Compare the theoretical speeds of sound in hydrogen (MHMH = 2.0 g/mol, ƔH =1.4) with helium (MHe = 4.0 g mol⁻¹ƔHe = 1.66 & R = 8334 j k⁻¹ mol⁻¹) at 0°C .
( vHe = 0.77 vH)


Given:

MH = 2.0 g/mol
ƔH =1.4
MHe = 4.0 g mol⁻¹
ƔHe = 1.66 
R = 8334 j k⁻¹ mol⁻¹
T = 0°C = 273 K

To Find:

Comparison of the theoretical speeds of sound in hydrogen with helium = vHevH = ?

Solution:

To find the speed v of sound in a gas is given by:

v = ƔRTM

Speed `\v_{He} of sound in Helium (He) gas

vHeƔHeRTM

vHe  = 1.668334jk¹mol¹273K4kg

vHe  = 944,200.53m²s²

vHe = 972 m s⁻¹

Speed vH of sound in Hydrogen (H) gas

vH = ƔHRTM

vH = 1.48334jk¹mol¹273K2kg

vH = 1,592627.4m²s²

vH = 1262 m s⁻¹


Now 

vHevH = 972ms¹1262ms¹

vHevH = 0.77

or

vHe = 0.77 vH



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