A Level Physics Notes: Thermal Physics and Gases – Ratio of the Specific Heat Capacities at Constant Pressure and Volume for Real Gases



The ratioof the specific heat capacity at constant pressure,to that at constant volume, is found experimentally by some method and the results shown below.

Gas

Temp./°C

γ




Monatomic gases



Helium

0

1.63

Argon

0

1.67

Neon

19

1.64

Krypton

19

1.69

Xenon

19

1.67

Mercury vapour

310

1.67




Diatomic gases



Air (dry)

−79.3

1.41

Air (dry)

0–17

1.401/2

Air (dry)

500

1.36

Air (dry)

900

1.32

Hydrogen

4–17

1.407/8

Nitrogen

20

1.40

Oxygen

5–14

1.4

Carbon monoxide

1 800

1.30

Nitric oxide

—

1.39




Triatomic gases



Ozone

—

1.29†

Water vapour

100

1.33

Carbon dioxide

4–11

1.3

Carbon dioxide

300

1.22

Carbon dioxide

500

1.2

Ammonia, NH_3

50

1.31

Nitrous oxide, N_2 O

—

1.32

Nitrogen peroxide N_2 O_4

20

1.17

Sulphur dioxide S0_2

16–34

1.26




Polyatomic gases



Methane, CH4

20

1.31

Ethane, C2H6

20

1.20

Propane, C3H8

20

1.14

Acetylene, C2H2

20

1.24

Ethylene, C2H4

20

1.25

Benzene C6H6

20

1.4

Benzene C6H6

99.7

1.11

Chloroform CHCl3

24–42

1.11

CCl4

—

1.13

Methyl alcohol

99.7

1.26

Methyl bromide

—

1.27

Methyl chloride

19–30

1.28

Methyl iodide

—

1.29

Ethyl alcohol

53

1.13

Ethyl alcohol

99.8

1.13

Ethyl bromide

—

1.19

Ethyl chloride

22.7

1.19

Ethyl ether

12–20

1.02

Ethyl ether

99.7

1.11

Acetic acid

136.5

1.15

The value ofis a result of many factors. Theory says that the energy is distributed over all the energy states equally – vibrational, translational, rotational, and for large molecules there may be many vibrational energy states. Since (this equation only applies to ideal gases) we expect the ratio to decrease for large molecules.

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