IDEAL GAS LAWS 263
- A spherical vessel has a diameter of
2.0 m and contains hydrogen at a pres-
sure of 300 kPa and a temperature of
− 30 °C. Determine the mass of hydro-
gen in the vessel. Assume the charac-
teristic gas constantRfor hydrogen is
4160 J/(kg K). [1.24 kg]
- A cylinder 200 mm in diameter and
1.5 m long contains oxygen at a pressure
of 2 MPa and a temperature of 20°C.
Determine the mass of oxygen in the
cylinder. Assume the characteristic gas
constant for oxygen is 260 J/(kg K).
[1.24 kg]
- A gas is pumped into an empty cylinder
of volume 0.1 m^3 until the pressure is
5 MPa. The temperature of the gas is
40 °C. If the cylinder mass increases by
5.32 kg when the gas has been added,
determine the value of the characteristic
gas constant. [300 J/(kg K)]
- The mass of a gas is 1.2 kg and it
occupies a volume of 13.45 m^3 at STP.
Determine its characteristic gas constant.
[4160 J/(kg K)]
- 30 cm^3 of air initially at a pressure
of 500 kPa and temperature 150°Cis
expanded to a volume of 100 cm^3 at
a pressure of 200 kPa. Determine the
final temperature of the air, assuming no
losses during the process. [291°C]
- A quantity of gas in a cylinder occupies
a volume of 0.05 m^3 at a pressure of
400 kPa and a temperature of 27°C. It
is compressed according to Boyle’s law
until its pressure is 1 MPa, and then
expanded according to Charles’ law until
its volume is 0.03 m^3. Determine the
final temperature of the gas. [177°C]
- Some air at a temperature of 35°Cand
pressure 2 bar occupies a volume of
0.08 m^3. Determine the mass of the air
assuming the characteristic gas constant
for air to be 287 J/(kg K). (1 bar =
105 Pa) [0.181 kg]
- Determine the characteristic gas constant
R of a gas that has a specific volume
of 0.267 m^3 /kg at a temperature of 17°C
and pressure 200 kPa. [184 J/(kg K)]
23.8 Further worked problems on the
characteristic gas equation
Problem 14. A vessel has a volume of
0.80 m^3 and contains a mixture of helium
and hydrogen at a pressure of 450 kPa and a
temperature of 17°C. If the mass of helium
present is 0.40 kg determine (a) the partial
pressure of each gas, and (b) the mass of
hydrogen present. Assume the characteristic
gas constant for helium to be 2080 J/(kg K)
and for hydrogen 4160 J/(kg K).
(a) V= 0 .80 m^3 ,p=450 kPa,
T=( 17 + 273 )K=290 K,mHe= 0 .40 kg,
RHe=2080 J/(kg K).
IfpHeis the partial pressure of the helium, then
using the characteristic gas equation,
pHeV=mHeRHeTgives:
(pHe)( 0. 80 )=( 0. 40 )( 2080 )( 290 )
from which,the partial pressure of the
helium,
pHe=
( 0. 40 )( 2080 )( 290 )
( 0. 80 )
= 301 .6kPa
By Dalton’s law of partial pressure the total
pressurepis given by the sum of the partial
pressures, i.e.p=pH+pHe, from which,the
partial pressure of the hydrogen,
pH=p−pHe= 450 − 301. 6
= 148 .4kPa
(b) From the characteristic gas equation,
pHV=mHRHT.
Hence ( 148. 4 × 103 )( 0. 8 )=mH( 4160 )( 290 )
from which,mass of hydrogen,
mH=
( 148. 4 × 103 )( 0. 8 )
( 4160 )( 290 )
= 0 .098 kgor98 g
Problem 15. A compressed air cylinder has
a volume of 1.2 m^3 and contains air at a
pressure of 1 MPa and a temperature of
