SME
Engineering Thermodynamics · Problem type
Mass of an ideal gas in a tank
Use this for “A 0.8 m³ tank holds nitrogen (M = 28.01 kg/kmol) at 300 kPa and 298 K. Find the mass of nitrogen in it.”
Diagram
Rᵤ = 8.314 kJ/(kmol·K).
PV = n × Rᵤ × T, which gives 500 × 0.5 = 0.1002 × 8.314 × 300 = 250.
Each particle drawn stands for 0.005 kmol: about 20 particles.
This is an example. Type your own values to start a new problem.
R (kJ/(kg·K))
=
8.314
÷
M (kg/kmol)
P (kPa)
×
V (m³)
=
m (kg)
×
R (kJ/(kg·K))
×
T (K)
n
Amount of gas
calculated · kmol
Formulas
P
×
V
=
m
×
R
×
T
500 × 0.5 = 2.9037 × 0.287 × 300
R
=
8.314
M
0.287
=
8.314
28.97
n
=
m
M
0.1002
=
2.9037
28.97
P
×
V
=
n
×
8.314
×
T
500 × 0.5 = 0.1002 × 8.314 × 300
Assumptions
•
The gas is ideal: its pressure is low and its temperature high compared with its critical point.
•
P is the absolute pressure, not the gauge reading, and T is in kelvins.
•
R = Rᵤ ÷ M with Rᵤ = 8.314 kJ/(kmol·K); for air M = 28.97 kg/kmol, so R = 0.287 kJ/(kg·K).
•
Above about 10 MPa at room temperature, check Z on a compressibility chart.
Step-by-step
WE KNOW
P = 500 kPa, V = 0.5 m³, T = 300 K, M = 28.97 kg/kmol
FIND
gas constant (R), amount of gas (n), mass (m)
Step 1 · Find gas constant (R)
Use R = 8.314 ÷ M
Each
gas
has
its
own
R
:
the
universal
Rᵤ
shared
over
the
kilograms
in
one
kilomole.
R
=
8.314
28.97
R
=
0.28699
kJ/(kg·K)
Step 2 · Find amount of gas (n)
Use P × V = n × 8.314 × T
The same law counted in kilomoles: divide both sides by RuT.
n
=
P
×
V
8.314 ×
T
n
=
500
×
0.5
8.314 × 300
n
=
500
×
0.5
2,494.2
n
=
250
2,494.2
n
=
0.1002
kmol
Step 3 · Find mass (m)
Use P × V = m × R × T
Divide
both
sides
by
RT;
kPa
×
m
3
is
kJ,
and
kJ
kJ/(kg·K) × K
leaves
kg.
m
=
P
×
V
R
×
T
m
=
500
×
0.5
0.28699 × 300
m
=
500
×
0.5
86.097
m
=
250
86.097
m
=
2.9037
kg
Check
Put the numbers back in. Both sides should match.
500 × 0.5 = 2.9037 × 0.28699 × 300 ✓
0.28699
=
8.314
28.97
✓
0.1002
=
2.9037
28.97
✓
500 × 0.5 = 0.1002 × 8.314 × 300 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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