Speed of sound in atmosphere at a height `h_(0)'` is `1080 km hr^( –1)`. The variation of temperature and pressure of the atmosphere with height `h` from the surface is given by
`T=T_(0)- beta h` and `P=P_(0) (1-(betah)/T_(0))^((Mg)/(R beta))`
Where `T_(0)=` temperature at the surface of the earth `=273 K`,
`P_(0)=` atmospheric pressure at the surface of the earth,
`beta=0.006 .^(@)C//m, M=` molar mass of air `cong 29 g mol^(-1), g=9.8 ms^(-2)`
`R=` gas constant `=8.31 J mol^(-1) K^(-1)`
consider air to be a mixture of diatomic hases and calculate the atmospheric temperature and pressure at height `h_(0)`. Also find `h_(0)`. Take `(0.82)^(5.7)=0.32`.

Answer

`T=224 K, P=0.32 P_(0), h_(0)=8167 m`