# what is the velocity of sound in vanderwals force and derive expression for it ?

Saurabh Kumar
8 years ago
The velocity of sound is a vector u whose magnitude |u| is the speed of sound u and whose direction is normal to the surface of constant phase. The speed of sound is a property of the medium through which the sound travels and is therefore usually of more interest than the velocity itself which depends upon both u and the manner in which the sound is generated.

In discussing the relation between u and the properties of the medium is it useful to distinguish between homogeneous fluids and solids. In the former, the speed of sound is the same in all directions whereas, in the latter, this is not necessarily the case.

In a perfectly elastic (nondissipative) fluid the speed of sound is given for small-amplitude sound waves by(1)where p is pressure, ρ density, cp specific heat at constant pressure, S entropy and κS is the isentropic compressibility. Consequently, u may be determined from the thermodynamic Equation of State of the fluid or, conversely, information about the equation of state may be deduced from the u2(T, p) [see Trusler (1991)]. For the special case of the Perfect Gas, for which ρ = Mp/RT, the speed of sound is given by
where M is the molar mass and γpg is the heat-capacity ratio for the perfect gas. Thus the speed of sound in a perfect gas is proportional to but independent of pressure. All real gases approach this behavior at sufficiently low pressures, but generally u(T, p)/ is a slowly varying function of both T and p. Some examples of u(T, p → 0) for gases at T = 300 K are: 4He, 1019 m/s; CH4, 451 m/s; N2, 352 m/s; air 348 m/s; and n-butane, 194 m/s
pa1
357 Points
8 years ago
The velocity of sound is a vector u whose magnitude |u| is the speed of sound u and whose direction is normal to the surface of constant phase. The speed of sound is a property of the medium through which the sound travels and is therefore usually of more interest than the velocity itself which depends upon both u and the manner in which the sound is generated.In discussing the relation between u and the properties of the medium is it useful to distinguish between homogeneous fluids and solids. In the former, the speed of sound is the same in all directions whereas, in the latter, this is not necessarily the case.In a perfectly elastic (nondissipative) fluid the speed of sound is given for small-amplitude sound waves by(1)where p is pressure, ρ density, cp specific heat at constant pressure, S entropy and κS is the isentropic compressibility. Consequently, u may be determined from the thermodynamic Equation of State of the fluid or, conversely, information about the equation of state may be deduced from the u2(T, p) [see Trusler (1991)]. For the special case of the Perfect Gas, for which ρ = Mp/RT, the speed of sound is given bywhere M is the molar mass and γpg is the heat-capacity ratio for the perfect gas. Thus the speed of sound in a perfect gas is proportional to but independent of pressure. All real gases approach this behavior at sufficiently low pressures, but generally u(T, p)/ is a slowly varying function of both T and p. Some examples of u(T, p → 0) for gases at T = 300 K are: 4He, 1019 m/s; CH4, 451 m/s; N2, 352 m/s; air 348 m/s; and n-butane, 194 m/s