IDEAL GAS LAWS 265Now try the following exercise
Exercise 124 Further questions on ideal
gas laws- A vesselP contains gas at a pressure of
800 kPa at a temperature of 25°C. It is
connected via a valve to vessel Qthat
is filled with similar gas at a pressure of
1.5 MPa and a temperature of 25°C. The
volume of vesselP is 1.5 m^3 and that
of vesselRis 2.5 m^3. Determine the final
pressure at 25°C when the valve is opened
and the gases are allowed to mix. Assume
Rfor the gas to be 297 J/(kg K).
[1.24 MPa] - A vessel contains 4 kg of air at a pressure
of 600 kPa and a temperature of 40°C.
The vessel is connected to another by a
short pipe and the air exhausts into it. The
final pressure in both vessels is 250 kPa
and the temperature in both is 15°C. If
the pressure in the second vessel before
the air entered was zero, determine the
volume of each vessel. AssumeRfor air
is 287 J/(kg K). [0.60 m^3 ,0.72m^3 ] - A vessel has a volume of 0.75 m^3 and
contains a mixture of air and carbon diox-
ide at a pressure of 200 kPa and a temper-
ature of 27°C. If the mass of air present
is 0.5 kg determine (a) the partial pres-
sure of each gas, and (b) the mass of
carbon dioxide. Assume the characteris-
tic gas constant for air to be 287 J/(kg K)
and for carbon dioxide 184 J/(kg K).
[(a) 57.4 kPa, 142.6 kPa (b) 1.94 kg] - A mass of gas occupies a volume of
0.02 m^3 when its pressure is 150 kPa and
its temperature is 17°C. If the gas is
compressed until its pressure is 500 kPa
and its temperature is 57°C, determine
(a) the volume it will occupy and (b) its
mass, if the characteristic gas constant for
the gas is 205 J/(kg K).
[(a) 0.0068 m^3 (b) 0.050 kg] - A compressed air cylinder has a volume
of 0.6 m^3 and contains air at a pressure
of 1.2 MPa absolute and a temperature of
37 °C. After use the pressure is 800 kPa
absolute and the temperature is 17°C.
Calculate (a) the mass of air removed
from the cylinder, and (b) the volume the
mass of air removed would occupy at STP
conditions. TakeRfor air as 287 J/(kg K)
and atmospheric pressure as 100 kPa.
[(a) 2.33 kg (b) 1.82 m^3 ]Exercise 125 Short answer questions on
ideal gas laws- State Boyle’s law.
- State Charles’ law.
- State the Pressure law.
- State Dalton’s law of partial pressures.
- State the relationship between the Celsius
and the thermodynamic scale of tempera-
ture. - What is (a) an isothermal change, and
(b) an isobaric change? - Define an ideal gas.
- State the characteristic gas equation.
- What is meant by STP?
Exercise 126 Multi-choice questions on
ideal gas laws (Answers on
page 285)- Which of the following statements is
false?
(a) At constant temperature, Charles’
law applies.
(b) The pressure of a given mass of
gas decreases as the volume is
increased at constant temperature.
(c) Isobaric changes are those which
occur at constant pressure.
(d) Boyle’s law applies at constant
temperature. - A gas occupies a volume of 4 m^3 at a
pressure of 400 kPa. At constant tem-
perature, the pressure is increased to
500 kPa. The new volume occupied by
the gas is:
(a) 5 m^3 (b) 0.3 m^3
(c) 0.2 m^3 (d) 3.2 m^3