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| Velocity of Sound in Different Gases |
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| As seen from equation (1-28), the velocity of sound in a gas depends on g, the ratio of the principle specific heats of the gas. This, in turn, depends on the atomicity of the gas. An approximate equation connecting g and the degrees of freedom is |
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| Where n is the number of degrees of freedom. For a monatomic gas n= 3, for a diatomic gas n = 5 and for a triatomic gas n = 7. Hence, the value of g for these gases will be about 1.67, 1.4 and 1.3 respectively. |
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| If two gases having the same value of g are considered, like, hydrogen and oxygen, then |
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| When their pressures are same, oxygen is nearly 16 times heavier than hydrogen. The velocity of sound in hydrogen has to be four times that in oxygen. The measured values of the velocities of sound in oxygen and hydrogen are 316ms-1 and 1284ms-1 at NTP. This closely agrees with the predicted values. |
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According to the kinetic theory of gases, pressure exerted by a gas is
given by  represents the mean square velocity of the molecules of the gas. Substituting in equation (1-28), |
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| Thus, the velocity of sound in gases having the same value of g, varies directly as the root mean square velocity of the molecules of the gas. |
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Measurement of velocity of sound in a gas enables one to determine
the ratio of the principle specific heats (g) and
the r.m.s velocity  of the molecules of the gas. |
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