Many gases at low pressure, i. e. atmospheric pressure and below for water vapour and up to several bar for gases such as nitrogen, oxygen and argon, obey simple relations between their pressure, volume and temperature, with sufficient accuracy for engineering purposes. Such gases are called ‘ideal’.

Boyle’s Law states that, for an ideal gas, the product of pressure and volume at constant temperature is a constant:

PV = constant

Example 1.4

A volume of an ideal gas in a cylinder and at atmospheric pressure is compressed to half the volume at constant temperature. What is the new pressure?

P1V1 = constant

= P2V2

Vl = 2


So p2 = 2 x p1

= 2 x 1.013 25 bar (101 325 Pa)

= 2.0265 bar (abs.)

Charles’ Law states that, for an ideal gas, the volume at constant pressure is proportional to the absolute temperature:


— = constant T

Example 1.5

A mass of an ideal gas occupies 0.75 m3 at 20°C and is heated at constant pressure to 90°C. What is the final volume?

273 + 90 . , …

= 0.75 x————— (temperatures to the nearest K)

273+ 20

= 0.93 m3

Boyle ’s and Charles’ laws can be combined into the ideal gas equation: pV = (a constant) x T

The constant is mass x R, where R is the specific gas constant, so:

PV = mRT

Example 1.6

What is the volume of 5 kg of an ideal gas, having a specific gas constant of 287 J/(kg K), at a pressure of one standard atmosphere and at 25°C?

PV = V =

подпись: pv = v =MRT mRT


5 x 287(273 + 25)

101 325 4.22 m3

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