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3.1 Ideal gas law: Air

3.1 Ideal gas law: Air#

Problem Statement:#

Imagine \(1\:kg\) of air confined in a space of \(1\:m^3\) volume. If the air is kept at room temperature, assuming ideal gas law applies to air in this case,

a) calculate air pressure in \(kPa\)?

b) what if the temperature increases to \(100 ^{\circ} C\)?

c) what if \(1\:kg\) air is added to the same compartment?

d) what if the space within which the air in kept is compressed to decrease the volume to \(0.8\:m^3\)

Solution Approach for a)#

The ideal gas law is an equation of state (EOS) which helps with predicting the state of a material based on its properties Pressure \((P)\), specific volume \((v)\), and temperature \((T)\) as following:

\(Pv=RT\) ,which can also be written as
\(PV=mRT\) where \(m\) is the mass of the material

to calculate pressure:
\(P=mRT/V\)

#defining variables
m = 1 #mass of air in kg
R = 0.287 #air gas constant in kJ/kg.K
V = 1 #volume of air in m3
T = 25 + 273.15 #room temperature in K

# using ideal gas equation of state to calculate pressure
P = m * R * T / V #air pressure in kPa

print('The air pressure is:', f"{P:.1f}", 'kPa')

The air pressure is: 85.6 kPa

Solution Approach for b)#

for part b, the temperature increases to \(100 ^{\circ} C\). As a result, an increase in pressure is expected.

T = 100 + 273.15 #increased room temperature in K
P = m * R * T / V #air pressure in kPa
print('The air pressure is:', f"{P:.1f}", 'kPa')

The air pressure is: 107.1 kPa

Solution Approach for c)#

for part c, the number of air molecules increases. As a result, an increase in pressure is expected.

m = 2 #increased mass of air in kg
P = m * R * T / V #air pressure in kPa
print('The air pressure is:', f"{P:.1f}", 'kPa')

The air pressure is: 214.2 kPa

Solution Approach for d)#

for part c, the volume of air decreases resulting in more air molecules per unit volume. As a result, an increase in pressure is expected.

V = 0.8 #compressed volume of air in m3
P = m * R * T / V #air pressure in kPa
print('The air pressure is:', f"{P:.1f}", 'kPa')

The air pressure is: 267.7 kPa
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