不同温度和压力下的声速教学教材.doc

不同温度和压力下的声速

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不同温度和压力下的声速

The classical ideal gas law may be written as pV=nRT, from which the expression for gas density ρ relating to pressure p could be deduced: ρ=pM/RT, wherein V and n correspond to volume and number of moles of a substance, respectively; T, M and R are respectively corresponding to absolute temperature, molar mass and ideal gas constant, approximately 8.3144621 J/(mol·K).

The sound speed of sound in an ideal gas depends only on its temperature and composition. The speed has a weak dependence on frequency and pressure in ordinary air, deviating slighty from ideal behavior. In general, the speed of sound c is given by the Newton-Laplace equation: c=(Kf/ρ)1/2, in which the bulk modulus Kf is simply the gas pressure p multiplied by the dimensionless adiabatic index γ, which is about 1.4 for air.

理想气体状态方程PV=nRT, 推导得ρ=PM/RT.
0°C,1标准大气压下空气密度约为1.293g/L, 就用空气做个例子算一算.P=101325(标准大气压),M=29(空气摩尔质量),R=8.314J/(mol·k)(理想气体常数,定值),T=0+273.15K(开尔文温度),代入公式,计算出结果,这里要注意的是R值对应压力和体积的单位是Pa和M3,所以算出的ρ单位是KG/M3

声速的平方跟压力成正比，跟密度成反比；跟温度成线性关系所以声速不仅仅受压力影响
气体中：u=√(γP/ρ),其中γ为比热比,P为压力,ρ为密度
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