volume of the gas at 25 kPa and 120°C,
`V_1 = 4 m^3`

`P_1=25 kPa+ 101.3 kpa=126.3 kpa`

(Absolute pressure is equal to sum of gauge pressure ant atmospheric pressure.)

`T_1=120^oC=393.15 K`

Moles of gas ,
`n_1=(m_1)/(M)`

`(P_1V_1M)/(m_1T_1)=R`...(1)

Volume of the gas at 101.3 kPa and 20°C,
`V_2= ? m^3`

`P_2=101.3 kpa,T_2=20^oC=293.15 K`

Moles of gas ,
`n_2=(m_2)/(M)`

Volume asked for the same mass of gas:

`m_1=m_2`

`(P_1V_1M)/(m_2T_1)=R`..(2)

`(P_1V_1M)/(m_2T_1)=(P_2V_2M)/(m_2T_2)=R`

`(P_1V_1)/(T_1)=(P_2V_2)/(T_2)`

Substituting all the given values we get value of
`[V_2`:

`V_2=3.72 m^3`